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Study on droplet velocity in a pulsed sieve plate extraction column by four-sensor optical fiber probe
Chemical Engineering Research and Design 1 4 4 ( 2 0 1 9 ) 550–558
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Study on droplet velocity in a pulsed sieve plate extraction column by four-sensor optical fiber probe Yandong Sun a,b , Yang Gao a,∗ , Hongguo Hou a , Caishan Jiao a , Yu Zhou a , Meng Zhang a a
Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, College of Nuclear Science and Technology, Harbin Engineering University, Harbin, Heilongjiang Province, 150001, China b China Institute of Atomic Energy, P. O. Box 275 (126), Beijing, 102413, China
a r t i c l e
i n f o
a b s t r a c t
Article history:
In this paper, the hydrodynamic characteristics including the droplet velocity, the droplet
Received 1 November 2018
diameter, and the droplet movement direction in a 38 pulsed sieve plate extraction column
Received in revised form 29 January
were measured with a four-sensor optical probe, where water and 40% (VO /VO ) octanol-
2019
kerosene were used as the continuous phase and the dispersed phase, respectively. The
Accepted 20 February 2019
influence of the pulsation intensity on the droplet characteristics was investigated. Experi-
Available online 1 March 2019
mental results showed that with the increase of the pulsation intensity, the droplet velocity and the angle between the droplet movement direction and the probe increase, and the
Keywords:
droplet diameter decreases. Under the same experimental condition, the velocity of larger
Droplet velocity
droplets is larger than that of smaller droplets. It is demonstrated that the four-sensor optical
Droplet diameter
probe is reliable to the measurement of the dispersed phase hydrodynamic characteristics
Droplet movement direction
in liquid-liquid two-phase flow through the analysis and estimation of error caused by the
Pulsed sieve
time delay of the probe signal and the direction deviation of the probe.
Plate extraction column
© 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Four optical fiber probe
1.
Introduction
Hydrodynamic characteristics such as the droplet velocity, the droplet diameter, the holdup of the dispersed phase are of great impor-
Liquid–liquid extraction is one of the classical techniques for separation process which can be applied in many industries including pharmaceutical engineering, petroleum processing, food processing,
tance in the design and scaling-up of an extraction column, all of which
and especially in the treatment of waste in nuclear fuel reprocessing (Panahinia et al., 2017; Khajenoori et al., 2015; Amani et al., 2017; Aoun
Gholam Samani et al., 2012; Amani and Esmaieli, 2017; Hemmati et al., 2015). To obtain these hydrodynamic characteristics, several measure-
Nabli et al., 1998). Because of different mechanisms on mass transfer
ment methods have been developed including optical probe method, volume displacement method, and photographing method, etc. (Yuan
regimes, solvent extraction processes were carried out with different equipment and contactors (Arab et al., 2017). Compared with other extraction equipment, pulsed extraction column has many advantages such as high mass transfer coefficient, short residence time and large processing capacity and so on (Yuan and Gao, 2017). In particular, the pulsation unit can be separated from the column, so the pulsed extraction column is very useful in processing corrosive or radioactive solutions (Yadav and Patwardhan, 2008).
∗
affect the mass transfer coefficient strongly (Somkuwar et al., 2014; Yi et al., 2017; Xie et al., 2015; Torab-Mostaedi et al., 2011; Lade et al., 2013;
and Gao, 2017). Volume displacement method can be only used for the measurement of the holdup, and photographing method mainly provides the information about the diameter of the droplets. Optical fiber probe method is a kind of invasive technique, which can obtain several hydrodynamic characteristics simultaneously by piercing droplets, and has been applied extensively in the field of liquid-liquid two phase flow (Yuan and Gao, 2017; Xie et al., 2015; Hamad et al., 2000).
Corresponding author. E-mail address: [email protected] (Y. Gao). https://doi.org/10.1016/j.cherd.2019.02.031 0263-8762/© 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Chemical Engineering Research and Design 1 4 4 ( 2 0 1 9 ) 550–558
Nomenclature List of symbols n The number of the droplets in a designated condition ni The number of the droplets with the size equal to 1.0–1.3, 1.3–1.6,. . .,3.4–3.7,3.7–4.0 mm, respectively nv The number of the droplets with the velocity equal to 0–10,10-20,. . .,180-190,190–200 mm/s, respectively n␥ The number of the droplets with the velocity direction equal to 0–5,5–10. . .,40–45,45-50◦ Pd The probability distribution of the droplet diameter The probability distribution of the droplet Pv velocity P The probability distribution of the droplet movement direction Instantaneous velocity of droplet, mm/s v vi Instantaneous velocity of single droplet, mm/s Instantaneous velocity of droplet, mm/s V VO The volume of the two kind of organic phase Average velocity of droplets, mm/s V¯ Droplet diameter, mm d A Amplitude of pulsation, mm Frequency of pulsation,1/s f Af Pulsation intensity, amplitude-frequency product, mm/s The angle between the droplet movement direction and the z axis Time delay between first contact of droplet with tka leading sensor 4 and first contact of droplet with rear sensor k, s(k = 1,2,3) tkb Time delay between first contact of droplet with leading sensor 4 and last contact of droplet with rear sensor k, s(k = 1,2,3) tkc Time delay between last contact of droplet with leading sensor 4 and last contact of droplet with rear sensor k, s(k = 1,2,3) Minimum error in droplet diameter, droplet Emin velocity or droplet movement direction Emax Maximum error in droplet diameter, droplet velocity or droplet movement direction E¯ Average error in droplet diameter, droplet velocity or droplet movement direction Time interval, s(t=±0.0002, ±0.0004, ±0.001) t |s4-k | Distance vector between the leading sensor tip and sensor k’s tip, mm (xk , yk , zk ) Relative coordinate of sensor k corresponding to sensor 4, mm(k = 1,2,3) Droplet radius, mm |r|
According to the number of the optical fibers within the probe, optical fiber probes can be divided into single, double, triple and four optical fiber probe (Zhou et al., 2014; Yang et al., 2009; Shen and Nakamura, 2013). Single optical fiber probe can be only used for the measurement of the dispersed phase volume fraction, and double optical fiber probe can not only be used for the measurement of the dispersed phase volume fraction, but also provide the information about the onedimensional velocity and the chord length of the droplets (Xie et al., 2015; Ojha, 2018).Triple optical fiber probe can obtain two-dimensional velocity of the droplets with an iterative algorithm (Yang et al., 2009).
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Four optical fiber probe can measure the three-dimensional velocity of the droplets, and can measure the drop diameter with higher accuracy than the other optical fiber probe techniques (Yuan and Gao, 2017; Ojha, 2018). Until now, there have been extensive work on the droplet diameter and the holdup of the extraction columns, and numerous empirical correlations about the drop Sauter diameter and the holdup have been proposed. However, due to the limitation of the measurement technique, little information is available in the literature regarding the droplet velocity. Bardin (2003) adopted Lagrangian simulation approach to investigate the behavior of the dispersed phase droplets in the discs and doughnuts pulsed column. It was found that the mean residence time in a compartment is a decreasing function of the droplet diameter and of the pulsation intensity, which indirectly indicated that with the increase of the pulsation intensity and the droplet diameter, the droplet velocity increases. Wegener et al. (2014) estimated the effect of the droplet diameter on the droplet terminal velocity, and found that the terminal velocity of a single droplet increases with the increase of the droplet diameter, which is in agreement with the results obtained by Eiswirth et al. (2011), Azizi (2017) and Bäumler et al. (2011). Yuan and Gao (2017) applied the four optical fiber probe technique to study the droplet movement direction in a pulsed sieve plate extraction column, and found that the movement direction of droplets is not simply straight up. Bäumler et al. (2011) investigated the fluid dynamic behavior of single organic droplets rising in a quiescent ambient liquid, and found that when the droplet deforms, its rising path significantly deviates from the vertical axis. Li et al. (2016) studied the movement of the small bubble in a simple shear flow in water, and noticed that the rising path of the bubbles was zigzag, which is similar to the results obtained by Tomiyama et al. (2002). To optimize the design of extraction columns, extensive work (Lade et al., 2013; Gholam Samani et al., 2012; Amani and Esmaieli, 2017; Hemmati et al., 2015) was carried out to explore the relationship between the operational conditions and the hydrodynamic characteristics. The most studied operational conditions usually include the continuous phase superficial velocity, the dispersed phase superficial velocity, and the pulsation intensity. Many results showed that the pulsation intensity has a significant impact on the hydrodynamic characteristics, such as the droplet diameter and the holdup. Compared with the pulsation intensity, the two phase superficial velocities have much less influence on these hydrodynamic characteristics. In a word, the information on the dispersed phase droplet characteristics, especially on the droplet velocity in the extraction columns is still inadequate. In this paper, the droplet velocity and the droplet size were studied using a self-made four optical fiber probe in a 38 pulsed sieve plate extraction column, and the influence of the pulsation intensity on the hydrodynamic characteristics was investigated. The relationship between the droplet velocity and the droplet diameter was also analyzed.
2.
Material and methods
2.1.
Experimental setup and materials
Fig. 1 shows the schematic and the actual diagrams of the experimental apparatus. It mainly consists of three parts: one extraction section which is a 1474 mm long glass tube with 38 mm inner diameter. Two clarification sections with 79 mm inner diameter are used to separate the two phases. There are 30 sieve plates with a distance of 50 mm mounted on a stainless steel rod of 6 mm at the center of the extraction section. Each sieve contains 32 circular holes of 3 mm diameter, providing a 23% free area. An air pulse is connected with a down separating chamber by a pulse leg with a 16 mm diameter and a height of 1624 mm. Pulsation intensity is regulated by a digital regulator and stepper motor. Water was taken as the continuous phase and 40% (VO /VO ) octanol-kerosene was used as the dispersed phase. Because
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Fig. 1 – (a) the schematic diagram and (b) the actual diagram of the pulsed sieve plate extraction column.
Fig. 2 – Diagram of the four-sensor optical fiber probe (Yuan and Gao, 2017).
Table 1 – Physical properties of the two phases. Parameters
Water
40% Octanol-Kerosene
Interfacial tension (mN/m) Viscosity of the phase (mPa·s) Density of the phase (kg/m3 )
0.0 0.99 998.2
16.1 2.39 782.6
probe was placed in the middle of the 12th and 13th plates from the bottom of the active section, and was perpendicular with respect to the sieve plate. Fig. 3 is the photos of the four-sensor optical fiber probe with their size parameters.
2.3. the main focus was on the effect of the pulsation intensity, the continuous and the dispersed phase superficial velocities were adjusted to the fixed values, 2.51 mm/s and 2.08 mm/s, respectively. Table 1 gives the physical properties of the two phase flow. The interfacial tension was measured with a BZY-2 tensiometer, and the viscosities were measured with a NDJ-8S viscometer.
2.2.
The four-sensor optical fiber probe
Fig. 2 shows a schematic diagram of the four-sensor optical fiber probe. The probe has four sensors with sensor 4 as the leading sensor and sensors 1, 2, and 3 as the rear sensors. During the data processing process, sensor 4 was regarded as the origin, and the relative coordinates of sensors 1, 2, and 3 can be obtained by the distance between sensor 4 and themselves, which can be measured by a digital microscope. During the process of the experiment, the optical fiber
Measurement principle of optical fiber probe
As different liquids have different refractive indexes, the photoelectric transducer can receive different light intensities when the optical fiber probe is in different phases. Then the light intensity is converted to the corresponding voltage signal by computer. It is expected that the signal in one phase keeps constant, and the signal value in the aqueous phase is larger than that in the organic phase because the refractive index in the aqueous phase is larger, as shown in Fig. 4(a). However, because the aqueous membrane may adhere to the probe or the surface-interface interaction (Cartellier and Barrau, 1998a,b; Hamad et al., 2000), sometimes the signal response deviates from the expected signals, as shown in Fig. 4(b) and (c). In Fig. 4(b), although the signals in the aqueous phase and in the organic phase both keep a constant, the signal value in the organic phase is larger. In Fig. 4(c), the signal value in the organic phase does not keep a constant value.
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Fig. 3 – Photos of the optical fiber probe.
In order to fully obtain the detected signals, during the data processing process, two threshold values, X1 and X2 (X1 > X2 ) were set up, as shown in Fig. 4(c). If the signal value was between X1 and X2 , the optical fiber probe was considered to be in the aqueous phase. If the signal value was larger than X1 or was smaller than X2 , the organic phase was considered to be detected. Moreover, when the probe is actually in the organic phase, part signal values can be within X1 and X2 due to the signal fluctuation, as shown in Fig. 4(c), and a complete signal is possible to be recognized as several different signals. In order to avoid misjudging the phase in which the probe is located, an empirical value is set. Only when the number of the measured successive signals, whose value is in the range X1 and X2 , exceeds this experimental value (e.g. 10), an integrate signal but not a section signal is considered to be measured.
2.4.
The algorithm of droplet characteristics
The algorithm used in this paper to obtain the droplet size, the droplet velocity and the droplet movement direction was developed by Shen and Nakamura (Shen and Nakamura, 2014), and we also used this algorithm to study the hydrodynamic characteristics in a pulsed extractin column (Yuan and Gao, 2017). The corresponding equations are Eqs. (1)–(3), respectively, and the parameters in these equations are the same as in Yuan and Gao (2017). To establish these algorithm, the following hypothesizes was made. (1) The velocity and the size of the droplets are supposed to be constant in the penetration process. (2) The droplet is spheroidal.
|V| =
|r| =
A20 A21
+ A22 + A33
A24 + A25 + A26
= arccos
A20
|V| A 3
A0
A0 , A1 , A2 , A3, A4 , A5 , and A6 are given by, Fig. 4 – Illustration of the raw signal.
(1)
(2)
(3)
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Fig. 5 – Droplet size distribution with pulsation intensity.
x1 y1 A0 = x2 y2 x y 3
3
Fig. 6 – Droplet average velocity variation with pulsation intensity.
t1a + t1c y1 z1 z1 2 t2a + t2c z2 , A1 = y2 z2 , 2 t3a + t3c z3 y3 z3 2
x1 t1a + t1c z1 x1 y1 t1a + t1c 2 2 t + t t + t 2a 2c 2a 2c A2 = x2 z2 , A3 = x2 y2 (4) 2 2 x3 t3a + t3c z3 x3 y3 t3a + t3c 2
2
t1a · t1b · |V|2 − |s4−1 |2 y1 z1 2 t · t · |V|2 − |s |2 4−2 2b A4 = 2a y2 z2 , 2 t3a · t3b · |V|2 − |s4−3 |2 y3 z3 2 2 2 x1 t1a · t1b · |V| − |s4−1 | z1 2 2 2 A5 = x2 t2a · t2b · |V| − |s4−2 | z2 , 2 t3a · t3b · |V|2 − |s4−3 |2 x3 z3 2 2 2 x1 y1 t1a · t1b · |V| − |s4−1 | 2 2 2 t · t · |V| − |s | 2a 4−2 2b A6 = x2 y2 2 2 t3a · t3b · |V| − |s4−3 |2 x3 y3
Where n is the total number of the droplets, and ni is the number of the droplets whose diameter is within a given range such as 1.0–1.3 mm. At each operational condition, n is no less than 1500. It was found that the droplet size nearly follows the normal distribution, and the peak of Pd shifts to the left side as the pulsation intensity increases, which means that the droplet size decreases with the increase of the pulsation intensity. This phenomenon can be attributed to the shear force applied on the dispersed phase droplets. With the increase of the pulsation intensity, the shear force increases, and the possibility of the coalescence of the dispersed phase droplets in this regime decreases due to the high turbulence. Moreover, the decrease trend of the drop size slows down with the increase of the intensity pulsation. Lade et al. (2013) studied the effect of the pulsation intensity on the drop size of the kerosene–water system in a 76 mm diameter pulsed extraction column. They found that the drop size decreases with the increase of the pulsation intensity, and the drop size decreases faster at low pulsation intensity than at high pulsation intensity. Yuan and Gao (2017), Yi et al. (2017), Panahinia et al. (2017), Amani and Esmaieli (2017) also studied the effect of the pulsation intensity on the drop size, and observed that as the pulsation intensity increases, the drop size decreases.
3.2. The effects of the pulsation intensity on the droplet average velocity (5)
Fig. 6 depicts the dependence of the droplet average velocity ¯ defined as Eq. (7), on the pulsation intensity. (V), i=n
2
3.
¯ V=
Results and discussion
3.1. The effects of the pulsation intensity on the droplet size Fig. 5 shows the probability distribution Pd of the droplets with different sizses at different pulsation intensities, and Pd is defined as Eq. (6). Pd =
ni n
(6)
i=1
n
vi (7)
Where V¯ is the average velocity of the droplets, and vi is the instantaneous velocity of a single droplet. For each experimental condition, n is no less than 150. It is obvious that the pulsation intensity has different influences on the droplets with different sizes. The pulsation intensity has neglectable influence on the droplet average velocity for the droplets with 1.6 mm diameter, and for the droplets with 2.5 mm diameter, the droplet average velocity increases with the increase of the pulsation intensity. For the
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Where n is the total number of the droplets, and nv is the number of the droplets whose velocity is within a given range such as 40–50 mm/s. For each experimental condition, at least 150 droplets were measured. As the droplet diameter increases, the peak of Pv shifts to the right, which means that larger droplets incline to have higher velocity. It can be predicted that the droplet average velocity increases with the increase of the droplet size. It should be also noticed from Fig. 7 that the velocities of the droplets with similar size are quite different, which is possibly attributed to the different distances between the droplets and the sieve plate and the process of acceleration and deceleration in the droplet movement. Due to the complex breakage and coalescence behaviors of the droplets, it is difficult to analyze the acceleration and deceleration processes during the droplet rising accurately, and here the information about the droplet velocity distribution is provided.
3.4. The effects of the pulsation intensity on the angle between droplet movement direction and probe Because of the existence of the buoyancy, the pressure gradient, the drag and the added-mass forces, the dispersed droplets move up not simply in vertical inside the extraction column (Yuan and Gao, 2017; Bardin, 2003), even the movement of single organic droplets rising in a quiescent ambient liquid is not always straight up sometimes. Fig. 8 shows the probability distribution P of the droplets movement direction with respect to the probe. Here P is defined as Eq. (9). P =
Fig. 7 – Droplet velocity distribution (a) Af = 5.1 mm/s,(b) Af = 6.4 mm/s.
droplets with 3.4 mm diameter, with the increase of the pulsation intensity, the droplet average velocity increases overall with slight fluctuation. Moreover, larger droplets tend to have a larger average velocity at the same pulsation intensity. The results demonstrate that the pulsation intensity and the droplet diameter govern the droplet average velocity together. An increase in the pulsation intensity tends to increase the droplet velocity, at the same time, it favors the drop breakage, which decreases the droplet velocity via the size reduction of the droplet population (Bardin, 2003).
3.3. The effects of the droplet size on the droplet velocity Droplet velocity affects the residence time of the droplet and the holdup in the reactor (Yadav and Patwardhan, 2008). Droplet velocity is also related to the slip velocity of the dispersed phase, which controls the mass transfer coefficient (Torkaman et al., 2017). Fig. 7 shows the probability distribution Pv of the droplet with different velocities at two different pulsation intensities, and Pv is defined as Eq. (8). Pv =
nv n
(8)
n n
(9)
Where n is the total number of the droplets, and n is the number of the droplets whose movement angle is within a given range such as 0–5◦ . At each experimental condition, at least 150 droplets were considered. It can be seen from Fig. 8 that the pulsation intensity has different effects on the movement of the droplets with different sizes. For the droplets with 1.6 mm diameter, the peak value of P declines with the increase of the pulsation intensity, which means that the movement direction of the droplets becomes more random. For the droplets with 2.5 mm diameter, with the increase of the pulsation intensity, the distribution curve decreases slowly but shifts to the right more remarkablely, meaning that the added-tubulence energy makes the movement direction divate more from the vertical direction. For the droplets with 3.4 mm diameter, with the increase of the pulsation intensity, there is no obvious decreasing or right shifting of the distribution curve. Therefore, in general the pulsation intensity has larger influence on the movement direction of smaller droplets. Fig. 8. Droplet movement direction distribution (a) d = 1.6 mm,(b) d = 2.5 mm, (c) d = 3.4 mm To have a comprehensive understanding about the effects of the pulsation intensity and the droplets diameter on the movement direction of the droplets, all the experimental data in different pulsation intensities was combined, and the corresponding results are shown in Fig. 9. Fig. 9 (a) shows the relationship between the droplet movement direction and the droplet diameter. With the increase of the droplet diameter, the peak value of P shifts to the left first, then shifts slightly to the right. For the droplets with 1.6 mm diameter, the distribution range of ␥ is the largest, indicat-
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Fig. 9 – Droplet movement direction distribution (a) Af = 5.1–6.4 mm/s, (b) d =. 1–4 mm. ing that the movement direction of the small droplets is the most random. Fig. 9(b) shows the relationship between the droplet movement direction distribution and the pulsation intensity. With the increase of the pulsation intensity, the distribution curve shifts to the right, indicating that the added tubulence energy stengths the random movement of the droplets. Also, the phenomena shown in Fig. 9(b) can be predicted from Fig. 5 and Fig. 9(a). With the increase of the pulsation intensity, the droplet size decreases, and the angle between the droplet movement direction and the probe increases.
3.5.
Fig. 8 – Droplet movement direction distribution (a)d = 1.6 mm,(b) d = 2.5 mm, (c) d = 3.4 mm.
Error analysis
According to the previously reported results (Yuan and Gao, 2017; Mishra et al., 2002), the accuracy of the values of the droplet velocity v and the droplet diameter d depends on nine time delays (t1a ,t2a , t3a , t1b , t2b , t3b , t1c , t2c , t3c ) and the relative coordinates of the tips of the optical probe. To estimate the error caused by the time delays and the relative coordinates of the optical probe, the following
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Table 3a – Analysis of the droplet instantaneous velocity error caused by the probe coordinate. e
Axis
Emin Emax E¯
x+
x−
y+
y−
−5.83% 5.46% 0.46%
−6.19% 5.14% 0.22%
−6.21% 5.12% 0.24%
−6.25% 5.08% 0.20%
Table 3b – Analysis of error caused by the probe coordinate on the droplet diameter. e
Axis
Emin Emax E¯
Fig. 10 – Illustration of the diviation of the probe. Table 2a – Analysis of the droplet instantaneous velocity error caused by the time delay. e
Emin Emax E¯
t +0.0004
+0.001
−0.0002
−0.0004
−0.001
−1.68% 8.83% 3.20%
0.99% 16.24% 6.09%
2.77% 32.66% 13.72%
−11.09% 1.71% −3.09%
−24.00% −1.12% −6.58%
−42.25% −2.82% −18.17%
Table 2b – Analysis of the droplet diameter error caused by the time delay. e
Emin Emax E¯
t +0.0002
+0.0004
+0.001
−0.0002
−0.0004
−0.001
−0.38% 27.03% 5.12%
−0.93% 28.32% 9.05%
−2.58% 44.40% 18.77%
−16.86% 24.55% −3.19%
−39.30% 23.38% −8.04%
−82.28% 20.35% −24.62%
Table 2c – Analysis of the droplet movement direction error caused by the time delay. e
t +0.0002
+0.0004
+0.001
−0.0002 −0.0004 −0.001
Emin (◦ ) −4.4627 −4.1675 −3.3669 −5.1024 −5.4496 −10.2215 3.5575 6.9752 1.1590 0.5229 0.2186 Emax (◦ ) 2.8186 0.1778 0.6863 2.0820 −0.9448 −1.5599 −3.6376 E¯ (◦ )
steps are taken. First, according to the sampling time interval 0.0002 s, six time intervals(t), that is, ±0.0002 s, ±0.0004 s and ±0.001 s, are added to the nine time delays respectively to evaluate the influence of signal response time on droplet characteristics. Then, it is hypothesized that the probe deviates 10◦ from the direction of z axis to the positive and negative axes of x and y respectively, as illustrated in Fig. 10. The data used to analyze error are obtained with the pulsation intensity 5.1 mm/s. The error analysis results are shown in Tables 2a–2c and Tables 3a–3c, where Emin , Emax , E¯ refer to the maximum error, the minimum error and the average error, respectively. It can be seen from Tables 2a–2c that, the error increases with the increase of |t |. When t is less than zero, the value of E¯ is also less than zero, which means that the increase of the signal width tends to increase the measured droplet diameter, droplet velocity and droplet movement direction,
x−
y+
y−
−6.28% 12.31% 1.22%
−6.72% 11.85% 0.98%
−6.87% 11.78% 0.82%
−6.81% 11.75% 0.93%
Table 3c – Analysis of error caused by the probe coordinate on the droplet movement direction. e
Axis
◦
+0.0002
x+
Emin ( ) Emax (◦ ) ¯ ◦) E(
x+
x−
y+
y−
−15.0518 10.2182 −6.3085
−10.2060 10.9944 2.3860
−10.3419 12.2324 0.5706
−13.1602 9.5582 −4.84378
and vice versa. Tables 2a–2c also indicates that when |t| is less than 0.0004 s, the average error is less than 10% for the droplet diameter and the droplet velocity, and is less than 2◦ for the droplet movement direction. Considering that the sampling time interval is 0.0002 s, the four optical fiber probe method is reliable for the measurement on the droplet characteristics. Tables 3a–3c show the analysis results of the error caused by the probe coordinate. Compared with Tables 2a–2c, it can be found that the error of the droplet diameter and the droplet velocity casued by the probe coordinate is much smaller than that caused by the time delay. The direction deviation of the probe imposed more influence on the droplet movement direction.
4.
Conclusions
Hydrodynamic characteristics of the dispersed phase, including the droplet velocity, the droplet size, the droplet movement direction and their distribution were meaured using a four optical fiber probe in a pulsed sieve plate extraction column, in which water and 40% (VO /VO ) octanol-kerosene were used as the continuous and dispersed phases, respectively. The influences of the pulsation intensity on these hydrodynamic characteristics were investigated. Results showed that the droplet size decreases but the droplet velocity increases with the increase of the pulsation intensity. As the pulsation intensity increases, the angle deviation of the droplet movement from the vertical direction also increases. Compared with the larger droplets, the movement direction of the smaller droplets are dependent more on the pulsation intensity. In addition, larger droplets generally have larger velocity under the same experimental condition. It is demonstrated by the error analysis that the four optical fibre probe method is an accurate and reliable technique for the measurement of these hydrodynamic characteristics of the liquid-liquid two phase flow. It is anticipated that these results will provide fur-
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ther insight into the droplet beheviors of the dispersed phase in the real pulsed sive plate columns used in the spent fuel reprocesing plants.
Acknowledgements The work was supported by Young Scientist Fund of Heilongjiang Province Natural Science Foundation (QC2015006) and Special Fund of Central University Basic Scientific Research Fee (GK2150260152).
Appendix A. Supplementary data Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/10.1016/ j.cherd.2019.02.031.
References Amani, P., Esmaieli, M., 2017. Drop behaviour characteristics in different operating regimes in an L-shaped pulsed sieve-plate column. Can. J. Chem. Eng. 96 (1), 285–296. Amani, P., Safdari, J., Gharib, A., et al., 2017. Mass transfer studies in a horizontal pulsed sieve-plate column for uranium extraction by tri-n-octylamine using axial dispersion model. Prog. Nucl. Energy 98, 71–84. Aoun Nabli, M.S., Guiraud, P., Gourdon, C., 1998. CFD contribution to a design procedure for discs and doughnuts extraction columns. Chem. Eng. Res. Des. 76 (8), 951–960. Arab, E., Ghaemi, A., Torab-Mostaedi, M., 2017. Experimental investigation of slip velocity and dispersed phase holdup in a kühni extraction column. Asia-Pac. J. Chem. Eng. 12 (4), 620–630. Azizi, Z., 2017. Experimental investigation of terminal velocity and sherwood number of rising droplet in an extraction column. Heat Mass Transfer. 53 (10), 3027–3035. Bardin, N., 2003. Lagrangian simulations contribution to the knowledge of discs and doughnuts pulsed solvent extraction columns hydrodynamics. Chem. Eng. Process. Process Intensification 42 (7), 503–516. Bäumler, K., Wegener, M., Paschedag, A.R., et al., 2011. Drop rise velocities and fluid dynamic behavior in standard test systems for liquid/liquid extraction—experimental and numerical investigations. Chem. Eng. Sci. 66 (3), 426–439. Cartellier, A., Barrau, E., 1998a. Monofiber optical probes for gas detection and gas velocity measurements: conical probes. Int. J. Multiphase Flow 24 (8), 1265–1294. Cartellier, A., Barrau, E., 1998b. Monofiber optical probes for gas detection and gas velocity measurements: optimised sensing tips. Int. J. Multiphase Flow 24 (8), 1295–1315. Eiswirth, R.T., Bart, H.J., Atmakidis, T., et al., 2011. Experimental and numerical investigation of a free rising droplet. Chem. Eng. Process. 50 (7), 718–727. Gholam Samani, M., Haghighi Asl, A., Safdari, J., et al., 2012. Drop size distribution and mean drop size in a pulsed packed extraction column. Chem. Eng. Res. Des. 90 (12), 2148–2154. Hamad, F.A., Pierscionek, B.K., Bruun, H.H., 2000. A dual optical probe for volume fraction, drop velocity and drop size measurements in liquid-liquid two-phase flow. Meas. Sci. Technol. 11 (9), 1307. Hemmati, A., Torab-Mostaedi, M., Shirvani, M., et al., 2015. A study of drop size distribution and mean drop size in a
perforated rotating disc contactor (PRDC). Chem. Eng. Res. Des. 96, 54–62. Khajenoori, M., Safdari, J., Asl, A.H., et al., 2015. Slip and characteristic velocities in a horizontal pulsed-plate extraction column. Chem. Eng. Technol. 38 (10), 1783–1792. Lade, V.G., Rathod, V.K., Bhattacharyya, S., et al., 2013. Comparison of normal phase operation and phase reversal studies in a pulsed sieve plate extraction column. Chem. Eng. Res. Des. 91 (6), 1133–1144. Li, Z., Zhao, Y., Song, X., et al., 2016. Experimental investigation of single small bubble motion in linear shear flow in water. Nucl. Eng. Des. 305, 334–346. Mishra, R., Lucas, G.P., Kieckhoefer, H., 2002. A model for obtaining the velocity vectors of spherical droplets in multiphase flows from measurements using an orthogonal four-sensor probe. Meas. Sci. Technol. 13 (9), 1488. Ojha, A., 2018. Investigation of local gas holdup and bubble dynamics using Four-Point optical probe technique in a Split-cylinder airlift reactor. Int. J. Multiphase Flow 102, 1–15. Panahinia, F., Ghannadi-Maragheh, M., Safdari, J., et al., 2017. Experimental investigation concerning the effect of mass transfer direction on mean drop size and holdup in a horizontal pulsed plate extraction column. RSC Adv. 7 (15), 8908–8921. Shen, X., Nakamura, H., 2013. Local interfacial velocity measurement method using a four-sensor probe. Int. J. Heat Mass Transfer 67, 843–852. Shen, X., Nakamura, H., 2014. Spherical-bubble-based four-sensor probe signal processing algorithm for two-phase flow measurement. Int. J. Multiphase Flow 60, 11–29. Somkuwar, N., Kolhe, N., Rathod, V., 2014. Hydrodynamics of a pulsed sieve plate extraction column. Indian Chem. Eng. 56 (3), 235–257. Tomiyama, A., Tamai, H., Zun, I., et al., 2002. Transverse migration of single bubbles in simple shear flows. Chem. Eng. Sci. 57 (11), 1849–1858. Torab-Mostaedi, M., Ghaemi, A., Asadollahzadeh, M., 2011. Flooding and drop size in a pulsed disc and doughnut extraction column. Chem. Eng. Res. Des. 89 (12), 2742–2751. Torkaman, R., Asadollahzadeh, M., Torab-Mostaedi, M., 2017. Determination of slip and characteristic velocities in reactive extraction with experiments in the Oldshue–Rushton column and presence of samarium and gadolinium metals. Chem. Eng. Process. 111, 7–13. Wegener, M., Paul, N., Kraume, M., 2014. Fluid dynamics and mass transfer at single droplets in liquid/liquid systems. Int. J. Heat Mass Transfer 71, 475–495. Xie, T., Gao, Y., Liu, W., 2015. Droplet velocity, size, and local holdup measurements in an extraction column by tri-sensor optical probe. AlChE J. 61 (11), 3958–3963. Yadav, R.L., Patwardhan, A.W., 2008. Design aspects of pulsed sieve plate columns. Chem. Eng. J. 138 (1-3), 389–415. Yang, R., Zheng, R., Zhou, F., et al., 2009. Measurement of two-dimensional bubble velocity by using tri-fiber-optical probe. J. Phys. Conf. Ser. 147, 012028. Yi, H., Wang, Y., Smith, K.H., et al., 2017. Hydrodynamic performance of a pulsed solvent extraction column with novel ceramic internals: holdup and drop size. Ind. Eng. Chem. Res. 56 (4), 999–1007. Yuan, Y., Gao, Y., 2017. A study on hydrodynamic characteristics in a 38 pulsed extraction column by four-sensor optical fiber probe. AlChE J. 63 (2), 801–811. Zhou, Y., Dudukovic, M.P., Al-Dahhan, M.H., et al., 2014. Multiphase hydrodynamics and distribution characteristics in a monolith bed measured by optical fiber probe. AlChE J. 60 (2), 740–748.
Contents lists available at ScienceDirect
Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd
Study on droplet velocity in a pulsed sieve plate extraction column by four-sensor optical fiber probe Yandong Sun a,b , Yang Gao a,∗ , Hongguo Hou a , Caishan Jiao a , Yu Zhou a , Meng Zhang a a
Fundamental Science on Nuclear Safety and Simulation Technology Laboratory, College of Nuclear Science and Technology, Harbin Engineering University, Harbin, Heilongjiang Province, 150001, China b China Institute of Atomic Energy, P. O. Box 275 (126), Beijing, 102413, China
a r t i c l e
i n f o
a b s t r a c t
Article history:
In this paper, the hydrodynamic characteristics including the droplet velocity, the droplet
Received 1 November 2018
diameter, and the droplet movement direction in a 38 pulsed sieve plate extraction column
Received in revised form 29 January
were measured with a four-sensor optical probe, where water and 40% (VO /VO ) octanol-
2019
kerosene were used as the continuous phase and the dispersed phase, respectively. The
Accepted 20 February 2019
influence of the pulsation intensity on the droplet characteristics was investigated. Experi-
Available online 1 March 2019
mental results showed that with the increase of the pulsation intensity, the droplet velocity and the angle between the droplet movement direction and the probe increase, and the
Keywords:
droplet diameter decreases. Under the same experimental condition, the velocity of larger
Droplet velocity
droplets is larger than that of smaller droplets. It is demonstrated that the four-sensor optical
Droplet diameter
probe is reliable to the measurement of the dispersed phase hydrodynamic characteristics
Droplet movement direction
in liquid-liquid two-phase flow through the analysis and estimation of error caused by the
Pulsed sieve
time delay of the probe signal and the direction deviation of the probe.
Plate extraction column
© 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Four optical fiber probe
1.
Introduction
Hydrodynamic characteristics such as the droplet velocity, the droplet diameter, the holdup of the dispersed phase are of great impor-
Liquid–liquid extraction is one of the classical techniques for separation process which can be applied in many industries including pharmaceutical engineering, petroleum processing, food processing,
tance in the design and scaling-up of an extraction column, all of which
and especially in the treatment of waste in nuclear fuel reprocessing (Panahinia et al., 2017; Khajenoori et al., 2015; Amani et al., 2017; Aoun
Gholam Samani et al., 2012; Amani and Esmaieli, 2017; Hemmati et al., 2015). To obtain these hydrodynamic characteristics, several measure-
Nabli et al., 1998). Because of different mechanisms on mass transfer
ment methods have been developed including optical probe method, volume displacement method, and photographing method, etc. (Yuan
regimes, solvent extraction processes were carried out with different equipment and contactors (Arab et al., 2017). Compared with other extraction equipment, pulsed extraction column has many advantages such as high mass transfer coefficient, short residence time and large processing capacity and so on (Yuan and Gao, 2017). In particular, the pulsation unit can be separated from the column, so the pulsed extraction column is very useful in processing corrosive or radioactive solutions (Yadav and Patwardhan, 2008).
∗
affect the mass transfer coefficient strongly (Somkuwar et al., 2014; Yi et al., 2017; Xie et al., 2015; Torab-Mostaedi et al., 2011; Lade et al., 2013;
and Gao, 2017). Volume displacement method can be only used for the measurement of the holdup, and photographing method mainly provides the information about the diameter of the droplets. Optical fiber probe method is a kind of invasive technique, which can obtain several hydrodynamic characteristics simultaneously by piercing droplets, and has been applied extensively in the field of liquid-liquid two phase flow (Yuan and Gao, 2017; Xie et al., 2015; Hamad et al., 2000).
Corresponding author. E-mail address: [email protected] (Y. Gao). https://doi.org/10.1016/j.cherd.2019.02.031 0263-8762/© 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
Chemical Engineering Research and Design 1 4 4 ( 2 0 1 9 ) 550–558
Nomenclature List of symbols n The number of the droplets in a designated condition ni The number of the droplets with the size equal to 1.0–1.3, 1.3–1.6,. . .,3.4–3.7,3.7–4.0 mm, respectively nv The number of the droplets with the velocity equal to 0–10,10-20,. . .,180-190,190–200 mm/s, respectively n␥ The number of the droplets with the velocity direction equal to 0–5,5–10. . .,40–45,45-50◦ Pd The probability distribution of the droplet diameter The probability distribution of the droplet Pv velocity P The probability distribution of the droplet movement direction Instantaneous velocity of droplet, mm/s v vi Instantaneous velocity of single droplet, mm/s Instantaneous velocity of droplet, mm/s V VO The volume of the two kind of organic phase Average velocity of droplets, mm/s V¯ Droplet diameter, mm d A Amplitude of pulsation, mm Frequency of pulsation,1/s f Af Pulsation intensity, amplitude-frequency product, mm/s The angle between the droplet movement direction and the z axis Time delay between first contact of droplet with tka leading sensor 4 and first contact of droplet with rear sensor k, s(k = 1,2,3) tkb Time delay between first contact of droplet with leading sensor 4 and last contact of droplet with rear sensor k, s(k = 1,2,3) tkc Time delay between last contact of droplet with leading sensor 4 and last contact of droplet with rear sensor k, s(k = 1,2,3) Minimum error in droplet diameter, droplet Emin velocity or droplet movement direction Emax Maximum error in droplet diameter, droplet velocity or droplet movement direction E¯ Average error in droplet diameter, droplet velocity or droplet movement direction Time interval, s(t=±0.0002, ±0.0004, ±0.001) t |s4-k | Distance vector between the leading sensor tip and sensor k’s tip, mm (xk , yk , zk ) Relative coordinate of sensor k corresponding to sensor 4, mm(k = 1,2,3) Droplet radius, mm |r|
According to the number of the optical fibers within the probe, optical fiber probes can be divided into single, double, triple and four optical fiber probe (Zhou et al., 2014; Yang et al., 2009; Shen and Nakamura, 2013). Single optical fiber probe can be only used for the measurement of the dispersed phase volume fraction, and double optical fiber probe can not only be used for the measurement of the dispersed phase volume fraction, but also provide the information about the onedimensional velocity and the chord length of the droplets (Xie et al., 2015; Ojha, 2018).Triple optical fiber probe can obtain two-dimensional velocity of the droplets with an iterative algorithm (Yang et al., 2009).
551
Four optical fiber probe can measure the three-dimensional velocity of the droplets, and can measure the drop diameter with higher accuracy than the other optical fiber probe techniques (Yuan and Gao, 2017; Ojha, 2018). Until now, there have been extensive work on the droplet diameter and the holdup of the extraction columns, and numerous empirical correlations about the drop Sauter diameter and the holdup have been proposed. However, due to the limitation of the measurement technique, little information is available in the literature regarding the droplet velocity. Bardin (2003) adopted Lagrangian simulation approach to investigate the behavior of the dispersed phase droplets in the discs and doughnuts pulsed column. It was found that the mean residence time in a compartment is a decreasing function of the droplet diameter and of the pulsation intensity, which indirectly indicated that with the increase of the pulsation intensity and the droplet diameter, the droplet velocity increases. Wegener et al. (2014) estimated the effect of the droplet diameter on the droplet terminal velocity, and found that the terminal velocity of a single droplet increases with the increase of the droplet diameter, which is in agreement with the results obtained by Eiswirth et al. (2011), Azizi (2017) and Bäumler et al. (2011). Yuan and Gao (2017) applied the four optical fiber probe technique to study the droplet movement direction in a pulsed sieve plate extraction column, and found that the movement direction of droplets is not simply straight up. Bäumler et al. (2011) investigated the fluid dynamic behavior of single organic droplets rising in a quiescent ambient liquid, and found that when the droplet deforms, its rising path significantly deviates from the vertical axis. Li et al. (2016) studied the movement of the small bubble in a simple shear flow in water, and noticed that the rising path of the bubbles was zigzag, which is similar to the results obtained by Tomiyama et al. (2002). To optimize the design of extraction columns, extensive work (Lade et al., 2013; Gholam Samani et al., 2012; Amani and Esmaieli, 2017; Hemmati et al., 2015) was carried out to explore the relationship between the operational conditions and the hydrodynamic characteristics. The most studied operational conditions usually include the continuous phase superficial velocity, the dispersed phase superficial velocity, and the pulsation intensity. Many results showed that the pulsation intensity has a significant impact on the hydrodynamic characteristics, such as the droplet diameter and the holdup. Compared with the pulsation intensity, the two phase superficial velocities have much less influence on these hydrodynamic characteristics. In a word, the information on the dispersed phase droplet characteristics, especially on the droplet velocity in the extraction columns is still inadequate. In this paper, the droplet velocity and the droplet size were studied using a self-made four optical fiber probe in a 38 pulsed sieve plate extraction column, and the influence of the pulsation intensity on the hydrodynamic characteristics was investigated. The relationship between the droplet velocity and the droplet diameter was also analyzed.
2.
Material and methods
2.1.
Experimental setup and materials
Fig. 1 shows the schematic and the actual diagrams of the experimental apparatus. It mainly consists of three parts: one extraction section which is a 1474 mm long glass tube with 38 mm inner diameter. Two clarification sections with 79 mm inner diameter are used to separate the two phases. There are 30 sieve plates with a distance of 50 mm mounted on a stainless steel rod of 6 mm at the center of the extraction section. Each sieve contains 32 circular holes of 3 mm diameter, providing a 23% free area. An air pulse is connected with a down separating chamber by a pulse leg with a 16 mm diameter and a height of 1624 mm. Pulsation intensity is regulated by a digital regulator and stepper motor. Water was taken as the continuous phase and 40% (VO /VO ) octanol-kerosene was used as the dispersed phase. Because
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Fig. 1 – (a) the schematic diagram and (b) the actual diagram of the pulsed sieve plate extraction column.
Fig. 2 – Diagram of the four-sensor optical fiber probe (Yuan and Gao, 2017).
Table 1 – Physical properties of the two phases. Parameters
Water
40% Octanol-Kerosene
Interfacial tension (mN/m) Viscosity of the phase (mPa·s) Density of the phase (kg/m3 )
0.0 0.99 998.2
16.1 2.39 782.6
probe was placed in the middle of the 12th and 13th plates from the bottom of the active section, and was perpendicular with respect to the sieve plate. Fig. 3 is the photos of the four-sensor optical fiber probe with their size parameters.
2.3. the main focus was on the effect of the pulsation intensity, the continuous and the dispersed phase superficial velocities were adjusted to the fixed values, 2.51 mm/s and 2.08 mm/s, respectively. Table 1 gives the physical properties of the two phase flow. The interfacial tension was measured with a BZY-2 tensiometer, and the viscosities were measured with a NDJ-8S viscometer.
2.2.
The four-sensor optical fiber probe
Fig. 2 shows a schematic diagram of the four-sensor optical fiber probe. The probe has four sensors with sensor 4 as the leading sensor and sensors 1, 2, and 3 as the rear sensors. During the data processing process, sensor 4 was regarded as the origin, and the relative coordinates of sensors 1, 2, and 3 can be obtained by the distance between sensor 4 and themselves, which can be measured by a digital microscope. During the process of the experiment, the optical fiber
Measurement principle of optical fiber probe
As different liquids have different refractive indexes, the photoelectric transducer can receive different light intensities when the optical fiber probe is in different phases. Then the light intensity is converted to the corresponding voltage signal by computer. It is expected that the signal in one phase keeps constant, and the signal value in the aqueous phase is larger than that in the organic phase because the refractive index in the aqueous phase is larger, as shown in Fig. 4(a). However, because the aqueous membrane may adhere to the probe or the surface-interface interaction (Cartellier and Barrau, 1998a,b; Hamad et al., 2000), sometimes the signal response deviates from the expected signals, as shown in Fig. 4(b) and (c). In Fig. 4(b), although the signals in the aqueous phase and in the organic phase both keep a constant, the signal value in the organic phase is larger. In Fig. 4(c), the signal value in the organic phase does not keep a constant value.
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Fig. 3 – Photos of the optical fiber probe.
In order to fully obtain the detected signals, during the data processing process, two threshold values, X1 and X2 (X1 > X2 ) were set up, as shown in Fig. 4(c). If the signal value was between X1 and X2 , the optical fiber probe was considered to be in the aqueous phase. If the signal value was larger than X1 or was smaller than X2 , the organic phase was considered to be detected. Moreover, when the probe is actually in the organic phase, part signal values can be within X1 and X2 due to the signal fluctuation, as shown in Fig. 4(c), and a complete signal is possible to be recognized as several different signals. In order to avoid misjudging the phase in which the probe is located, an empirical value is set. Only when the number of the measured successive signals, whose value is in the range X1 and X2 , exceeds this experimental value (e.g. 10), an integrate signal but not a section signal is considered to be measured.
2.4.
The algorithm of droplet characteristics
The algorithm used in this paper to obtain the droplet size, the droplet velocity and the droplet movement direction was developed by Shen and Nakamura (Shen and Nakamura, 2014), and we also used this algorithm to study the hydrodynamic characteristics in a pulsed extractin column (Yuan and Gao, 2017). The corresponding equations are Eqs. (1)–(3), respectively, and the parameters in these equations are the same as in Yuan and Gao (2017). To establish these algorithm, the following hypothesizes was made. (1) The velocity and the size of the droplets are supposed to be constant in the penetration process. (2) The droplet is spheroidal.
|V| =
|r| =
A20 A21
+ A22 + A33
A24 + A25 + A26
= arccos
A20
|V| A 3
A0
A0 , A1 , A2 , A3, A4 , A5 , and A6 are given by, Fig. 4 – Illustration of the raw signal.
(1)
(2)
(3)
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Fig. 5 – Droplet size distribution with pulsation intensity.
x1 y1 A0 = x2 y2 x y 3
3
Fig. 6 – Droplet average velocity variation with pulsation intensity.
t1a + t1c y1 z1 z1 2 t2a + t2c z2 , A1 = y2 z2 , 2 t3a + t3c z3 y3 z3 2
x1 t1a + t1c z1 x1 y1 t1a + t1c 2 2 t + t t + t 2a 2c 2a 2c A2 = x2 z2 , A3 = x2 y2 (4) 2 2 x3 t3a + t3c z3 x3 y3 t3a + t3c 2
2
t1a · t1b · |V|2 − |s4−1 |2 y1 z1 2 t · t · |V|2 − |s |2 4−2 2b A4 = 2a y2 z2 , 2 t3a · t3b · |V|2 − |s4−3 |2 y3 z3 2 2 2 x1 t1a · t1b · |V| − |s4−1 | z1 2 2 2 A5 = x2 t2a · t2b · |V| − |s4−2 | z2 , 2 t3a · t3b · |V|2 − |s4−3 |2 x3 z3 2 2 2 x1 y1 t1a · t1b · |V| − |s4−1 | 2 2 2 t · t · |V| − |s | 2a 4−2 2b A6 = x2 y2 2 2 t3a · t3b · |V| − |s4−3 |2 x3 y3
Where n is the total number of the droplets, and ni is the number of the droplets whose diameter is within a given range such as 1.0–1.3 mm. At each operational condition, n is no less than 1500. It was found that the droplet size nearly follows the normal distribution, and the peak of Pd shifts to the left side as the pulsation intensity increases, which means that the droplet size decreases with the increase of the pulsation intensity. This phenomenon can be attributed to the shear force applied on the dispersed phase droplets. With the increase of the pulsation intensity, the shear force increases, and the possibility of the coalescence of the dispersed phase droplets in this regime decreases due to the high turbulence. Moreover, the decrease trend of the drop size slows down with the increase of the intensity pulsation. Lade et al. (2013) studied the effect of the pulsation intensity on the drop size of the kerosene–water system in a 76 mm diameter pulsed extraction column. They found that the drop size decreases with the increase of the pulsation intensity, and the drop size decreases faster at low pulsation intensity than at high pulsation intensity. Yuan and Gao (2017), Yi et al. (2017), Panahinia et al. (2017), Amani and Esmaieli (2017) also studied the effect of the pulsation intensity on the drop size, and observed that as the pulsation intensity increases, the drop size decreases.
3.2. The effects of the pulsation intensity on the droplet average velocity (5)
Fig. 6 depicts the dependence of the droplet average velocity ¯ defined as Eq. (7), on the pulsation intensity. (V), i=n
2
3.
¯ V=
Results and discussion
3.1. The effects of the pulsation intensity on the droplet size Fig. 5 shows the probability distribution Pd of the droplets with different sizses at different pulsation intensities, and Pd is defined as Eq. (6). Pd =
ni n
(6)
i=1
n
vi (7)
Where V¯ is the average velocity of the droplets, and vi is the instantaneous velocity of a single droplet. For each experimental condition, n is no less than 150. It is obvious that the pulsation intensity has different influences on the droplets with different sizes. The pulsation intensity has neglectable influence on the droplet average velocity for the droplets with 1.6 mm diameter, and for the droplets with 2.5 mm diameter, the droplet average velocity increases with the increase of the pulsation intensity. For the
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Where n is the total number of the droplets, and nv is the number of the droplets whose velocity is within a given range such as 40–50 mm/s. For each experimental condition, at least 150 droplets were measured. As the droplet diameter increases, the peak of Pv shifts to the right, which means that larger droplets incline to have higher velocity. It can be predicted that the droplet average velocity increases with the increase of the droplet size. It should be also noticed from Fig. 7 that the velocities of the droplets with similar size are quite different, which is possibly attributed to the different distances between the droplets and the sieve plate and the process of acceleration and deceleration in the droplet movement. Due to the complex breakage and coalescence behaviors of the droplets, it is difficult to analyze the acceleration and deceleration processes during the droplet rising accurately, and here the information about the droplet velocity distribution is provided.
3.4. The effects of the pulsation intensity on the angle between droplet movement direction and probe Because of the existence of the buoyancy, the pressure gradient, the drag and the added-mass forces, the dispersed droplets move up not simply in vertical inside the extraction column (Yuan and Gao, 2017; Bardin, 2003), even the movement of single organic droplets rising in a quiescent ambient liquid is not always straight up sometimes. Fig. 8 shows the probability distribution P of the droplets movement direction with respect to the probe. Here P is defined as Eq. (9). P =
Fig. 7 – Droplet velocity distribution (a) Af = 5.1 mm/s,(b) Af = 6.4 mm/s.
droplets with 3.4 mm diameter, with the increase of the pulsation intensity, the droplet average velocity increases overall with slight fluctuation. Moreover, larger droplets tend to have a larger average velocity at the same pulsation intensity. The results demonstrate that the pulsation intensity and the droplet diameter govern the droplet average velocity together. An increase in the pulsation intensity tends to increase the droplet velocity, at the same time, it favors the drop breakage, which decreases the droplet velocity via the size reduction of the droplet population (Bardin, 2003).
3.3. The effects of the droplet size on the droplet velocity Droplet velocity affects the residence time of the droplet and the holdup in the reactor (Yadav and Patwardhan, 2008). Droplet velocity is also related to the slip velocity of the dispersed phase, which controls the mass transfer coefficient (Torkaman et al., 2017). Fig. 7 shows the probability distribution Pv of the droplet with different velocities at two different pulsation intensities, and Pv is defined as Eq. (8). Pv =
nv n
(8)
n n
(9)
Where n is the total number of the droplets, and n is the number of the droplets whose movement angle is within a given range such as 0–5◦ . At each experimental condition, at least 150 droplets were considered. It can be seen from Fig. 8 that the pulsation intensity has different effects on the movement of the droplets with different sizes. For the droplets with 1.6 mm diameter, the peak value of P declines with the increase of the pulsation intensity, which means that the movement direction of the droplets becomes more random. For the droplets with 2.5 mm diameter, with the increase of the pulsation intensity, the distribution curve decreases slowly but shifts to the right more remarkablely, meaning that the added-tubulence energy makes the movement direction divate more from the vertical direction. For the droplets with 3.4 mm diameter, with the increase of the pulsation intensity, there is no obvious decreasing or right shifting of the distribution curve. Therefore, in general the pulsation intensity has larger influence on the movement direction of smaller droplets. Fig. 8. Droplet movement direction distribution (a) d = 1.6 mm,(b) d = 2.5 mm, (c) d = 3.4 mm To have a comprehensive understanding about the effects of the pulsation intensity and the droplets diameter on the movement direction of the droplets, all the experimental data in different pulsation intensities was combined, and the corresponding results are shown in Fig. 9. Fig. 9 (a) shows the relationship between the droplet movement direction and the droplet diameter. With the increase of the droplet diameter, the peak value of P shifts to the left first, then shifts slightly to the right. For the droplets with 1.6 mm diameter, the distribution range of ␥ is the largest, indicat-
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Fig. 9 – Droplet movement direction distribution (a) Af = 5.1–6.4 mm/s, (b) d =. 1–4 mm. ing that the movement direction of the small droplets is the most random. Fig. 9(b) shows the relationship between the droplet movement direction distribution and the pulsation intensity. With the increase of the pulsation intensity, the distribution curve shifts to the right, indicating that the added tubulence energy stengths the random movement of the droplets. Also, the phenomena shown in Fig. 9(b) can be predicted from Fig. 5 and Fig. 9(a). With the increase of the pulsation intensity, the droplet size decreases, and the angle between the droplet movement direction and the probe increases.
3.5.
Fig. 8 – Droplet movement direction distribution (a)d = 1.6 mm,(b) d = 2.5 mm, (c) d = 3.4 mm.
Error analysis
According to the previously reported results (Yuan and Gao, 2017; Mishra et al., 2002), the accuracy of the values of the droplet velocity v and the droplet diameter d depends on nine time delays (t1a ,t2a , t3a , t1b , t2b , t3b , t1c , t2c , t3c ) and the relative coordinates of the tips of the optical probe. To estimate the error caused by the time delays and the relative coordinates of the optical probe, the following
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Table 3a – Analysis of the droplet instantaneous velocity error caused by the probe coordinate. e
Axis
Emin Emax E¯
x+
x−
y+
y−
−5.83% 5.46% 0.46%
−6.19% 5.14% 0.22%
−6.21% 5.12% 0.24%
−6.25% 5.08% 0.20%
Table 3b – Analysis of error caused by the probe coordinate on the droplet diameter. e
Axis
Emin Emax E¯
Fig. 10 – Illustration of the diviation of the probe. Table 2a – Analysis of the droplet instantaneous velocity error caused by the time delay. e
Emin Emax E¯
t +0.0004
+0.001
−0.0002
−0.0004
−0.001
−1.68% 8.83% 3.20%
0.99% 16.24% 6.09%
2.77% 32.66% 13.72%
−11.09% 1.71% −3.09%
−24.00% −1.12% −6.58%
−42.25% −2.82% −18.17%
Table 2b – Analysis of the droplet diameter error caused by the time delay. e
Emin Emax E¯
t +0.0002
+0.0004
+0.001
−0.0002
−0.0004
−0.001
−0.38% 27.03% 5.12%
−0.93% 28.32% 9.05%
−2.58% 44.40% 18.77%
−16.86% 24.55% −3.19%
−39.30% 23.38% −8.04%
−82.28% 20.35% −24.62%
Table 2c – Analysis of the droplet movement direction error caused by the time delay. e
t +0.0002
+0.0004
+0.001
−0.0002 −0.0004 −0.001
Emin (◦ ) −4.4627 −4.1675 −3.3669 −5.1024 −5.4496 −10.2215 3.5575 6.9752 1.1590 0.5229 0.2186 Emax (◦ ) 2.8186 0.1778 0.6863 2.0820 −0.9448 −1.5599 −3.6376 E¯ (◦ )
steps are taken. First, according to the sampling time interval 0.0002 s, six time intervals(t), that is, ±0.0002 s, ±0.0004 s and ±0.001 s, are added to the nine time delays respectively to evaluate the influence of signal response time on droplet characteristics. Then, it is hypothesized that the probe deviates 10◦ from the direction of z axis to the positive and negative axes of x and y respectively, as illustrated in Fig. 10. The data used to analyze error are obtained with the pulsation intensity 5.1 mm/s. The error analysis results are shown in Tables 2a–2c and Tables 3a–3c, where Emin , Emax , E¯ refer to the maximum error, the minimum error and the average error, respectively. It can be seen from Tables 2a–2c that, the error increases with the increase of |t |. When t is less than zero, the value of E¯ is also less than zero, which means that the increase of the signal width tends to increase the measured droplet diameter, droplet velocity and droplet movement direction,
x−
y+
y−
−6.28% 12.31% 1.22%
−6.72% 11.85% 0.98%
−6.87% 11.78% 0.82%
−6.81% 11.75% 0.93%
Table 3c – Analysis of error caused by the probe coordinate on the droplet movement direction. e
Axis
◦
+0.0002
x+
Emin ( ) Emax (◦ ) ¯ ◦) E(
x+
x−
y+
y−
−15.0518 10.2182 −6.3085
−10.2060 10.9944 2.3860
−10.3419 12.2324 0.5706
−13.1602 9.5582 −4.84378
and vice versa. Tables 2a–2c also indicates that when |t| is less than 0.0004 s, the average error is less than 10% for the droplet diameter and the droplet velocity, and is less than 2◦ for the droplet movement direction. Considering that the sampling time interval is 0.0002 s, the four optical fiber probe method is reliable for the measurement on the droplet characteristics. Tables 3a–3c show the analysis results of the error caused by the probe coordinate. Compared with Tables 2a–2c, it can be found that the error of the droplet diameter and the droplet velocity casued by the probe coordinate is much smaller than that caused by the time delay. The direction deviation of the probe imposed more influence on the droplet movement direction.
4.
Conclusions
Hydrodynamic characteristics of the dispersed phase, including the droplet velocity, the droplet size, the droplet movement direction and their distribution were meaured using a four optical fiber probe in a pulsed sieve plate extraction column, in which water and 40% (VO /VO ) octanol-kerosene were used as the continuous and dispersed phases, respectively. The influences of the pulsation intensity on these hydrodynamic characteristics were investigated. Results showed that the droplet size decreases but the droplet velocity increases with the increase of the pulsation intensity. As the pulsation intensity increases, the angle deviation of the droplet movement from the vertical direction also increases. Compared with the larger droplets, the movement direction of the smaller droplets are dependent more on the pulsation intensity. In addition, larger droplets generally have larger velocity under the same experimental condition. It is demonstrated by the error analysis that the four optical fibre probe method is an accurate and reliable technique for the measurement of these hydrodynamic characteristics of the liquid-liquid two phase flow. It is anticipated that these results will provide fur-
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ther insight into the droplet beheviors of the dispersed phase in the real pulsed sive plate columns used in the spent fuel reprocesing plants.
Acknowledgements The work was supported by Young Scientist Fund of Heilongjiang Province Natural Science Foundation (QC2015006) and Special Fund of Central University Basic Scientific Research Fee (GK2150260152).
Appendix A. Supplementary data Supplementary material related to this article can be found, in the online version, at doi:https://doi.org/10.1016/ j.cherd.2019.02.031.
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