- Email: [email protected]
Experimental study of slug and churn flows in a vertical pipe using plug-in optical fiber and conductance sensors
Experimental Thermal and Fluid Science 107 (2019) 16–28
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Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Experimental study of slug and churn flows in a vertical pipe using plug-in optical fiber and conductance sensors
T
⁎
Q.Y. Yang, N.D. Jin , L.S. Zhai, D.Y. Wang, F. Wang School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Gas-liquid two-phase flow Slug flow Churn flow Plug-in optical fiber and conductance sensors
It is of great significance to explore the flow structures in gas-liquid slug and churn flows. Aiming at this purpose, a novel plug-in optical probe combined with conductance sensors are designed. Furthermore, we perform experimental study of gas-liquid flows in vertical upward pipe with 20 mm inner diameter. Simultaneously, the local time average of void fraction in axial direction, cross-correlation velocity and instantaneous bubble chord distribution in slug and churn flows at seven radial positions are obtained. The research results show that big deformed bubbles in churn flow spiral up in test pipe, but sometimes they rise along pipe center just as gas slugs in slug flow. Besides, bubble chord length distributions in liquid slug of slug and churn flows are analyzed in this study.
1. Introduction Slug and churn flows in gas-liquid two-phase flow widely exist in petrochemical and nuclear industries. In particular, the churn flow in vertical pipes is relatively chaotic. Unlike slug flow, gas slugs in churn flow are relatively unstable, and present large and elongated bubble shape. Churn flow is an intermediate flow condition between slug flow and mist flow, and occurs at relatively high gas velocity. As the gas velocity increases, it changes into annular flow. Therefore, exploring the flow structures in gas-liquid slug and churn flows is of great significance on sensor optimization, analytical model research and local parameters measurement under these two flow patterns. In term of gas-liquid flow patterns research, high speed photography a direct and effective method. However, complex flow structures located in pipe center could not be clearly captured because they are sheltered by liquid film, especially in slug and churn flows. Emerson et al. [1] analyzed capacitance signals to calculate the film thickness in slug flows under different conditions by power spectrum density and probability density function. Hewitt and Roberts [2] obtained the structures of churn flow with X-ray, and discovered complex interface structure and diverse dispersed phase structures. Wire-mesh sensor was used for the study of interaction between bubbles and wisp-like structures in vertical gas-liquid churn flow [3–5]. Wang et al. [6] found that liquid film at the pipe wall violently fluctuate and they also experimentally studied the droplet entrainment mechanism in churn flow. As for analytical models research on gas-liquid slug and churn flows,
⁎
Femandes et al. [7] discovered alternately rising gas and liquid slugs in slug flows and developed a hydrodynamic model for this flow pattern. Van Hout et al. [8] divided the liquid slug of gas-liquid slug flow into three distinct regions: the wake region, the intermediate region and the developed region. Kaya et al. [9] predicted pressure drop and liquid holdup of churn flows through two different models, and concluded that churn flow is a chaotic flow composed of Taylor bubbles and twisted liquid slugs. Montoya et al. [10] expressed that churn flow is characterized by large spiraling, transient, vortex-like structures, and large deformed gas bubbles are followed by small bubbles. Bubbles size and bubbles interaction in churn flow are also studied by analytical models [11–14]. Existing researches about gas-liquid two-phase flow models mostly focused on bubble flow [15–17]. Gas-liquid churn flow is a complex flow pattern composed of small bubbles and large deformed bubbles simultaneously. The deformation in flow structure makes it difficult to establish a theoretical model. Further understanding of local flow structure in gas-liquid flows is an important way to reveal its temporal and spatial evolution characteristics [18–21]. For the study of gas structure and local flow parameters, micro-sensors have advantages over traditional macro-sensors. Experimental studies [22–23] of gasliquid two-phase flow using conductance probes shown that gas holdup of gas slug tail is higher near pipe wall. The large bubbles mainly distribute in the center of pipe, while small ones distribute near the pipe wall in slug flows. However, it is limited for electrical probes to perform long-term accurate measurement because of polarization effect. In
Corresponding author. E-mail address: [email protected] (N.D. Jin).
https://doi.org/10.1016/j.expthermflusci.2019.05.005 Received 11 January 2019; Received in revised form 25 April 2019; Accepted 12 May 2019 Available online 14 May 2019 0894-1777/ © 2019 Elsevier Inc. All rights reserved.
Experimental Thermal and Fluid Science 107 (2019) 16–28
Q.Y. Yang, et al.
addition, the large tip size of electric probe is liable to cause error in small gas bubbles measurement. Therefore, the optical probe with small size, corrosion resistance, fast response and high precision is widely used in the measurement of gas-liquid two-phase flow parameters. Abuaf et al. [24] investigated the electrical and hydraulic responses of tip structure of optical probes to gas-liquid two-phase flow, and measured the local time average of void fraction in axial direction and gas superficial velocity. Cartellier et al. [25] compared effects of various optical probes based on measuring gas holdup and velocity. Fordham et al. [26] used dual optical probes to measure local holdup distribution characteristics of oil-water, gas-water and oil-gas-water three-phase flow, respectively, which confirmed the validity of optical probes. Some other researchers maximized the advantages of optical probe and hotfilm probe, and analyzed the influence of water superficial velocity and water holdup on the radial flow parameter distribution [27]. Thus, a local gas characteristic sensor system consisting of plug-in optical probe and conductance sensors is proposed by considering high precision of optical probe and great long-range correlation of conductance sensor. Furthermore, dynamic experiment of gas-liquid flows was carried out to measure local time average of void fraction in axial direction, cross-correlation velocity and gas chord length distribution in small pipe because the understanding of gas-liquid flows in small pipe is significant [28].
Fig. 2. Schematic diagram of plug-in movable optical fiber and conductance sensors.
A movable plug-in optical probe and conductance sensors is used to measure local flow characteristics of vertical upward gas-water flows. As presented in Fig. 2, the optical fiber probe, with 1 mm length and 35° cone angle, is made by multimode fiber [29] with 62.5 μm inner diameter and fixed in a holder. When optical fiber is immersed in gas and water phase, the reflected light intensity is different. The high voltage corresponds to gas phase while low voltage corresponds to water phase. The upstream and downstream cross-correlative conductance rings (EA, MA, EB, MB) are flush mounted in the outer wall of the holder, in which EA, EB represent the upstream and downstream excitation electrodes, and MA, MB represent the upstream and downstream measuring electrodes, respectively. Finally, the total sensor is inserted into test pipe as shown in Fig. 1. The sensor model was built based on the cylindrical coordinate system as shown in Fig. 3, and the electrode structure was optimized using finite element method. In order to get a homogenous and high sensitive detection field, the height h of exciting electrode and measuring electrode, the distance L between exciting electrode and measuring electrode, and the spacing s between two pairs of conducting rings are optimized. The electric field distribution of sensor can be described by Laplace equation with boundary conditions:
2. Experimental facility The experiment was carried out in the multiphase flow loop facility in Tianjin University. As shown in Fig. 1, the facility consists of the plug-in optical probe and conductance sensors, a high speed camera, an arc-shape conductance sensor and a vertical test pipe with 20 mm inner diameter. The arc-shape conductance sensor is 1834 mm away from the entrance. The total height of the movable plug-in optical probe and conductance sensors is 230 mm. To clearly observe the characteristics of different flow patterns, a high-speed camera is mounted near the test pipe. Seven measurement positions in the radial direction of the pipe are shown in Fig. 1, which correspond to the X coordinates: −8mm, −6mm, −3mm, 0 mm, 3 mm, 6 mm, and 8 mm.
∇2 u =
1 ∂ ⎛ ∂u ⎞ 1 ∂ 2u ∂ 2u r + 2 + 2 =0 r ∂r ⎝ ∂r ⎠ r ∂φ ∂z
(1)
The boundary conditions of the sensor electric field distribution are as follows:
φ = 2π , z = [s /2, s /2 + h], r = d/2 ⎧u = 0 ⎪u = 0 φ = 2π , z = [s /2 + h + L, s /2 + 2h + L], r = d/2 ⎪ ∂u/ ∂r = I / Se φ = 2π , z = [−s /2, −s /2 − h], r = d/2 ⎨ ⎪ ∂u/ ∂r = I / Se φ = 2π , z = [−s /2 − h − L, −s /2 − 2h − L], r = d/2 ⎪ ∂u/ ∂z = 0 z = ± H /2 ⎩ (2) where u is the voltage, and r2 = x2 + y2. The diameter of insert is d, and H is the length of pipe. I is the exciting current and Se is the area of electrode surface. The calculation of the sensitivity of different positions in sensor detection field is performed based on the Cartesian coordinate system. An insulating sphere with 500 μm diameter is set in the electric field to simulate gas bubbles in gas-water flows. The output of conductance sensor could be obtained as U0 when the pipe is full of water. The intervention of sphere causes the output voltage U. The voltage variation ΔU caused by the sphere can be calculated as: ΔU = U-U0. Then the
Fig. 1. Schematic diagram of gas-water flows loop facility. 17
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Fig. 3. The simulation model of plug-in optical fiber and conductance sensors.
sensitivity of the sensor detection field can be defined as:
ΔU (x , y, z ) [ΔU (x , y, z )]max
S (x , y, z ) =
0.70
0.60
Savg
∑ Sj
Sder
∑ (S (x , y, z ) − Savg j=1
0.50
45
0.45
40 35
25 1
3
4
5
6
7
Fig. 4. Values of Savg and SVP in different intervals between exciting and measuring electrodes.
(5)
exciting electrode is stimulated by a +5 V excitation voltage and measuring electrode is connected to ground. With intention to obtain an optimal value of s, the following two conditions should be satisfied. Firstly, there should be no crosstalk between the electric fields of two pairs of electrodes. Secondly, upstream and downstream signals should have good correlation. As shown in Fig. 5, the crosstalk between two electric fields is gradually to zero until s increases to 30 mm. To ensure correlation between upstream and downstream signals, the optimal value of s is determined as 30 mm. The experimental conditions include two flow patterns, slug flow and churn flow. In the process of experiment, water superficial velocity Usw is set from 0.0368 m/s to 0.8832 m/s, and gas superficial velocity Usg is set from 0.0552 m/s to 0.5888 m/s. Firstly, the gas superficial velocity is fixed, and with the increase of Usg, the optical and electrical sensor responses at seven radial measuring positions of the pipe are obtained by moving the plug-in movable optical fiber and conductance sensors. When all the Usw are finished, the Usg is changed and the experiment procedure repeated. The fluctuating signals of sensors are collected by PXI-4472 synchronization card of National Instruments (NI) Company. The sampling frequency and sampling time are set as 2 kHz and 30 s.
1 2
⎤ )2 ⎥ ⎦
2
L / mm
where Sder represents the standard deviation of average sensitivity in pipe which can be defined as: M
50
30
Sder × 100% Savg
⎡1 =⎢ M ⎣
0.55
0.35
(4)
j=1
where Sj is the relative sensitivity of the sensor when the sphere is located at different positions in detection area, M is the total number of positions. The sensitivity variation parameter SVP can be formulated as:
SVP =
60 55
0.40
M
65
SVP / %
Savg
SVP
(3)
where ΔU (x, y, z) is the voltage variation induced by the sphere at position (x, y, z), [ΔU (x, y, z)] max is the maximum value of voltage variation. The sensitivity variation parameter SVP and the average sensitivity Savg are taken as the optimization indicators. Savg can be calculated with the following expression:
1 = M
Savg
0.65
(6)
It can be seen from the definition of Savg and SVP that highly sensitive sensor is positively correlated with Savg, while homogeneous detection field is negatively correlated with SVP. To investigate the characteristics of sensor detection field, we fix s and h to calculate Savg and SVP with different value of L. It can be seen from Fig. 4 that the value of Savg is the highest while SVP presents the lowest when L is 5 mm. This means that the detection field presents high sensitivity and homogeneity under this value of L. With the same method, we fix the electrode spacing L and the spacing between upstream and downstream electrodes s to achieve optimal value of h by calculating Savg and SVP. The simulation results show that the optimal value of h is 3 mm. For the purpose of obtaining the optimal value of s, we fix h and L, then the values of s are set as 10 mm, 20 mm and 30 mm. Fig. 5 Shows the current density distribution under three different values of s. The 18
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series {y1 , y2 , y3 , …yn } and reconstructing the phase space → → Yj = {yj , yj + τ , …, yj + (m − 1) τ }, (j = 1, 2, …, N ) , then the distances between Xi → and Yj are calculated one by one. A cross recurrence matrix CRi,j is built and the formula of cross recurrence matrix is:
s = 10mm
→ → CRi, j = Θ(ε − ∥Xi − Yj ∥ )
In this paper, we employ this method to conductance sensor signals to analyze the flow structure differences in axial direction with parameters as: delay time τ = 2, embedding dimension m = 3, and empirical coefficient α = 0.25 [37]. By defining the upstream and downstream time series of arc-shape conductance sensor as Xa(t) and Yb(t), we can reconstruct a phase space from the time series Xa(t) and Yb(t), then the phase space trajectories Xa(i) and Yb(j) can be obtained. Afterwards, a cross recurrence plot algorithm is applied to investigate the recursive features of corresponding flow conditions. Slug flows with higher gas and lower water superficial velocities appears pseudo-periodic characteristics. The gas slug is almost full of pipe with liquid flows downward as liquid film near the wall. With the increase of gas velocity, the liquid slugs become more aerated [38]. The crush and coalescence of small bubbles at the tail of gas slug occur more violently. Fig. 6 presents high-speed camera images of two typical slug flows. Fig. 6(a) shows a slug flow with a relatively small gas superficial velocity. Gas slugs with obviously parabolic head are separated by continuous liquid phase which bridge the pipe and contain small gas bubbles. As shown in Fig. 6(b), the slug flow has a diameter almost equal to pipe diameter and move uniformly upward with relatively high gas superficial velocity, while the liquid film flows downward. Fig. 7 illustrates cross recurrence plots of slug flows. As shown in Fig. 7, there possesses apparent black rectangle structures, which shows an obvious recurrence phenomenon and indicates that gas and liquid slugs appear alternately when rise along the pipe. With the increase of gas superficial velocity, the length of gas slug increases, corresponds to larger outlines of black rectangle in Fig. 7(b). As for churn flow, it usually appears in conditions with large mixture velocities. The distinguishing feature of churn flow is an oscillatory up and down motion of the liquid slug as well as the liquid film on the pipe wall [38]. On the other hand, it is characterized by large spiraling, transient, vortex-like structures which move throughout the pipe. These vortices contain large, highly distorted bubbles following small bubbles in their wake [10]. High-speed camera images of two typical churn flows are shown in Fig. 8. Large deformed bubbles alternate with liquid slugs while the continuity of water phase between successive deformed bubbles is frequently destroyed by gas phase. Fig. 8(a) shows that large gas bubbles are distorted and flow upward along the pipe center, which is similar to the developing slug flow [39]. As shown in Fig. 8(b), large deformed bubble at center position is spiraling while it rises. The center position of deformed bubbles in 1, 2, and 3 is offset to right side of the pipe, and the deformed bubbles in 4 and 5 rise along the pipe center. But the center position of deformed bubbles in 6–8 is offset to the left side. Among them, deformed bubbles in 4–6 are twisted and broken during the flow. Cross recurrence plots of typical churn flows are shown in Fig. 9. The texture structure is composed of lines instead of rectangle structure, implying that compared with slug flow, churn flow has internal certainty without periodicity. As mixture velocity increases, large gas structures are gradually broken, corresponding to the shorter line structure in plots. Conclusively, due to obvious difference between slug and churn flow structures, the analysis of cross recurrence plot can be effectively used to identify flow patterns and reveal the differences of flow structures in gas-water flows.
s = 20mm
s = 30mm Fig. 5. Current density distribution with different distances of upstream and downstream electrodes.
3. Identification of slug and churn flows It is difficult to identify slug and churn flows by high speed photography method [30], especially for slug and churn flows in small pipe. Therefore, the responses of arc-shape conductance sensor [31] are used to identify the flow patterns. In view of more concentrated electric field due to focusing effect of guard electrodes at both sides, its ability to capture the dispersed phase of two-phase flow is stronger and the gas holdup measurement has good spatial and temporal resolution characteristics. In the present study, we use the cross recurrence plot algorithm for flow pattern identification which can achieve satisfactory results [32]. Eckman et al. [33] proposed recurrence plot algorithm that visualizes the recurrence characteristic to reveal the inside structure and further present similarity and predictability of time series. This method could be used to identify different two-phase flow patterns [34,35]. The basic principles are as follows: Given an original time series {x1, x2 , x3 , …x n} , according to the embedding theory of Takens [36], we set the embedding dimension m and delay time τ. After phase space reconstruction, the time series is:
→ Xi = {x i , x i + τ , …, x i + (m − 1) τ }, (i = 1, 2, …, N )
(7)
where N = n − (m − 1) τ . In the new time series, define the European norm as the distance between any two elements:
→ → dij = ∥Xi − Xj ∥
(8)
The threshold is ε = α·std (x i ) , where std (x i ) refers to the standard deviation of reconstructed time series and α is an empirical coefficient. Afterward, the recurrence matrix is established as Rij = Heaviside (ε − dij ) , and the Heaviside function is formulated as:
Heaviside (x ) =
{10
x⩾0 x<0
(10)
(9)
The threshold ε defines a sphere with xi as its center and ε as its radius. If xj locates in this sphere, this state is considered to be similar to xi. In this case, Rij = 1 and a point is plotted at (i,j) in a coordinate plane whose horizontal axis and vertical axis both represent the total length of time series. By this means, the recurrence plot of the reconstructed phase space can be acquired. On that basis, a cross recurrence plot [37] is raised to better reveal the similarity of two series, and the more similar two series are, the more recursive the characteristic is. By introducing the second time 19
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Q.Y. Yang, et al.
(a) Usg =0.1104 m/s Usw=0.0368m/s
(b) Usg =0.5888 m/s Usw=0.0368m/s Fig. 6. High-speed camera images of two typical slug flows.
4. Measurement characteristics of slug and churn flows
indicates that small bubbles in continuous water phase are in contact with probe irregularly. Compared Fig. 10(a) with Fig. 10(b), we can see that high level duration becomes longer with increasing Usg. This is because bubbles are more concentrated at the center region of pipe, which leads to less bubbles around the pipe wall. For churn flows in Fig. 11, slugs are decomposed into large deformed bubbles by enhancing turbulent energy, and they are followed by liquid slugs full of bubbles as shown in positions 2 to 6 in center region. It is worth noting that high level duration in position 3 and 5 are the longest, which is verified in Fig. 8(b), indicating that big deformed bubbles move away
4.1. Optical signal at seven measurement positions in radial direction Fluctuation signals of optical probe at seven different positions for typical slug and churn flows are shown in Figs. 10 and 11. For slug flows in Fig. 10, large bubbles cannot be crushed by low turbulence energy and they coalesce to gas slugs with tails full of small bubbles as shown in positions 2 to 6. But for positions 1 and 7 which are close to pipe wall, we can see that levels jump with high frequency, which
(a) Usg= 0.1104m/s Usw= 0.0368 m/s
(b) Usg= 0.5888 m/s Usw= 0.0368 m/s
Fig. 7. Cross recurrence plots of typical slug flows. 20
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(a) Usg =0.2944m/s Usw=0.2944m/s
1
2
3
7 6 4 5 (b) Usg =0.2944m/s Usw=0.8096m/s
8
9
Fig. 8. High-speed camera images of two typical churn flows.
from pipe center while they rise. In this paper, self-adjusting double-threshold algorithm [40] is adopted to transform optical signals to binary rectangular wave signals under reasonable threshold [41–44] and acquire the gas holdup. Results are displayed in Figs. 12 and 13, which represents the gas holdup distribution at seven radial positions in slug and churn flows with different Usg and Usw.
As is shown in Fig. 12, local time average of void fraction in axial direction at pipe wall is always much lower than that at the pipe center as falling liquid film exist near the pipe wall and local time average of void fraction decreases at every position with the increase of Usw. When Usg is relatively low in Fig. 12(a), the profile appears in parabola shape, which is consistent with the structure in Fig. 6(a) acquired by high speed camera. When Usg increases to 0.5888 m/s in Fig. 12(b), the
(a) Usg= 0.2944 m/s Usw= 0.2944 m/s
(b) Usg= 0.2944 m/s Usw= 0.8096 m/s
Fig. 9. Cross recurrence plots of typical churn flows. 21
Experimental Thermal and Fluid Science 107 (2019) 16–28
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Usg=0.1104m/s,Usw=0.0368m/s
(a)
10
Position 1
5
Position 1
5
0 10
0 10
Position 2
0 10
Position 3
5 0 10
Position 4
5 0 10
Position 5
5 0 10
Position 6
5
Position 2
5
Optical probe signals (V)
5
Optical probe signals(V)
Usg=0.5888m/s,Usw=0.0368m/s
(b)
10
0 10
0 10
Position 3
5 0 10
Position 4
5 0 10
Position 5
5 0 10
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5
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4
Position 7
5
0
0
5
0
Time(s)
1
2
3
4
5
Time(s)
(a)
(b)
Fig. 10. Optical probe signals at seven radial positions of two typical slug flows.
profile fluctuates smoothly in center region of pipe, which correspond to the gas slug structure full of whole pipe without parabola tip in Fig. 6(b). Fig. 13 shows the distribution of local time average of void fraction in axial direction at seven radial measurement positions under two typical churn flow conditions. As shown in this figure, for the churn flow, the local time average of void fraction in axial direction at the pipe wall is significantly lower than that at the pipe center, and the concentration profiles at the middle five positions distribute in three trends: (a) parabolic trend, that is, the highest value occures at the pipe center and decrease gradually on both sides; (b) the value at the center is relatively lower and it increases and then decrease; (c) the value at the center is lowest and it increases to both sides. As churn flow is very chaotic and disordered, it has a asymmetric profile under a certain flow condition. This reflects that the complex flow structure of churn flow and the concentration profile does not have a good regularity, which is consistent with the complex structure captured by high-speed camera in Fig. 8. Moreover, local time average of void fraction in axial direction do not always reaches its peak in pipe center, which may be caused by the spiral rise of deformed bubbles. Local time average of void fraction in axial direction decreases with Usw increasing, which is similar to slug flow.
Fig. 14 shows the profile of local time average of void fraction at 5 middle measurement positions in different time periods for slug flows, and each period is 5 s. The maximum gas holdup value is marked by red rectangular. It can be seen that the profile of local time average of void fraction in axial direction in slug flow is relatively stable during the fluid flow. Fig. 15 shows the profiles of churn flows. It can see that the profiles of local time average of void fraction in each periods are different, which indicates that large deformed bubbles of churn flow are irregular and they unevenly distributes in the water phase.
4.2. Local gas chord length measurement in radial direction Combined with optical probe signals and local velocity measured by the upstream and downstream conductance sensors, the distribution of gas chord lengths in seven radial positions could be obtained. The upstream and downstream signals of slug and churn flows at seven radial positions and their cross-correlation functions are shown in Figs. 16 and 17. Fig. 16(a) represents the fluctuating signals of upstream and downstream conductance sensors at different measurement positions in slug flow. “Position nU, Position nD” represent the upstream and downstream signals at position n, respectively. The output is high when
Usg=0.2944m/s, Usw=0.2944m/s
(a)
10
Position 1
5
Position 1
5
0 10
0 10
Position 2
0 10
Position 3
5 0 10
Position 4
5 0 10
Position 5
5 0 10
Position 6
5
Position 2
5
Optical probe signals(V)
5
Optical probe signals(V)
Usg=0.2944m/s, Usw=0.8096m/s
(b)
10
0 10
Position 3
5 0 10
Position 4
5 0 10
Position 5
5 0 10
Position 6
5 0 10
0 10
Position 7
5
Position 7
5 0
0 0
1
2
3
4
0
5
Time(s)
(a)
1
2
Time(s)
(b)
Fig. 11. Optical probe signals at seven radial positions of two typical churn flows. 22
3
4
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Experimental Thermal and Fluid Science 107 (2019) 16–28
Q.Y. Yang, et al.
(a) 70
60
60
50
50
40
40
(b)
(%)
(%)
70
30
30
Usg=0.1104m/s, Usw=0.0368m/s
20
Usg=0.5888m/s, Usw=0.0368m/s
20
Usg=0.5888m/s, Usw=0.0736m/s
Usg=0.1104m/s, Usw=0.0736m/s Usg=0.1104m/s, Usw=0.1472m/s
10
Usg=0.5888m/s, Usw=0.1472m/s
10
0
0
1
2
3
4
5
6
7
1
2
3
4
5
6
7
Radial measurement position
Radial measurement position
Fig. 12. Distribution of local time average of void fraction in axial direction at seven radial positions in slug flows.
gas slugs flow through measurement area. Gas slug and liquid slug alternately rise in slug flow, and the upstream and downstream conductance signals at seven measurement positions exhibit a good correlation. The cross-correlation function corresponding to Fig. 16(a) is shown in Fig. 16(b). The transit time τ0 could be obtained precisely because of the obvious cross-correlation peaks at seven measurement positions. For churn flow, signals of upstream and downstream conductance sensors at seven measurement positions and their cross-correlation function are shown in Fig. 17. Although there are small gas structures passing through two locations near the pipe wall, the upstream and downstream conductance signals still have good correlation at all sampling time. It can be seen from Fig. 17(b) that the correlation peak is obvious, so the transit time calculation is accurate. Local average gas velocity can be calculated based on correlation signals [45–48]. The upstream conductance signal and the downstream conductance signal are x(t) and y(t), respectively, and the delay time is τo . The calculation formula of cross-correlation function is as follows [49]:
Rxy (τ ) = lim
T →∞
1 T
∫0
T
x (t ) y (t + τ ) dt
obtained:
Fig. 18(a) and (b) represent the profiles of local average gas velocity around the measurement position Uccj (j = 1,2,3,…,7) with increasing water superficial velocity Usw and fixed gas superficial velocities Usg in slug flows. It can be seen that the gas velocity increases with the increase of water superficial velocity. Under the same conditions, the gas velocity distribution presents parabolic shape. The velocities at five middle positions are higher, and the velocities on both sides are lower because of the existence of liquid film near pipe wall. Fig. 19(a) and (b) represent the typical profiles of local gas velocity with increasing water superficial velocity Usw and two constant gas superficial velocities Usg in churn flows. The profiles of local gas velocity have no good regularity, similar to the profiles of local time average of void fraction in axial direction in churn flow. Large deformed bubbles flow away from pipe center, therefore the local gas velocity in the center of pipe is not the maximum. On the other hand, the oscillation and fluctuation of liquid film in churn flow may be the reason of the asymmetry of local velocity near the pipe wall. Optical probe signals are transformed into binary square wave signals using self-adjusting double-threshold algorithm, from which the duration of high level corresponds to the time of probe piercing gas bubble could be obtained. ti (i = 1,2,3,…,n) represents the time that probe pierces gas bubble. Based on the acquired seven radial local gas velocity Uccj (j = 1,2,3,…,7), the chord length of gas dij is:
(11)
where Rxy(τ) is the cross-correlation function of x(t) and y(t). The time τo corresponding to the maximum value of Rxy(τ) is the transit time. It has known that the spacing s between upstream and downstream conductance sensors is 30 mm, and the average gas velocity Ucc can be
(a)
70
60
60
50
50
(%)
(%)
70
40 30
(b)
40 30
Usg=0.2944m/s, Usw=0.2944m/s Usg=0.2944m/s, Usw=0.5888m/s
20
(12)
Ucc = s / τ0
Usg=0.4784m/s, Usw=0.7360m/s Usg=0.4784m/s, Usw=0.8096m/s
20
Usg=0.2944m/s, Usw=0.8096m/s
Usg=0.4784m/s, Usw=0.8832m/s
10
10 1
2
3
4
5
6
1
7
2
3
4
5
6
Radial measurement position
Radial measurement position
Fig. 13. Distribution of local time average of void fraction in axial direction at seven radial positions in churn flows. 23
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65
54 45
60
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36
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(%)
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54
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60
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36
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60
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36
45
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60
36
45
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60
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54
(%)
Usg=0.5888m/s, Usw=0.0368m/s
(b)
Usg=0.1104m/s, Usw=0.0368m/s
(a)
1-6s
55
27
50
1
2
3
4
5
6
1
7
2
3
4
5
6
7
Radial measurement position
Radial measurement position
Fig. 14. Local time average of void fraction in axial direction distribution of typical slug flows in different time periods.
dij = Uccj ·ti
alternates with short chord lengths corresponding to bubbles distributing in liquid slug, which exhibits a quasi-periodic featured in slug flow. Fig. 20(b) exhibits bubble chord lengths in liquid slugs and liquid film. In terms of quantity, the number of bubbles in liquid film is much less than that in liquid slug, and the largest value of bubble number is not in pipe center. The bubble size and fluctuation amplitude of chord
(13)
Fig. 20(a) represents the series of gas chord lengths in slug flow at seven radial positions at same sampling time. The chord length range at position 1 and position 7 is significantly smaller than that at the middle five positions, which indicates that the liquid film contains bubbles. In middle five positions, large chord length corresponding to gas slug
Usg=0.2944m/s, Usw=0.2944m/s
(a)
Usg=0.2944m/s, Usw=0.8096m/s
(b)
60
50
55
25-30s
25-30s
45
50 40
60
50
55
19-24s
19-24s
45
50 40 50
55
13-18s
(%)
(%)
60
13-18s
45
50 40
60
50
55
7-12s
7-12s
45
50 40
60
50
55
0-6s
1-6s
45
50 40
1
2
3
4
5
6
1
7
Radial measurement position
2
3
4
5
6
Radial measurement position
Fig. 15. Local time average of void fraction in axial direction distribution of typical churn flows in different time periods. 24
7
Experimental Thermal and Fluid Science 107 (2019) 16–28
Q.Y. Yang, et al.
Usg=0.5888m/s, Usw=0.0368m/s 300
Position 1D
0 3000 1500 0 -1500 3000 0 -3000 600 0 -600 4000 0 -4000 2000
Position 2U Position 2D
4 2 3
Position 3U Position 3D
4 2 3 4 3 2 3
Position 4U Position 4D Position 5U Position 5D
4 2 3 4 3 4
Position 6U Position 6D Position 7U Position 7D
3 0.0
0.5
1.0
1.5
2.0
2.5
Times (s)
3.0
3.5
4.0
4.5
Usg=0.5888m/s, Usw=0.0368m/s
(b) Position 1U
Rxy( )
Upstream and downstream conductance probe signals (V)
(a) 4 3 4 3 4 3 2 3
=0.0393s
Position 1
=0.0361s
Position 2
=0.0342s
Position 3
=0.0334s
Position 4
=0.0348s
Position 5 =0.0361s
Position 6
0 -2000 400
=0.0380s
Position 7
0 -400
0.0
5.0
0.5
1.0
1.5
Time(s)
2.0
Usg=0.2944m/s, Usw=0.8096m/s
(a) 4 3 4 3
Position 2U Position 2D
2 4 2 3
Position 3U Position 3D Position 4U
4 2 4 2 3 4
Position 4D Position 5U Position 5D
2 3
Position 6U Position 6D
3 2 3
Position 7U Position 7D
3
0.0
600 0
=0.0357s
500 0 -500 4000 0 -4000 300
=0.0315s
Position 1D
3 4
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Usg=0.2944m/s, Usw=0.8096m/s
(b) Position 1U
Rxy( )
Upstream and downstream conductance probe signals (V)
Fig. 16. Upstream and downstream conductance signals of slug flow and the corresponding cross-correlation function.
0 4000 2000 0 -2000 3000 0 -3000 3000 0
Position 1 Position 2
=0.0315s
Position 3
=0.0336s
Position 4
=0.0339s
Position 5
=0.0308s
Position 6
=0.0336s
Position 7
0.0
5.0
0.5
1.0
1.5
2.0
Time(s)
Time (s)
Fig. 17. Upstream and downstream conductance signals of churn flow and the corresponding cross-correlation function. 1.2
(a)
2.0
Usg=0.1104m/s, Usw=0.0368m/s
Usg=0.5888m/s, Usw=0.0368m/s
(b)
Usg=0.5888m/s, Usw=0.0736m/s
Usg=0.1104m/s, Usw=0.0736m/s
1.0
Usg=0.5888m/s, Usw=0.1472m/s
Usg=0.1104m/s, Usw=0.1472m/s 1.6
Vi (m/s)
Vi (m/s)
0.8
0.6
1.2 0.4
0.8
0.2 1
2
3
4
5
6
7
1
Radial measurement position
2
3
4
5
6
7
Radial measurement position
Fig. 18. Distribution of local gas velocity at seven radial positions in slug flows.
marked by rectangular is calculated. The chord length at position 1 and 7 is significantly lower than the chord length at five middle positions, which indicates that liquid film of churn flow at the pipe wall contains small bubbles. The chord length range of gas phase at five middle positions are large and distribute irregularly, which corresponds to the randomness and inconsistency of large gas structures in churn flows. Besides, maximum mean value of large deformed bubble chord length is not located at center of pipe, which can be attributed to the irregular movement and deformation of gas structures.
length in pipe center are the largest, which are reflected by mean value and standard deviation of bubble chord length series. Large difference of average bubble chord length in pipe center indicates that bubbles with various sizes are measured in this position. The distribution of bubble chord length in liquid film in slug flow is uniformly and the bubble chord length are mainly 2 mm or less. The series of gas chord lengths in churn flow at seven measurement positions in same sampling time are shown in Fig. 21(a), and the average chord length of large deformed bubbles in five middle positions 25
Experimental Thermal and Fluid Science 107 (2019) 16–28
Q.Y. Yang, et al.
2.0
(a)
(b)
Usg=0.2944m/s, Usw=0.2944m/s
Usg=0.4784m/s, Usw=0.7360m/s
2.0
Usg=0.2944m/s, Usw=0.5888m/s
Usg=0.4784m/s, Usw=0.8096m/s Usg=0.4784m/s, Usw=0.8832m/s
Usg=0.2944m/s, Usw=0.8096m/s 1.5
Vi (m/s)
Vi (m/s)
1.6
1.0
1.2
0.8 0.5 1
2
3
4
5
6
7
1
2
3
4
5
6
7
Radial measurement position
Radial measurement position
Fig. 19. Distribution of local gas velocity at seven radial positions in churn flows.
(a)
12
mean value 1.90mm
Position 1 0
0 0
50
100
150
200
mean value = 377mm
0
250
12
0 100
200
300
400
500
mean value = 381mm
600
Bubble Chord Length (mm)
Gas Chord Length (mm)
0 0
Position 3
100
200
300
400
500
mean value = 392mm
600
Position 4
250 0 0 500
100
200
300
400
mean value = 384mm
500
Position 5
250 0 0 500
200
300
400
500
mean value = 376mm
600
150
200
1.49
100
Position 6
200
250
Position 2
300
mean value 2.61mm
1.79
0 0 100 12 mean value 3.26mm
2.09
400
500
Position 3
6
200
300
400
500
Position 4
6 0
0
12
100
mean value 2.69mm
200
300
400
1.58
Position 5
6
0
12
100
mean value 2.30mm
200
300
400
1.65
Position 6
6 0 100
200
300
400
500
0
600
12
Position 7
100
mean value 2.12mm
200
300
400
1.16
500
Position 7
6
250 0 0
0
12
0 100
250 0 0 500
100
6
250
500
50
mean value 2.31mm
Position 2
250 0 0 500
Position 1
1.17
6
250
500
Usg=0.5888m/s, Usw=0.0368 m/s
(b)
Usg=0.5888m/s, Usw=0.0368 m/s
500
0 50
100
150
200
0
250
50
100
150
200
250
Bubble Series
Bubble Series
Fig. 20. Distribution of gas chords at seven radial positions in slug flow.
5. Conclusions
Fig. 21(b) shows the series of bubble chord lengths at seven radial positions without large gas structures. The thicker liquid film [50] of churn flow results in a larger range of bubble chord length compared with slug flow. Position 1 and 7 occasionally have large chord that appear randomly, which indicates that optical fiber pierces into large gas structures at these two positions. In terms of quantity, the numbers of bubble chord lengths at position 2 and 6 are large, which may be caused by the interaction between large gas structures and liquid film.
We propose a novel plug-in optical probe and conductance sensors by considering high precision of optical probe and great long-range correlation of conductance sensor in this paper. The vertical upward experiment of gas-liquid two-phase flow is carried out to investigate the local time average of void fraction in axial direction, cross-correlation velocity and instantaneous bubble chord distribution in slug and churn flows. The conclusions can be summarized as follows: It is typical phenomenon in churn flows that amount of large spiraling, distorted, deformed bubbles flow in continuous water. In some 26
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Usg=0.2944m/s, Usw=0.8096 m/s
(a) 120
Usg=0.2944m/s, U w=0.8096 m/s
(b)
Position 1
20
Position 1
mean value = 2.56mm =2.80
60
120
100
200
300
400
mean value = 96.7mm
Position 2
60 0 0
Gas Chord Length (mm)
120
200
400
600
800
mean value = 94.4mm
Position 3
60 0 0 120
200
400
600
800
mean value = 86.4mm
Position 4
60 0 0 120
200
400
600
800
mean value = 92.4mm
1000
Position 5
60 0 0 120
200
400
600
800
mean value = 86.3mm
Position 6
60 0 0 120
200
400
600
800
Position 7
0 0 20
100
200
300
400
mean value = 3.13mm =2.56
Position 2
10 0 0 20
200
400
600
800
mean value = 2.77mm =2.67
Position 3
10 0 0 20
200
400
600
mean value = 2.95mm =3.08
800
Position 4
10 0 0 20
200
400
600
800
mean value = 2.68mm =2.53
Position 5
10 0 0 20
200
400
600
800
mean value = 2.89mm =2.83
Position 6
10 0 0 20
60 0 0
Bubble Chord Length without large deformed bubbles (mm)
10
0 0
200
400
600
800
mean value = 3.17mm =1.90
Position 7
10
100
200
300
0 0
400
100
200
300
400
Bubble Series
Bubble Series
Fig. 21. Distribution of gas chords at seven radial positions in churn flow.
churn conditions, some large gas bubbles flow along the pipe center just as the behavior of gas slugs in developing slug flow. In slug flow, gas bubble chord length in liquid film are in similar size. As for the distribution of bubble chord length in slug flow at seven radial positions, the variation range of chord length is largest at the pipe center and smallest at positions near the pipe wall. In comparison with slug flow, the variation ranges of chord length at seven different radial positions of churn flow are large, which means that the bubble shape is diverse.
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Declaration of Competing Interest The authors declared that they have no conflicts of interest to this work. Acknowledgments This study was supported by National Natural Science Foundation of China (Grant Nos. 51527805, 11572220). References [1] R. Emerson, G.J. Leonardo, Characterization of slug flows in horizontal piping by signal analysis from a capacitive probe, Flow Meas. Instrum. 21 (2010) 347–355. [2] G.F. Hewitt, D.N. Roberts, Studies of two-phase patterns by simultaneous X-ray and flash photography, Atomic Energy Res. Establishm. (1969). [3] D. Lucas, E. Krepper, H.M. Prasser, Development of co-current air-water flow in vertical pipe, Int. J. Multiph. Flow 31 (2005) 1304–1328. [4] D. Lucas, M. Beyer, L. Szalinski, P. Schutz, A new database on the evolution of airwater flows along a large vertical pipe, Int. J. Therm. Sci. 49 (2010) 664–674. [5] V.H. Perez, B.J. Azzopardi, R. Kaji, M.J. da Silva, M. Beyer, U. Hampel, Wisp-like structures in vertical gas-liquid pipe flow revealed by wire mesh sensor studies, Int. J. Multiph. Flow 36 (2010) 908–915.
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28
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Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Experimental study of slug and churn flows in a vertical pipe using plug-in optical fiber and conductance sensors
T
⁎
Q.Y. Yang, N.D. Jin , L.S. Zhai, D.Y. Wang, F. Wang School of Electrical and Information Engineering, Tianjin University, Tianjin 300072, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Gas-liquid two-phase flow Slug flow Churn flow Plug-in optical fiber and conductance sensors
It is of great significance to explore the flow structures in gas-liquid slug and churn flows. Aiming at this purpose, a novel plug-in optical probe combined with conductance sensors are designed. Furthermore, we perform experimental study of gas-liquid flows in vertical upward pipe with 20 mm inner diameter. Simultaneously, the local time average of void fraction in axial direction, cross-correlation velocity and instantaneous bubble chord distribution in slug and churn flows at seven radial positions are obtained. The research results show that big deformed bubbles in churn flow spiral up in test pipe, but sometimes they rise along pipe center just as gas slugs in slug flow. Besides, bubble chord length distributions in liquid slug of slug and churn flows are analyzed in this study.
1. Introduction Slug and churn flows in gas-liquid two-phase flow widely exist in petrochemical and nuclear industries. In particular, the churn flow in vertical pipes is relatively chaotic. Unlike slug flow, gas slugs in churn flow are relatively unstable, and present large and elongated bubble shape. Churn flow is an intermediate flow condition between slug flow and mist flow, and occurs at relatively high gas velocity. As the gas velocity increases, it changes into annular flow. Therefore, exploring the flow structures in gas-liquid slug and churn flows is of great significance on sensor optimization, analytical model research and local parameters measurement under these two flow patterns. In term of gas-liquid flow patterns research, high speed photography a direct and effective method. However, complex flow structures located in pipe center could not be clearly captured because they are sheltered by liquid film, especially in slug and churn flows. Emerson et al. [1] analyzed capacitance signals to calculate the film thickness in slug flows under different conditions by power spectrum density and probability density function. Hewitt and Roberts [2] obtained the structures of churn flow with X-ray, and discovered complex interface structure and diverse dispersed phase structures. Wire-mesh sensor was used for the study of interaction between bubbles and wisp-like structures in vertical gas-liquid churn flow [3–5]. Wang et al. [6] found that liquid film at the pipe wall violently fluctuate and they also experimentally studied the droplet entrainment mechanism in churn flow. As for analytical models research on gas-liquid slug and churn flows,
⁎
Femandes et al. [7] discovered alternately rising gas and liquid slugs in slug flows and developed a hydrodynamic model for this flow pattern. Van Hout et al. [8] divided the liquid slug of gas-liquid slug flow into three distinct regions: the wake region, the intermediate region and the developed region. Kaya et al. [9] predicted pressure drop and liquid holdup of churn flows through two different models, and concluded that churn flow is a chaotic flow composed of Taylor bubbles and twisted liquid slugs. Montoya et al. [10] expressed that churn flow is characterized by large spiraling, transient, vortex-like structures, and large deformed gas bubbles are followed by small bubbles. Bubbles size and bubbles interaction in churn flow are also studied by analytical models [11–14]. Existing researches about gas-liquid two-phase flow models mostly focused on bubble flow [15–17]. Gas-liquid churn flow is a complex flow pattern composed of small bubbles and large deformed bubbles simultaneously. The deformation in flow structure makes it difficult to establish a theoretical model. Further understanding of local flow structure in gas-liquid flows is an important way to reveal its temporal and spatial evolution characteristics [18–21]. For the study of gas structure and local flow parameters, micro-sensors have advantages over traditional macro-sensors. Experimental studies [22–23] of gasliquid two-phase flow using conductance probes shown that gas holdup of gas slug tail is higher near pipe wall. The large bubbles mainly distribute in the center of pipe, while small ones distribute near the pipe wall in slug flows. However, it is limited for electrical probes to perform long-term accurate measurement because of polarization effect. In
Corresponding author. E-mail address: [email protected] (N.D. Jin).
https://doi.org/10.1016/j.expthermflusci.2019.05.005 Received 11 January 2019; Received in revised form 25 April 2019; Accepted 12 May 2019 Available online 14 May 2019 0894-1777/ © 2019 Elsevier Inc. All rights reserved.
Experimental Thermal and Fluid Science 107 (2019) 16–28
Q.Y. Yang, et al.
addition, the large tip size of electric probe is liable to cause error in small gas bubbles measurement. Therefore, the optical probe with small size, corrosion resistance, fast response and high precision is widely used in the measurement of gas-liquid two-phase flow parameters. Abuaf et al. [24] investigated the electrical and hydraulic responses of tip structure of optical probes to gas-liquid two-phase flow, and measured the local time average of void fraction in axial direction and gas superficial velocity. Cartellier et al. [25] compared effects of various optical probes based on measuring gas holdup and velocity. Fordham et al. [26] used dual optical probes to measure local holdup distribution characteristics of oil-water, gas-water and oil-gas-water three-phase flow, respectively, which confirmed the validity of optical probes. Some other researchers maximized the advantages of optical probe and hotfilm probe, and analyzed the influence of water superficial velocity and water holdup on the radial flow parameter distribution [27]. Thus, a local gas characteristic sensor system consisting of plug-in optical probe and conductance sensors is proposed by considering high precision of optical probe and great long-range correlation of conductance sensor. Furthermore, dynamic experiment of gas-liquid flows was carried out to measure local time average of void fraction in axial direction, cross-correlation velocity and gas chord length distribution in small pipe because the understanding of gas-liquid flows in small pipe is significant [28].
Fig. 2. Schematic diagram of plug-in movable optical fiber and conductance sensors.
A movable plug-in optical probe and conductance sensors is used to measure local flow characteristics of vertical upward gas-water flows. As presented in Fig. 2, the optical fiber probe, with 1 mm length and 35° cone angle, is made by multimode fiber [29] with 62.5 μm inner diameter and fixed in a holder. When optical fiber is immersed in gas and water phase, the reflected light intensity is different. The high voltage corresponds to gas phase while low voltage corresponds to water phase. The upstream and downstream cross-correlative conductance rings (EA, MA, EB, MB) are flush mounted in the outer wall of the holder, in which EA, EB represent the upstream and downstream excitation electrodes, and MA, MB represent the upstream and downstream measuring electrodes, respectively. Finally, the total sensor is inserted into test pipe as shown in Fig. 1. The sensor model was built based on the cylindrical coordinate system as shown in Fig. 3, and the electrode structure was optimized using finite element method. In order to get a homogenous and high sensitive detection field, the height h of exciting electrode and measuring electrode, the distance L between exciting electrode and measuring electrode, and the spacing s between two pairs of conducting rings are optimized. The electric field distribution of sensor can be described by Laplace equation with boundary conditions:
2. Experimental facility The experiment was carried out in the multiphase flow loop facility in Tianjin University. As shown in Fig. 1, the facility consists of the plug-in optical probe and conductance sensors, a high speed camera, an arc-shape conductance sensor and a vertical test pipe with 20 mm inner diameter. The arc-shape conductance sensor is 1834 mm away from the entrance. The total height of the movable plug-in optical probe and conductance sensors is 230 mm. To clearly observe the characteristics of different flow patterns, a high-speed camera is mounted near the test pipe. Seven measurement positions in the radial direction of the pipe are shown in Fig. 1, which correspond to the X coordinates: −8mm, −6mm, −3mm, 0 mm, 3 mm, 6 mm, and 8 mm.
∇2 u =
1 ∂ ⎛ ∂u ⎞ 1 ∂ 2u ∂ 2u r + 2 + 2 =0 r ∂r ⎝ ∂r ⎠ r ∂φ ∂z
(1)
The boundary conditions of the sensor electric field distribution are as follows:
φ = 2π , z = [s /2, s /2 + h], r = d/2 ⎧u = 0 ⎪u = 0 φ = 2π , z = [s /2 + h + L, s /2 + 2h + L], r = d/2 ⎪ ∂u/ ∂r = I / Se φ = 2π , z = [−s /2, −s /2 − h], r = d/2 ⎨ ⎪ ∂u/ ∂r = I / Se φ = 2π , z = [−s /2 − h − L, −s /2 − 2h − L], r = d/2 ⎪ ∂u/ ∂z = 0 z = ± H /2 ⎩ (2) where u is the voltage, and r2 = x2 + y2. The diameter of insert is d, and H is the length of pipe. I is the exciting current and Se is the area of electrode surface. The calculation of the sensitivity of different positions in sensor detection field is performed based on the Cartesian coordinate system. An insulating sphere with 500 μm diameter is set in the electric field to simulate gas bubbles in gas-water flows. The output of conductance sensor could be obtained as U0 when the pipe is full of water. The intervention of sphere causes the output voltage U. The voltage variation ΔU caused by the sphere can be calculated as: ΔU = U-U0. Then the
Fig. 1. Schematic diagram of gas-water flows loop facility. 17
Experimental Thermal and Fluid Science 107 (2019) 16–28
Q.Y. Yang, et al.
Fig. 3. The simulation model of plug-in optical fiber and conductance sensors.
sensitivity of the sensor detection field can be defined as:
ΔU (x , y, z ) [ΔU (x , y, z )]max
S (x , y, z ) =
0.70
0.60
Savg
∑ Sj
Sder
∑ (S (x , y, z ) − Savg j=1
0.50
45
0.45
40 35
25 1
3
4
5
6
7
Fig. 4. Values of Savg and SVP in different intervals between exciting and measuring electrodes.
(5)
exciting electrode is stimulated by a +5 V excitation voltage and measuring electrode is connected to ground. With intention to obtain an optimal value of s, the following two conditions should be satisfied. Firstly, there should be no crosstalk between the electric fields of two pairs of electrodes. Secondly, upstream and downstream signals should have good correlation. As shown in Fig. 5, the crosstalk between two electric fields is gradually to zero until s increases to 30 mm. To ensure correlation between upstream and downstream signals, the optimal value of s is determined as 30 mm. The experimental conditions include two flow patterns, slug flow and churn flow. In the process of experiment, water superficial velocity Usw is set from 0.0368 m/s to 0.8832 m/s, and gas superficial velocity Usg is set from 0.0552 m/s to 0.5888 m/s. Firstly, the gas superficial velocity is fixed, and with the increase of Usg, the optical and electrical sensor responses at seven radial measuring positions of the pipe are obtained by moving the plug-in movable optical fiber and conductance sensors. When all the Usw are finished, the Usg is changed and the experiment procedure repeated. The fluctuating signals of sensors are collected by PXI-4472 synchronization card of National Instruments (NI) Company. The sampling frequency and sampling time are set as 2 kHz and 30 s.
1 2
⎤ )2 ⎥ ⎦
2
L / mm
where Sder represents the standard deviation of average sensitivity in pipe which can be defined as: M
50
30
Sder × 100% Savg
⎡1 =⎢ M ⎣
0.55
0.35
(4)
j=1
where Sj is the relative sensitivity of the sensor when the sphere is located at different positions in detection area, M is the total number of positions. The sensitivity variation parameter SVP can be formulated as:
SVP =
60 55
0.40
M
65
SVP / %
Savg
SVP
(3)
where ΔU (x, y, z) is the voltage variation induced by the sphere at position (x, y, z), [ΔU (x, y, z)] max is the maximum value of voltage variation. The sensitivity variation parameter SVP and the average sensitivity Savg are taken as the optimization indicators. Savg can be calculated with the following expression:
1 = M
Savg
0.65
(6)
It can be seen from the definition of Savg and SVP that highly sensitive sensor is positively correlated with Savg, while homogeneous detection field is negatively correlated with SVP. To investigate the characteristics of sensor detection field, we fix s and h to calculate Savg and SVP with different value of L. It can be seen from Fig. 4 that the value of Savg is the highest while SVP presents the lowest when L is 5 mm. This means that the detection field presents high sensitivity and homogeneity under this value of L. With the same method, we fix the electrode spacing L and the spacing between upstream and downstream electrodes s to achieve optimal value of h by calculating Savg and SVP. The simulation results show that the optimal value of h is 3 mm. For the purpose of obtaining the optimal value of s, we fix h and L, then the values of s are set as 10 mm, 20 mm and 30 mm. Fig. 5 Shows the current density distribution under three different values of s. The 18
Experimental Thermal and Fluid Science 107 (2019) 16–28
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series {y1 , y2 , y3 , …yn } and reconstructing the phase space → → Yj = {yj , yj + τ , …, yj + (m − 1) τ }, (j = 1, 2, …, N ) , then the distances between Xi → and Yj are calculated one by one. A cross recurrence matrix CRi,j is built and the formula of cross recurrence matrix is:
s = 10mm
→ → CRi, j = Θ(ε − ∥Xi − Yj ∥ )
In this paper, we employ this method to conductance sensor signals to analyze the flow structure differences in axial direction with parameters as: delay time τ = 2, embedding dimension m = 3, and empirical coefficient α = 0.25 [37]. By defining the upstream and downstream time series of arc-shape conductance sensor as Xa(t) and Yb(t), we can reconstruct a phase space from the time series Xa(t) and Yb(t), then the phase space trajectories Xa(i) and Yb(j) can be obtained. Afterwards, a cross recurrence plot algorithm is applied to investigate the recursive features of corresponding flow conditions. Slug flows with higher gas and lower water superficial velocities appears pseudo-periodic characteristics. The gas slug is almost full of pipe with liquid flows downward as liquid film near the wall. With the increase of gas velocity, the liquid slugs become more aerated [38]. The crush and coalescence of small bubbles at the tail of gas slug occur more violently. Fig. 6 presents high-speed camera images of two typical slug flows. Fig. 6(a) shows a slug flow with a relatively small gas superficial velocity. Gas slugs with obviously parabolic head are separated by continuous liquid phase which bridge the pipe and contain small gas bubbles. As shown in Fig. 6(b), the slug flow has a diameter almost equal to pipe diameter and move uniformly upward with relatively high gas superficial velocity, while the liquid film flows downward. Fig. 7 illustrates cross recurrence plots of slug flows. As shown in Fig. 7, there possesses apparent black rectangle structures, which shows an obvious recurrence phenomenon and indicates that gas and liquid slugs appear alternately when rise along the pipe. With the increase of gas superficial velocity, the length of gas slug increases, corresponds to larger outlines of black rectangle in Fig. 7(b). As for churn flow, it usually appears in conditions with large mixture velocities. The distinguishing feature of churn flow is an oscillatory up and down motion of the liquid slug as well as the liquid film on the pipe wall [38]. On the other hand, it is characterized by large spiraling, transient, vortex-like structures which move throughout the pipe. These vortices contain large, highly distorted bubbles following small bubbles in their wake [10]. High-speed camera images of two typical churn flows are shown in Fig. 8. Large deformed bubbles alternate with liquid slugs while the continuity of water phase between successive deformed bubbles is frequently destroyed by gas phase. Fig. 8(a) shows that large gas bubbles are distorted and flow upward along the pipe center, which is similar to the developing slug flow [39]. As shown in Fig. 8(b), large deformed bubble at center position is spiraling while it rises. The center position of deformed bubbles in 1, 2, and 3 is offset to right side of the pipe, and the deformed bubbles in 4 and 5 rise along the pipe center. But the center position of deformed bubbles in 6–8 is offset to the left side. Among them, deformed bubbles in 4–6 are twisted and broken during the flow. Cross recurrence plots of typical churn flows are shown in Fig. 9. The texture structure is composed of lines instead of rectangle structure, implying that compared with slug flow, churn flow has internal certainty without periodicity. As mixture velocity increases, large gas structures are gradually broken, corresponding to the shorter line structure in plots. Conclusively, due to obvious difference between slug and churn flow structures, the analysis of cross recurrence plot can be effectively used to identify flow patterns and reveal the differences of flow structures in gas-water flows.
s = 20mm
s = 30mm Fig. 5. Current density distribution with different distances of upstream and downstream electrodes.
3. Identification of slug and churn flows It is difficult to identify slug and churn flows by high speed photography method [30], especially for slug and churn flows in small pipe. Therefore, the responses of arc-shape conductance sensor [31] are used to identify the flow patterns. In view of more concentrated electric field due to focusing effect of guard electrodes at both sides, its ability to capture the dispersed phase of two-phase flow is stronger and the gas holdup measurement has good spatial and temporal resolution characteristics. In the present study, we use the cross recurrence plot algorithm for flow pattern identification which can achieve satisfactory results [32]. Eckman et al. [33] proposed recurrence plot algorithm that visualizes the recurrence characteristic to reveal the inside structure and further present similarity and predictability of time series. This method could be used to identify different two-phase flow patterns [34,35]. The basic principles are as follows: Given an original time series {x1, x2 , x3 , …x n} , according to the embedding theory of Takens [36], we set the embedding dimension m and delay time τ. After phase space reconstruction, the time series is:
→ Xi = {x i , x i + τ , …, x i + (m − 1) τ }, (i = 1, 2, …, N )
(7)
where N = n − (m − 1) τ . In the new time series, define the European norm as the distance between any two elements:
→ → dij = ∥Xi − Xj ∥
(8)
The threshold is ε = α·std (x i ) , where std (x i ) refers to the standard deviation of reconstructed time series and α is an empirical coefficient. Afterward, the recurrence matrix is established as Rij = Heaviside (ε − dij ) , and the Heaviside function is formulated as:
Heaviside (x ) =
{10
x⩾0 x<0
(10)
(9)
The threshold ε defines a sphere with xi as its center and ε as its radius. If xj locates in this sphere, this state is considered to be similar to xi. In this case, Rij = 1 and a point is plotted at (i,j) in a coordinate plane whose horizontal axis and vertical axis both represent the total length of time series. By this means, the recurrence plot of the reconstructed phase space can be acquired. On that basis, a cross recurrence plot [37] is raised to better reveal the similarity of two series, and the more similar two series are, the more recursive the characteristic is. By introducing the second time 19
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(a) Usg =0.1104 m/s Usw=0.0368m/s
(b) Usg =0.5888 m/s Usw=0.0368m/s Fig. 6. High-speed camera images of two typical slug flows.
4. Measurement characteristics of slug and churn flows
indicates that small bubbles in continuous water phase are in contact with probe irregularly. Compared Fig. 10(a) with Fig. 10(b), we can see that high level duration becomes longer with increasing Usg. This is because bubbles are more concentrated at the center region of pipe, which leads to less bubbles around the pipe wall. For churn flows in Fig. 11, slugs are decomposed into large deformed bubbles by enhancing turbulent energy, and they are followed by liquid slugs full of bubbles as shown in positions 2 to 6 in center region. It is worth noting that high level duration in position 3 and 5 are the longest, which is verified in Fig. 8(b), indicating that big deformed bubbles move away
4.1. Optical signal at seven measurement positions in radial direction Fluctuation signals of optical probe at seven different positions for typical slug and churn flows are shown in Figs. 10 and 11. For slug flows in Fig. 10, large bubbles cannot be crushed by low turbulence energy and they coalesce to gas slugs with tails full of small bubbles as shown in positions 2 to 6. But for positions 1 and 7 which are close to pipe wall, we can see that levels jump with high frequency, which
(a) Usg= 0.1104m/s Usw= 0.0368 m/s
(b) Usg= 0.5888 m/s Usw= 0.0368 m/s
Fig. 7. Cross recurrence plots of typical slug flows. 20
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(a) Usg =0.2944m/s Usw=0.2944m/s
1
2
3
7 6 4 5 (b) Usg =0.2944m/s Usw=0.8096m/s
8
9
Fig. 8. High-speed camera images of two typical churn flows.
from pipe center while they rise. In this paper, self-adjusting double-threshold algorithm [40] is adopted to transform optical signals to binary rectangular wave signals under reasonable threshold [41–44] and acquire the gas holdup. Results are displayed in Figs. 12 and 13, which represents the gas holdup distribution at seven radial positions in slug and churn flows with different Usg and Usw.
As is shown in Fig. 12, local time average of void fraction in axial direction at pipe wall is always much lower than that at the pipe center as falling liquid film exist near the pipe wall and local time average of void fraction decreases at every position with the increase of Usw. When Usg is relatively low in Fig. 12(a), the profile appears in parabola shape, which is consistent with the structure in Fig. 6(a) acquired by high speed camera. When Usg increases to 0.5888 m/s in Fig. 12(b), the
(a) Usg= 0.2944 m/s Usw= 0.2944 m/s
(b) Usg= 0.2944 m/s Usw= 0.8096 m/s
Fig. 9. Cross recurrence plots of typical churn flows. 21
Experimental Thermal and Fluid Science 107 (2019) 16–28
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Usg=0.1104m/s,Usw=0.0368m/s
(a)
10
Position 1
5
Position 1
5
0 10
0 10
Position 2
0 10
Position 3
5 0 10
Position 4
5 0 10
Position 5
5 0 10
Position 6
5
Position 2
5
Optical probe signals (V)
5
Optical probe signals(V)
Usg=0.5888m/s,Usw=0.0368m/s
(b)
10
0 10
0 10
Position 3
5 0 10
Position 4
5 0 10
Position 5
5 0 10
Position 6
5 0 10
Position 7
5
0
1
2
3
4
Position 7
5
0
0
5
0
Time(s)
1
2
3
4
5
Time(s)
(a)
(b)
Fig. 10. Optical probe signals at seven radial positions of two typical slug flows.
profile fluctuates smoothly in center region of pipe, which correspond to the gas slug structure full of whole pipe without parabola tip in Fig. 6(b). Fig. 13 shows the distribution of local time average of void fraction in axial direction at seven radial measurement positions under two typical churn flow conditions. As shown in this figure, for the churn flow, the local time average of void fraction in axial direction at the pipe wall is significantly lower than that at the pipe center, and the concentration profiles at the middle five positions distribute in three trends: (a) parabolic trend, that is, the highest value occures at the pipe center and decrease gradually on both sides; (b) the value at the center is relatively lower and it increases and then decrease; (c) the value at the center is lowest and it increases to both sides. As churn flow is very chaotic and disordered, it has a asymmetric profile under a certain flow condition. This reflects that the complex flow structure of churn flow and the concentration profile does not have a good regularity, which is consistent with the complex structure captured by high-speed camera in Fig. 8. Moreover, local time average of void fraction in axial direction do not always reaches its peak in pipe center, which may be caused by the spiral rise of deformed bubbles. Local time average of void fraction in axial direction decreases with Usw increasing, which is similar to slug flow.
Fig. 14 shows the profile of local time average of void fraction at 5 middle measurement positions in different time periods for slug flows, and each period is 5 s. The maximum gas holdup value is marked by red rectangular. It can be seen that the profile of local time average of void fraction in axial direction in slug flow is relatively stable during the fluid flow. Fig. 15 shows the profiles of churn flows. It can see that the profiles of local time average of void fraction in each periods are different, which indicates that large deformed bubbles of churn flow are irregular and they unevenly distributes in the water phase.
4.2. Local gas chord length measurement in radial direction Combined with optical probe signals and local velocity measured by the upstream and downstream conductance sensors, the distribution of gas chord lengths in seven radial positions could be obtained. The upstream and downstream signals of slug and churn flows at seven radial positions and their cross-correlation functions are shown in Figs. 16 and 17. Fig. 16(a) represents the fluctuating signals of upstream and downstream conductance sensors at different measurement positions in slug flow. “Position nU, Position nD” represent the upstream and downstream signals at position n, respectively. The output is high when
Usg=0.2944m/s, Usw=0.2944m/s
(a)
10
Position 1
5
Position 1
5
0 10
0 10
Position 2
0 10
Position 3
5 0 10
Position 4
5 0 10
Position 5
5 0 10
Position 6
5
Position 2
5
Optical probe signals(V)
5
Optical probe signals(V)
Usg=0.2944m/s, Usw=0.8096m/s
(b)
10
0 10
Position 3
5 0 10
Position 4
5 0 10
Position 5
5 0 10
Position 6
5 0 10
0 10
Position 7
5
Position 7
5 0
0 0
1
2
3
4
0
5
Time(s)
(a)
1
2
Time(s)
(b)
Fig. 11. Optical probe signals at seven radial positions of two typical churn flows. 22
3
4
5
Experimental Thermal and Fluid Science 107 (2019) 16–28
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(a) 70
60
60
50
50
40
40
(b)
(%)
(%)
70
30
30
Usg=0.1104m/s, Usw=0.0368m/s
20
Usg=0.5888m/s, Usw=0.0368m/s
20
Usg=0.5888m/s, Usw=0.0736m/s
Usg=0.1104m/s, Usw=0.0736m/s Usg=0.1104m/s, Usw=0.1472m/s
10
Usg=0.5888m/s, Usw=0.1472m/s
10
0
0
1
2
3
4
5
6
7
1
2
3
4
5
6
7
Radial measurement position
Radial measurement position
Fig. 12. Distribution of local time average of void fraction in axial direction at seven radial positions in slug flows.
gas slugs flow through measurement area. Gas slug and liquid slug alternately rise in slug flow, and the upstream and downstream conductance signals at seven measurement positions exhibit a good correlation. The cross-correlation function corresponding to Fig. 16(a) is shown in Fig. 16(b). The transit time τ0 could be obtained precisely because of the obvious cross-correlation peaks at seven measurement positions. For churn flow, signals of upstream and downstream conductance sensors at seven measurement positions and their cross-correlation function are shown in Fig. 17. Although there are small gas structures passing through two locations near the pipe wall, the upstream and downstream conductance signals still have good correlation at all sampling time. It can be seen from Fig. 17(b) that the correlation peak is obvious, so the transit time calculation is accurate. Local average gas velocity can be calculated based on correlation signals [45–48]. The upstream conductance signal and the downstream conductance signal are x(t) and y(t), respectively, and the delay time is τo . The calculation formula of cross-correlation function is as follows [49]:
Rxy (τ ) = lim
T →∞
1 T
∫0
T
x (t ) y (t + τ ) dt
obtained:
Fig. 18(a) and (b) represent the profiles of local average gas velocity around the measurement position Uccj (j = 1,2,3,…,7) with increasing water superficial velocity Usw and fixed gas superficial velocities Usg in slug flows. It can be seen that the gas velocity increases with the increase of water superficial velocity. Under the same conditions, the gas velocity distribution presents parabolic shape. The velocities at five middle positions are higher, and the velocities on both sides are lower because of the existence of liquid film near pipe wall. Fig. 19(a) and (b) represent the typical profiles of local gas velocity with increasing water superficial velocity Usw and two constant gas superficial velocities Usg in churn flows. The profiles of local gas velocity have no good regularity, similar to the profiles of local time average of void fraction in axial direction in churn flow. Large deformed bubbles flow away from pipe center, therefore the local gas velocity in the center of pipe is not the maximum. On the other hand, the oscillation and fluctuation of liquid film in churn flow may be the reason of the asymmetry of local velocity near the pipe wall. Optical probe signals are transformed into binary square wave signals using self-adjusting double-threshold algorithm, from which the duration of high level corresponds to the time of probe piercing gas bubble could be obtained. ti (i = 1,2,3,…,n) represents the time that probe pierces gas bubble. Based on the acquired seven radial local gas velocity Uccj (j = 1,2,3,…,7), the chord length of gas dij is:
(11)
where Rxy(τ) is the cross-correlation function of x(t) and y(t). The time τo corresponding to the maximum value of Rxy(τ) is the transit time. It has known that the spacing s between upstream and downstream conductance sensors is 30 mm, and the average gas velocity Ucc can be
(a)
70
60
60
50
50
(%)
(%)
70
40 30
(b)
40 30
Usg=0.2944m/s, Usw=0.2944m/s Usg=0.2944m/s, Usw=0.5888m/s
20
(12)
Ucc = s / τ0
Usg=0.4784m/s, Usw=0.7360m/s Usg=0.4784m/s, Usw=0.8096m/s
20
Usg=0.2944m/s, Usw=0.8096m/s
Usg=0.4784m/s, Usw=0.8832m/s
10
10 1
2
3
4
5
6
1
7
2
3
4
5
6
Radial measurement position
Radial measurement position
Fig. 13. Distribution of local time average of void fraction in axial direction at seven radial positions in churn flows. 23
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Experimental Thermal and Fluid Science 107 (2019) 16–28
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65
54 45
60
25-30s
36
55
27
50 65
54 45 36
55
27
50 65
13-18s
(%)
45
55
27
50 65
54
55
27
50 65
54
7-12s
60
1-6s
36
13-18s
60
7-12s
36
45
19-24s
60
36
45
25-30s
60
19-24s
54
(%)
Usg=0.5888m/s, Usw=0.0368m/s
(b)
Usg=0.1104m/s, Usw=0.0368m/s
(a)
1-6s
55
27
50
1
2
3
4
5
6
1
7
2
3
4
5
6
7
Radial measurement position
Radial measurement position
Fig. 14. Local time average of void fraction in axial direction distribution of typical slug flows in different time periods.
dij = Uccj ·ti
alternates with short chord lengths corresponding to bubbles distributing in liquid slug, which exhibits a quasi-periodic featured in slug flow. Fig. 20(b) exhibits bubble chord lengths in liquid slugs and liquid film. In terms of quantity, the number of bubbles in liquid film is much less than that in liquid slug, and the largest value of bubble number is not in pipe center. The bubble size and fluctuation amplitude of chord
(13)
Fig. 20(a) represents the series of gas chord lengths in slug flow at seven radial positions at same sampling time. The chord length range at position 1 and position 7 is significantly smaller than that at the middle five positions, which indicates that the liquid film contains bubbles. In middle five positions, large chord length corresponding to gas slug
Usg=0.2944m/s, Usw=0.2944m/s
(a)
Usg=0.2944m/s, Usw=0.8096m/s
(b)
60
50
55
25-30s
25-30s
45
50 40
60
50
55
19-24s
19-24s
45
50 40 50
55
13-18s
(%)
(%)
60
13-18s
45
50 40
60
50
55
7-12s
7-12s
45
50 40
60
50
55
0-6s
1-6s
45
50 40
1
2
3
4
5
6
1
7
Radial measurement position
2
3
4
5
6
Radial measurement position
Fig. 15. Local time average of void fraction in axial direction distribution of typical churn flows in different time periods. 24
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Experimental Thermal and Fluid Science 107 (2019) 16–28
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Usg=0.5888m/s, Usw=0.0368m/s 300
Position 1D
0 3000 1500 0 -1500 3000 0 -3000 600 0 -600 4000 0 -4000 2000
Position 2U Position 2D
4 2 3
Position 3U Position 3D
4 2 3 4 3 2 3
Position 4U Position 4D Position 5U Position 5D
4 2 3 4 3 4
Position 6U Position 6D Position 7U Position 7D
3 0.0
0.5
1.0
1.5
2.0
2.5
Times (s)
3.0
3.5
4.0
4.5
Usg=0.5888m/s, Usw=0.0368m/s
(b) Position 1U
Rxy( )
Upstream and downstream conductance probe signals (V)
(a) 4 3 4 3 4 3 2 3
=0.0393s
Position 1
=0.0361s
Position 2
=0.0342s
Position 3
=0.0334s
Position 4
=0.0348s
Position 5 =0.0361s
Position 6
0 -2000 400
=0.0380s
Position 7
0 -400
0.0
5.0
0.5
1.0
1.5
Time(s)
2.0
Usg=0.2944m/s, Usw=0.8096m/s
(a) 4 3 4 3
Position 2U Position 2D
2 4 2 3
Position 3U Position 3D Position 4U
4 2 4 2 3 4
Position 4D Position 5U Position 5D
2 3
Position 6U Position 6D
3 2 3
Position 7U Position 7D
3
0.0
600 0
=0.0357s
500 0 -500 4000 0 -4000 300
=0.0315s
Position 1D
3 4
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
Usg=0.2944m/s, Usw=0.8096m/s
(b) Position 1U
Rxy( )
Upstream and downstream conductance probe signals (V)
Fig. 16. Upstream and downstream conductance signals of slug flow and the corresponding cross-correlation function.
0 4000 2000 0 -2000 3000 0 -3000 3000 0
Position 1 Position 2
=0.0315s
Position 3
=0.0336s
Position 4
=0.0339s
Position 5
=0.0308s
Position 6
=0.0336s
Position 7
0.0
5.0
0.5
1.0
1.5
2.0
Time(s)
Time (s)
Fig. 17. Upstream and downstream conductance signals of churn flow and the corresponding cross-correlation function. 1.2
(a)
2.0
Usg=0.1104m/s, Usw=0.0368m/s
Usg=0.5888m/s, Usw=0.0368m/s
(b)
Usg=0.5888m/s, Usw=0.0736m/s
Usg=0.1104m/s, Usw=0.0736m/s
1.0
Usg=0.5888m/s, Usw=0.1472m/s
Usg=0.1104m/s, Usw=0.1472m/s 1.6
Vi (m/s)
Vi (m/s)
0.8
0.6
1.2 0.4
0.8
0.2 1
2
3
4
5
6
7
1
Radial measurement position
2
3
4
5
6
7
Radial measurement position
Fig. 18. Distribution of local gas velocity at seven radial positions in slug flows.
marked by rectangular is calculated. The chord length at position 1 and 7 is significantly lower than the chord length at five middle positions, which indicates that liquid film of churn flow at the pipe wall contains small bubbles. The chord length range of gas phase at five middle positions are large and distribute irregularly, which corresponds to the randomness and inconsistency of large gas structures in churn flows. Besides, maximum mean value of large deformed bubble chord length is not located at center of pipe, which can be attributed to the irregular movement and deformation of gas structures.
length in pipe center are the largest, which are reflected by mean value and standard deviation of bubble chord length series. Large difference of average bubble chord length in pipe center indicates that bubbles with various sizes are measured in this position. The distribution of bubble chord length in liquid film in slug flow is uniformly and the bubble chord length are mainly 2 mm or less. The series of gas chord lengths in churn flow at seven measurement positions in same sampling time are shown in Fig. 21(a), and the average chord length of large deformed bubbles in five middle positions 25
Experimental Thermal and Fluid Science 107 (2019) 16–28
Q.Y. Yang, et al.
2.0
(a)
(b)
Usg=0.2944m/s, Usw=0.2944m/s
Usg=0.4784m/s, Usw=0.7360m/s
2.0
Usg=0.2944m/s, Usw=0.5888m/s
Usg=0.4784m/s, Usw=0.8096m/s Usg=0.4784m/s, Usw=0.8832m/s
Usg=0.2944m/s, Usw=0.8096m/s 1.5
Vi (m/s)
Vi (m/s)
1.6
1.0
1.2
0.8 0.5 1
2
3
4
5
6
7
1
2
3
4
5
6
7
Radial measurement position
Radial measurement position
Fig. 19. Distribution of local gas velocity at seven radial positions in churn flows.
(a)
12
mean value 1.90mm
Position 1 0
0 0
50
100
150
200
mean value = 377mm
0
250
12
0 100
200
300
400
500
mean value = 381mm
600
Bubble Chord Length (mm)
Gas Chord Length (mm)
0 0
Position 3
100
200
300
400
500
mean value = 392mm
600
Position 4
250 0 0 500
100
200
300
400
mean value = 384mm
500
Position 5
250 0 0 500
200
300
400
500
mean value = 376mm
600
150
200
1.49
100
Position 6
200
250
Position 2
300
mean value 2.61mm
1.79
0 0 100 12 mean value 3.26mm
2.09
400
500
Position 3
6
200
300
400
500
Position 4
6 0
0
12
100
mean value 2.69mm
200
300
400
1.58
Position 5
6
0
12
100
mean value 2.30mm
200
300
400
1.65
Position 6
6 0 100
200
300
400
500
0
600
12
Position 7
100
mean value 2.12mm
200
300
400
1.16
500
Position 7
6
250 0 0
0
12
0 100
250 0 0 500
100
6
250
500
50
mean value 2.31mm
Position 2
250 0 0 500
Position 1
1.17
6
250
500
Usg=0.5888m/s, Usw=0.0368 m/s
(b)
Usg=0.5888m/s, Usw=0.0368 m/s
500
0 50
100
150
200
0
250
50
100
150
200
250
Bubble Series
Bubble Series
Fig. 20. Distribution of gas chords at seven radial positions in slug flow.
5. Conclusions
Fig. 21(b) shows the series of bubble chord lengths at seven radial positions without large gas structures. The thicker liquid film [50] of churn flow results in a larger range of bubble chord length compared with slug flow. Position 1 and 7 occasionally have large chord that appear randomly, which indicates that optical fiber pierces into large gas structures at these two positions. In terms of quantity, the numbers of bubble chord lengths at position 2 and 6 are large, which may be caused by the interaction between large gas structures and liquid film.
We propose a novel plug-in optical probe and conductance sensors by considering high precision of optical probe and great long-range correlation of conductance sensor in this paper. The vertical upward experiment of gas-liquid two-phase flow is carried out to investigate the local time average of void fraction in axial direction, cross-correlation velocity and instantaneous bubble chord distribution in slug and churn flows. The conclusions can be summarized as follows: It is typical phenomenon in churn flows that amount of large spiraling, distorted, deformed bubbles flow in continuous water. In some 26
Experimental Thermal and Fluid Science 107 (2019) 16–28
Q.Y. Yang, et al.
Usg=0.2944m/s, Usw=0.8096 m/s
(a) 120
Usg=0.2944m/s, U w=0.8096 m/s
(b)
Position 1
20
Position 1
mean value = 2.56mm =2.80
60
120
100
200
300
400
mean value = 96.7mm
Position 2
60 0 0
Gas Chord Length (mm)
120
200
400
600
800
mean value = 94.4mm
Position 3
60 0 0 120
200
400
600
800
mean value = 86.4mm
Position 4
60 0 0 120
200
400
600
800
mean value = 92.4mm
1000
Position 5
60 0 0 120
200
400
600
800
mean value = 86.3mm
Position 6
60 0 0 120
200
400
600
800
Position 7
0 0 20
100
200
300
400
mean value = 3.13mm =2.56
Position 2
10 0 0 20
200
400
600
800
mean value = 2.77mm =2.67
Position 3
10 0 0 20
200
400
600
mean value = 2.95mm =3.08
800
Position 4
10 0 0 20
200
400
600
800
mean value = 2.68mm =2.53
Position 5
10 0 0 20
200
400
600
800
mean value = 2.89mm =2.83
Position 6
10 0 0 20
60 0 0
Bubble Chord Length without large deformed bubbles (mm)
10
0 0
200
400
600
800
mean value = 3.17mm =1.90
Position 7
10
100
200
300
0 0
400
100
200
300
400
Bubble Series
Bubble Series
Fig. 21. Distribution of gas chords at seven radial positions in churn flow.
churn conditions, some large gas bubbles flow along the pipe center just as the behavior of gas slugs in developing slug flow. In slug flow, gas bubble chord length in liquid film are in similar size. As for the distribution of bubble chord length in slug flow at seven radial positions, the variation range of chord length is largest at the pipe center and smallest at positions near the pipe wall. In comparison with slug flow, the variation ranges of chord length at seven different radial positions of churn flow are large, which means that the bubble shape is diverse.
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