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Measurement of gas entrainment from stationary liquid slug in horizontal tube with double-sensor conductivity probe
Flow Measurement and Instrumentation 27 (2012) 81–91
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Measurement of gas entrainment from stationary liquid slug in horizontal tube with double-sensor conductivity probe Xin Wang a,b,∗ , Tongji Wang a , Limin He a a
College of Pipeline and Civil Engineering, China University of Petroleum, Qingdao 266555, China
b
State Key Laboratory of Multiphase Flow, Xi’an Jiaotong University, Xi’an 710049, China
article
info
abstract
Keywords: Multiphase flow Slug flow Gas entrainment Interfacial structure
Slug flow is encountered frequently in oil and gas pipelines. Stationary liquid slug was constructed in horizontal pipe to study the process of gas entrainment in a slug front and the two-phase flow parameters of liquid slug were measured by a double-sensor conductivity probe. It was found that the gas entrainment flowrate increases as the Froude number and Reynolds number of the liquid film ahead of the slug front increases. A turbulent shear layer exists in the mixing region and the radial distributions of void fraction and bubble frequency have peaks in the layer. As the distance into the slug increases, the void fraction and bubble frequency decrease and tend to be linearly distributed. The radial distribution of the bubble velocity indicates that the velocity gradient is high in the velocity boundary layer near the bottom of the pipe at the mixing region. The velocity profile agrees well with 1/7-th power law in the fully developed zone of the liquid slug. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction
et al. [2] developed a slug tracking model to predict the evolution of slug length in the pipeline. Brauner and Ullmann [3] proposed a model of vertical slug flow which considered the gas entrainment process from the tail of Taylor bubble to liquid slug and announced that the bubble broken was connected with the turbulent kinetic energy loss when liquid film was injected into the liquid slug. Bonizzi and Issa [4] proposed a one-dimensional transient twofluid model which can capture the formation and evolution of liquid slug in horizontal and inclined pipes. On the basis of Brauner and Ullmann’s model, Issa and Bonizzi [5] proposed a model which can predict the liquid holdup well. Liquid holdup of liquid slug is a necessary correlation to close the slug flow model, which could be found in different forms developed from experimental data or some mechanisms in the literatures. The early research of liquid holdup focused on the development of purely empirical correlations from experimental data. For example, Gregory [6] proposed a widely used correlation and the liquid holdup could be expressed as a function of mixture velocity. Gomez [7] discussed the influence of inclination of the pipeline and put forward a general correlation suitable for 0–90° inclination pipe. These empirical correlations can be expressed in simple form, but cannot be used in the other operation conditions. Some researchers proposed mechanical models which were more complex but more accurate. Barnea and Brauner [8] proposed a mechanism model to predict the liquid holdup which presumed the bubbles were balanced by the force induced by the turbulence, the buoyancy and the surface tension. Chen [9] proposed a model to predict the transition from slug flow to bubbly flow and the
Slug flow is encountered frequently in long distance multiphase pipeline of the offshore petroleum industry. In horizontal or inclined pipeline, slug flow is characterized by alternating of elongated bubbles moving above liquid films and liquid slugs containing small dispersed bubbles. The parameters such as pressure drop and slug length are important for design and operation of the multiphase transport and separation system. In fact, the flow characteristics of liquid slug are affected seriously by the gas entrainment process at the slug front due to the breakup of the tail of the upstream elongated bubble. Recent studies showed that the mechanism of the gas entrainment process is very important for improving the prediction accuracy of slug flow parameters such as the liquid holdup, the slug length and the translational velocity of slug. It is difficult to get a clear idea of the physical mechanisms of the gas entrainment process because the turbulent eddies exist in the liquid slug and also large number of dispersed bubbles coalesce and break continuously. To understand this process, some theoretical and experimental works had been done although most research focused on the macroscopic and average parameters. Based on the unit cell model proposed by Dukler and Hubbard [1], Taitel
∗ Corresponding author at: College of Pipeline and Civil Engineering, China University of Petroleum, Qingdao 266555, China. Fax: +86 532 86981822. E-mail address: [email protected] (X. Wang). 0955-5986/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.flowmeasinst.2012.07.002
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Fig. 1. Schematic diagram of the experimental facility.
principle was based on the balance between turbulent kinetic energy of liquid and the surface free energy of dispersed bubbles. Zhang [10] adopted this model in his research and provided a new correlation to predict the liquid holdup. However the distribution of local void fraction in liquid slug has not been well studied until nowadays. The average velocity of the liquid slug can be calculated from the existing models if the liquid superficial velocity, the gas superficial velocity and the liquid holdup are known, but the velocity distribution in the liquid slug has not been understood thoroughly. Kvernvold [11] measured the velocity distribution in the liquid film zone and the slug zone with the LDV method and an optical probe. He found that the velocity of the liquid slug front was larger than that of the liquid film, the velocity decreased slowly with increasing distance into the slug. Because the slug and the long bubble move quickly in the pipeline, direct measurement of the local parameters is very difficult. Some researchers used stationary slug to study this entrainment process. Jepson [12] found that the gas entrainment phenomenon in the moving slug was similar to that in the stationary slug and also the local velocity distribution in the liquid slug zone was affected by the distribution of void fractions. Gomez [13] constructed two stationary long bubbles in the inclined pipe and measured the velocity field with a two dimensional laser doppler velocity tester. Gomez [14] found that the translational velocity of the long bubble depends not only on the velocity of the previous liquid slug but also on the distribution of the local velocity. Maley and Jepson [15] constructed stationary slug in horizontal pipe and studied the influence of the Froude number of liquid film on the distribution of liquid holdup with the isokinetic sample method. Julshamn [16] measured the gas entrainment flowrate in stationary slug in horizontal pipe and found that the gas entrainment flowrate is proportional to the liquid film Froude number. Delfos [17] constructed stationary slug in vertical pipe and found that the disturbance of the downward flow liquid film caused the gas entrainment, which was similar to the jet stream. Su [18] and Kockx [19] found the gas entrainment flowrate increases with an increasing of the length of the Taylor bubble in the experiments of stationary slug in vertical pipe respectively. But the study of gas entrainment in horizontal or inclined pipe is limited and further experimental work is needed to understand the gas entrainment mechanism and the distribution of the interface parameters in liquid slug. In this paper, an experimental test rig was built to study the process of gas entrainment in the slug front by a stationary water
jump in horizontal pipe and the two-phase flow properties of liquid slug were studied by a double-sensor conductivity probe. The air–water interface parameters were investigated in terms of the distributions of void fraction, bubble frequency and bubble velocity. 2. Experimental facility and measurement techniques The main purpose of this paper is to study the gas entrainment phenomenon in horizontal slug flow. A stationary slug experimental system was constructed to facilitate the measurement of local parameters in the slug zone. The main measurement method was a double-sensor conductivity probe. This section describes the details of the stationary slug experimental system, the corresponding data acquisition system, the double-sensor conductivity probe and the calculation methods of local parameters. 2.1. Flow loop and data acquisition system The experiments were performed in the facility shown in Fig. 1. The test section is 6.3 m long and made of 5 cm i.d. acrylic pipe for observation. It is supported by a steel beam which can be set at different inclination angles between −5 and 5°. Water is stored in a 1 m3 stainless steel tank which is pumped by a centrifugal pump and measured with an electromagnetic flowmeter. Oil is stored in a 2 m3 stainless steel tank which is supplied by a screw pump and measured with a Coriolis mass flowmeter. Air is compressed by a screw compressor into a buffer vessel and then measured with an orifice plate flowmeter or a rotameter. The air continuously injects into the test section through a 15 mm o.d. stainless steel tube. At the end of this tube there is a gate. Water and oil flows through a T -junction into the test section and flows under the gate to produce a liquid film. The air is released above the liquid film and forms an elongated bubble. At the end of the long bubble, a hydraulic jump is formed and the gas in the bubble is entrained into the liquid slug downstream of the long bubble. The mixture flows into the gas–liquid separator after the test section and then gas evacuates to the atmosphere. Water and oil flows into the water tank and oil tank respectively. In this study, air and tap water were chosen as the operated fluids and the test section is horizontal. The surface tension of tap water in room temperature is 72.7 mN/m. Two kinds of gates were used and the ratio of h (the height of the open area under the gate) to D (i.d. of the pipe) is 0.2 and 0.3 respectively.
X. Wang et al. / Flow Measurement and Instrumentation 27 (2012) 81–91
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Fig. 2. Schematic diagram of the test section.
The detailed description of the test section is shown in Fig. 2. Regulating the flowrates of both gas and liquid carefully, the liquid slug could be stabilized at a fixed axial location while the gas entrainment rate at the slug front is equal to the air flowrate. The intersection of the mixture layer and the liquid film at the nose of the slug front is defined as the impingement point. The gas in the long bubble is entrained into the liquid slug at the impingement point and then is broken into a large number of small bubbles due to the turbulent eddies in the slug. The twophase flow properties in the stationary slug were measured by the conductivity probe measurement system which consisted of a double-sensor conductivity probe, an electrical circuit, a high-speed acquisition board and the software used for signal processing. In this study a high speed NI PCI-6143 acquisition board was adopted and Labview 8.5 software installed on a personal computer was used for the conductivity probe signal acquisition. The sampling frequency was set at 40 kHz for each sensor and the sampling time was 80 s. The double-sensor conductivity probe is fixed at a specified axial location and the measurement system is assembled with a mechanical traverser which can adjust the vertical height of the double-sensor conductivity probe in the pipe. The displacement is measured by a vernier caliper which has an accuracy of 0.02 mm. The small diameter gas injection tube which perforates the gate can be moved along the pipe so that the axial location of the liquid slug can be adjusted expediently. In this manner, the local parameters of different axial and radial locations in the liquid slug were measured by the conductivity probe.
Fig. 3. Double-sensor conductivity probe.
2.2. Double-sensor conductivity probe As shown in Fig. 3, the probe consists of two sensors which are made of nickel chromium alloy wire with a diameter of 0.2 mm. The sensors have a sharp needle tip in one end and they are covered with insulated paint film, except the tiny region of the needle tip, where the length of the exposed tip is about 40–80 µm. Two sensors are inserted into an i.d. 0.9 mm, o.d. 1 mm stainless steel tube and the axial distance between two tips 1X is about 2 mm and the lateral distance between two tips 1Z is about 0.5 mm. The measurement principle of the double-sensor conductivity probe relies on the difference of the electrical resistance between air and water. The electrical resistance of air is about 1000 times higher than that of water; therefore the two sensors can distinguish the interface of the gas bubble clearly. The end of the stainless steel tube together with the sensors was bent into a 90° elbow and then it was put into the two-phase flow while the sensor tips were oriented toward the direction of upstream flow. When the sensor tips contact with water, the output voltage is high level and when the sensor tips pierce into a bubble, the output voltage is low level. There is a time delay between the two signals because
Fig. 4. Output signals of two sensors.
the two sensors work simultaneously and a certain distance exists between the two tips, as shown in Fig. 4. The row signals are not strictly square, because the size of the sensor tips are finitude and the electrical system needs some response time. Therefore a signal processing method should be adopted. Firstly, the signals were normalized and signal values set between 0 and 1. Then a threshold should be determined to translate the normalized signals to square signals. A single threshold is always adopted when measuring the air–water two phase flow parameters with a double-sensor conductivity probe. If the signal value is greater than the threshold, set it to 1 and if the signal value is less than the threshold, set it to 0. In the
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Fig. 6. Comparison of vertical radial distribution of void fraction measured by the upstream and downstream probe sensors.
Fig. 5. Comparison of raw signal, normalized signal and square signal.
research of open channel hydraulic jump measurement with a double-sensor conductivity probe, 50% of the signal range was commonly used as the threshold. Chanson and Cummings [20] used 50%, Murzyn and Chanson [21] used 45%–55% of the signal range as the threshold respectively in the research of air–water hydraulic jump. In the present work, the threshold value suggested by Chanson and Cummings [20] was used to regenerate the squarewave signal. The row signal, normalized signal and square signal of the upstream sensor in 0.2 s time intervals are shown in Fig. 5. A higher threshold value would generate a larger void fraction and bubble frequency because noise in the signals would be treated as gas bubbles. On the other hand, a smaller threshold value would generate a smaller void fraction and bubble frequency because some small size bubbles might be missed. Fig. 7. Comparison of vertical radial distribution of bubble frequency measured by the upstream and downstream probe sensors.
2.3. Hydrodynamic parameters calculation The signals of both upstream and downstream sensors are processed and the void fraction C , the bubble frequency F and the bubble velocity Vb could be calculated. Void fraction is defined as the ratio between the total time that the upstream probe sensor is in the gas phase and the sampling time, which can be expressed as: 1
(tTF − tTR )j .
T
(1)
j
Here T denotes the sampling time; Nb denotes the total number of bubbles pierced by the upstream probe sensor or the number of low levels in the upstream signal curve. (tTF − tTR )j denotes the low level duration time of the jth bubble. Bubble frequency is defined as the number of bubbles pierced by the upstream sensor of the probe in one second which can be expressed as: F =
Nb T
.
Fr = Re =
Nb
C =
tip and the head of the stationary slug Px = 6 cm. Here Fr and Re can be expressed as [15]:
(2)
The void fraction and bubble frequency could also be calculated from the downstream sensor signal. Figs. 6 and 7 show the vertical radial distribution of the void fraction and the bubble frequency measured from the upstream and downstream sensors respectively when the gate opening was h/D = 0.3, liquid film Froude number Fr = 6.7, liquid film Reynolds number Re = 74 760, the axial distance between the conductivity probe sensor
v
(3)
ghef
4v Alf
µS L
.
(4)
Here v denotes the average velocity of the liquid film; hef denotes the superficial height of the liquid film and can be expressed as hef = Alf /Lf ; Alf denotes the sectional area of the liquid film; SL denotes the wetted perimeter of the liquid film; µ is the dynamic viscosity of water. Fig. 8 shows the schematic diagram of the pipe cross section. From Figs. 6 and 7, it can be seen that the shape of the curves of both the void fraction and the bubble frequency between the upstream and downstream sensors are almost the same, except for some deviation in the upper region in the pipe which may be related to the eddy structure existing in that region. This verified the reasonableness of the probe and the signal processing method. The void fraction and bubble frequency mentioned below were all measured from the upstream sensor signal. There are two methods to calculate the bubble velocity: Hibiki [22] adopted the effective bubble method and Murzyn and Chanson [21] used the cross-correlation method. In this study, the latter method was chosen and the time delay between the upstream and downstream sensors is calculated from the
X. Wang et al. / Flow Measurement and Instrumentation 27 (2012) 81–91
Fig. 8. Schematic diagram of the pipe cross section. Table 1 Experimental matrix. Gate height
QL (m3 /h)
Fr
Re
Qg (m3 /h)
Px (cm)
h/D = 0.2
1.85 2.1 2.6
7 8 9.9
43 140 50 330 62 310
0.15 0.19 0.245
6, 12, 18, 24 6, 12, 18, 24 6, 12, 18, 24, 30
h/D = 0.3
2.5 3.1 3.9
4.3 5.3 6.7
47 930 59 430 74 760
0.05 0.12 0.19
6, 11, 18 6, 12, 18, 24 6, 12, 22
cross-correlation function and the velocity can be expressed as:
1X (5) 1t where 1X denotes the axial distance between the two sensor tips and 1t denotes the time delay between the two sensor signals
Vb =
determined by the cross-correlation. In this study two gates were adopted. Three liquid flowrates were performed in both gate openings. Table 1 gives the cases performed in this study. In every case the local flow parameters were measured along the radial direction with an interval of 2–3 mm at each specified axial location (Px). The data acquisition lasted 80 s for each experiment and the parameters mentioned above were averaged from the whole acquisition period time. 3. Results and discussion 3.1. Void fraction While the stationary slug is produced in the test section, it is observed that the stationary liquid slug in horizontal pipe is composed of four zones as shown in Fig. 9. The mixing region of the liquid slug comprises the recirculation zone and the turbulent shear layer. There is a free surface at the recirculation zone and the pipe section is filled partially and intermittently by the air–water flow, which is very similar to the water jump in open channel flow.
85
The pipe section in the rear part of the mixing region is full of liquid with high void fraction and high turbulence intensity. The gas pockets in the turbulent shear layer are broken up and the small bubbles leave in pulses to the shedding zone. After the shedding zone, it is the fully developed zone where the small bubbles have an approximately uniform distribution in the upper part of the pipe section. While the gas bubbles move downstream and rise upwards due to the buoyancy force, it is found that the bubbles congregate and coalesce into large bubbles in the middle and upper part of the pipe section from the visual observation from the side face of the pipe. At the end of the liquid slug, the large bubbles coalesce and transform to plug flow or stratified flow eventually. In experiments the location of the slug front along the pipe could be easily adjusted by moving the gas injection tube together with the gate and a specified axial location (Px) of the conductivity probe is reached. At every Px, the bubble parameters were measured at about 24 different vertical heights (Y ) on the vertical centerline across the pipe section. Here Y denotes the radial height of the conductivity probe from the pipe bottom. Fig. 10(a) shows the profiles of void fraction at five different axial locations for a film Froude number of 9.9 when h/D = 0.2. For a short axial distance away from the slug front (Px = 6 cm), the profile shows that the liquid layer near the bottom is free of gas bubbles and there is almost no liquid flow at the upper part of the pipe cross section. Visual observation showed that the air–water mixture partially filled the cross section of the pipe near the slug front and a layer of mixture flowed turbulently on the liquid film. There is a peak of void fraction at Y = 17.2 mm in the profile. Photographs and visual observations show that most of the gas is entrained at the intersection of the mixture layer and the liquid film at the nose of the slug front. After the impingement point, the entrained gas pockets are broken up into small bubbles in a high shear stress layer and then a great number of small bubbles are dispersed and advected in this turbulent shear layer at the lower part of the cross section, as indicated by the peaks of void fraction profiles at Px = 6, 12 cm in Fig. 10(a). Above this layer, the upper part is the recirculation zone which is observed with high turbulent bubble flow, large eddies, splashes and even reverse flow near the top of the pipe. Both zones compose the mixing region of the liquid slug. With increasing axial distance into the slug, the peak value of the void fraction profile decreases whereas the height corresponding to the peak rises. No obvious peak could be found in the void fraction profile while the axial distance is long enough. It reveals that with increasing distance into the slug, the thickness of the turbulent shear layer increases while the turbulent intensity decreases until this layer could not be identified. At Px = 24 cm, the flow is close to fully developed and the void fraction is near to linear distribution along the centerline. In this pipe section, the turbulent shear layer almost disappears. With the distance into the slug increasing, the small bubbles float upwards and coalesce into large bubbles. As shown at Px = 30 cm in Fig. 10(a), there is a rapid increase of void fraction near the top of the pipe. Compared with Fig. 10(a), Fig. 10(b)–(c) show similar void fraction profiles with a smaller liquid film Froude number. As shown in Table 1, the gas entrainment flowrate decreases as
Fig. 9. Schematic diagram of the stationary liquid slug.
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(a) Fr = 9.9, Re = 62 310.
(b) Fr = 8.0, Re = 50 330.
(c) Fr = 7.0, Re = 43 140. Fig. 10. Distributions of the void fraction along the liquid slug (h/D = 0.2).
the Froude number and Reynolds number of the liquid film ahead of the slug front decrease. Also with the film Froude number decreasing, the peak of the void fraction profile becomes indistinctive and also the axial length of the mixing region decreases. The flow reaches full development at a shorter axial distance (Px) which indicates that the turbulent intensity and the axial influence of the turbulent shear layer decreases as the film Froude number decreases. Chanson [23] concluded that the radial distribution of the void fraction profiles in the turbulent shear layer in the open channel flow is in agreement with Gaussian distribution and proposed a correlation. Fig. 10 shows that the experimental data correlated by Gaussian distribution in dash lines are compared with the Chanson’s correlation in solid lines in the turbulent shear layer zone. The results show that the deviation is small while the axial distance away from the slug front (Px) is short. With the distance into the slug increasing, the deviation is small in the lower part of the pipe section but it increases as the radial height increases, because the bubbles are affected not only by the turbulent force but also by the buoyancy force. In addition, the measurement error may increase because the lateral movement of bubbles and reverse flow are evident in this region. Fig. 11 shows the profiles of void fraction along the vertical centerline across the pipe section at different axial locations for three film Froude numbers when h/D = 0.3. It is seen that the distributions of void fraction are similar to Fig. 10. There are peaks in some radial distribution curves, confirming the existence of a turbulent shear layer. The radial heights corresponding to the peaks when h/D = 0.3 are generally higher than that of h/D = 0.2. The reason is that the radial height of the turbulent shear layer is related to the thickness of liquid film which is different for both gates. The initial thickness of the liquid film is 10 mm for h/D = 0.2 and 15 mm for h/D = 0.3 respectively. It is found that the vertical radial height of the void fraction peak in the region downstream of the impingement point corresponds with the film thickness and is slightly greater than it. The pipe cross-sectional average void fraction could be calculated from the data of local void fraction in different radial heights at every axial location measured by the double sensor conductivity probe. Because the distribution of local void fraction is not symmetrical relative to the pipe axis in horizontal slug flow,
the circle integral method proposed by Su [18] is not applicable in this study. A new method to calculate the cross-sectional average void fraction in horizontal pipe is presented. The sketch of the pipe section is shown in Fig. 12. The point along the vertical centerline represents the void fraction which is measured at the position. The pipe cross-section was divided into a number of sub-areas according to the radial measurement positions and two representative sub-areas are given in Fig. 12. While the average void fraction in each sub-area was calculated, an average void fraction over the cross-section of the liquid slug was then calculated by the following equation: Cmean =
1 A
D
Ci dAi
(6)
0
where A is the area of the pipe, Ci denotes the average void fraction of the ith sub-area and dAi denotes the area of the ith sub-area. However the void fraction in the sub-area may be not uniformly distributed in the horizontal direction, therefore an experiment was conducted to measure the distribution of the void fraction along the horizontal centerline of the pipe as shown in Fig. 12. This experiment was easily carried out by rotating the test section 90° and the radial distributions of the void fraction at three axial locations are presented in Fig. 13. It shows that there was maximum of the void fraction located at the center of the pipe cross section when the axial location of the measurement was a short distance from the slug head (Px = 6 cm). Then the void fraction decreased and equaled zero at the near-wall region. In the section at a longer axial distance from the slug head (Px = 22 cm), the radial distribution of the void fraction is nearly uniform. Therefore the liquid slug could be divided into two regions in the axial direction according to the influence of the turbulent shear layer. Firstly, the influence region of the turbulent shear layer is characterized so that the radial distribution of void fractions in the horizontal direction has maximum and is agreement with a parabolic curve. Hence the average void fraction of the sub-area in this region was calculated by the following equation: 2 Cmax i (7) 3 where Cmax i denotes the void fraction measured at the vertical centerline of the pipe section by the conductivity probe. Ci =
X. Wang et al. / Flow Measurement and Instrumentation 27 (2012) 81–91
(a) Fr = 6.7, Re = 74 760.
87
(b) Fr = 5.3, Re = 59 430.
(c) Fr = 4.3, Re = 47 930. Fig. 11. Distributions of the void fraction along the liquid slug (h/D = 0.3).
Secondly, the fully developed zone is characterized that the radial distribution of void fraction in horizontal direction could be assumed uniform and the average void fraction of the sub-area was equal to Cmax i . That is: Ci = Cmax i .
Fig. 12. Sketch of the pipe for calculation of average void fraction.
(8)
Then the average void fraction over the cross-section of the liquid slug at each axial location was calculated by Eq. (6). Fig. 14 shows the distribution of the average void fraction over the cross-section of the pipe along the liquid slug for all experiments. With the distance into the slug (Px) increasing, the average void fraction decreases quickly and then tends to be a relatively stable value. Maley and Jepson [15] reported that the length of the mixed region can be determined by the profile of the average void fraction. While it becomes constant with the increasing of Px, the end of the mixing region is passed and the flow is fully developed. The lengths of the mixing regions for every experiment are estimated and it is found that they increase with the film Froude number increasing. Also it shows that the average void fraction at the end of the mixing region increases with increasing of the liquid film Froude number, which is agreement with the higher gas entrainment rate for larger film Froude number. After the mixing region, the average void fraction increases with increasing of the distance into the slug, because the small bubbles coalesce into large bubbles and then they collect at the top of pipe and transform into plug flow or stratified flow finally. 3.2. Bubble frequency
Fig. 13. The horizontal distribution of void fraction at three axial locations (h/D = 0.3, QL = 3.9 m3 /h).
Fig. 15 shows the profiles of bubble frequency along the vertical centerline across the pipe section with the same condition of Fig. 10. It shows that the vertical radial distribution of the bubble frequency also has peaks within a certain axial distance into the slug. This distance is approximately equal to the length of the mixing zone determined by the axial distribution of the average void fraction over the cross-section of the pipe. The vertical radial height of the peak corresponds to the position of the turbulent shear layer in the mixing region. This indicated that the entrained gas pockets are broken up into a large number of small bubbles by the strong turbulence in this zone. Due to the strong vortex
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(a) h/D = 0.2.
(b) h/D = 0.3. Fig. 14. Distributions of the average void fraction along the liquid slug.
(a) Fr = 9.9, Re = 62 310.
(b) Fr = 8.0, Re = 50 330.
(c) Fr = 7.0, Re = 43 140. Fig. 15. Distributions of the bubble frequency along the liquid slug (h/D = 0.2).
and reverse flow existing in the turbulent shear layer, many small bubbles are trapped in this region and a high bubble frequency is measured. With the distance into the slug increasing, the bubble frequency peak tends to decrease and the vertical radial height of the peak tends to rise. It indicated that the thickness of the turbulent shear layer increases but the turbulent intensity decreases and the numbers of small bubbles in the cross section tend to have a linear distribution. While entering into the fully developed zone, most bubbles floated upward, only few bubbles could be detected in the lower part of the pipe, as shown in Fig. 15. With the Froude number of liquid film decreasing, the peak of bubble frequency at the same axial location decreases and the flow reaches the fully developed zone a short distance from the slug front, which indicated that the region of the turbulent shear layer decreases. Fig. 16 shows the profiles of bubble frequency along the vertical centerline across the pipe section when h/D = 0.3. It demonstrates that the profiles are similar to Fig. 15 of h/D = 0.2. Within a certain axial distance into the liquid slug there also exists a peak in the radial distribution of the bubble frequency. The vertical height of the bubble frequency peak for h/D = 0.3 was generally higher than that of h/D = 0.2.
Fig. 17 compares the vertical radial height of the peak of void fraction and bubble frequency in the turbulent shear layer for all experiments. It is shown that the vertical height of the peak of void fraction (YCmax ) was higher than that of the peak of bubble frequency (YFmax ) for most cases. This is consistent with the report by Murzyn and Chanson [21] from the experiment on the turbulent shear layer of hydraulic jump in open channel flow. They argued that the phenomenon may be associated with a double diffusion process where the vorticity and the air bubbles diffuse at a different rate and in a different manner downstream of the impingement point. At the same axial location, both the vertical height of the peak of void fraction and the bubble frequency increase with the decreasing of film Froude number. The reason is that the film Froude number decreasing results in a smaller turbulent intensity; the flow develops more quickly and the thickness of the turbulent shear layer is higher at the same axial location of the liquid slug. 3.3. Bubble velocity The bubble velocity is defined as the axial velocity of the bubble at a certain local position which is calculated by the crosscorrelation of the signals measured by the upstream sensor and the
X. Wang et al. / Flow Measurement and Instrumentation 27 (2012) 81–91
(a) Fr = 6.7, Re = 74 760.
89
(b) Fr = 5.3, Re = 59 430.
(c) Fr = 4.3, Re = 47 930. Fig. 16. Distributions of the bubble frequency along the liquid slug (h/D = 0.3).
Fig. 17. Comparison of the vertical radial height of the peak of void fraction and that of bubble frequency in the turbulence shear layer.
downstream sensor of the conductivity probe respectively. Fig. 18 shows the profiles of bubble velocity along the vertical centerline across the pipe section with the same condition of Fig. 10. The maximum of the bubble velocity in the cross section is located in the lower part of the pipe when the flow is in the mixing region. Bubble velocity decreases with high gradient when it is near to the pipe wall that indicates the existence of a velocity boundary layer. As the vertical radial position rises, the velocity decreases quickly above the maximum of the profile. These profiles demonstrate that the liquid film extended into the slug in the lower part of the pipe with high inertia. However above the liquid film there is a turbulent shear layer characterized by gas bubble flow with great turbulence intensity, in which the vortexes trap bubbles and reduce the axial velocity. Also above the turbulent shear layer there is the recirculation zone with high turbulent bubble flow, large eddies, splashes and even reverse flow near the top of the pipe. Hence the bubble velocity disturbance exists in this region. The sampling duration was 80 s for each measured point in the experiment. The raw signals were evenly divided into 40 segments and each segment lasted 2 s. The axial bubble velocity in each segment was calculated by cross-correlation of both signals
from the upstream and downstream sensors and then the bubble velocity in this measurement point was calculated by averaging all the 40 segments. It was noticed that some backflow might exist in the recirculation zone, but most of the calculated bubble velocities had good repeatability and only few bubble velocities of some segments were unreasonable and deleted in the averaging process. With the distance into the slug increasing, not only the maximum bubble velocity in the pipe section but also the fluctuation of the velocity decreases. The vertical radial height of the bubble velocity maximum tends to move up and the velocity reaches developed distribution slowly. In the recirculation zone of the slug head region, gas bubbles move slowly and even are detained in this region. However, the liquid as well as the small bubbles move fast in the narrow turbulent shear layer and the region below this layer. While the thickness of the turbulent shear layer increases with the axial distance into the slug increasing, the flow area expands and the liquid velocity decreases owing to continuity. In the fully developed region, it is found that the profile of bubble velocity changes little with an increasing of Px and the maximum of the bubble velocity in the cross section is located near the pipe cross-section center. Some researchers concluded that the velocity distribution of the turbulent boundary layer in the liquidphase pipe flow agree with 1/N-th power law while the flow is fully developed. The fully developed radial distributions of bubble velocity measured were compared with the velocity profiles of 1/7-th power law in Fig. 18(a)–(c) and the agreements were very well when the drifting velocity of the gas bubble was ignored. From Fig. 18, it is shown that the bubble velocity disturbance increases as the radial position moving downwards in the developed region. The reason is that fewer bubbles can be detected in the lower part of the pipe than that of the upper part. Fig. 19 shows the profiles of bubble velocity along the vertical centerline across the pipe section for h/D = 0.3 and can be compared with Fig. 18 for h/D = 0.2. At a given axial location Px, the gas flowrate of the cross section Qgc can be calculated from the measured data as: Qgc = Cmean Vmean A
(9)
where Cmean denotes the average void fraction over the cross section of the liquid slug; Vmean denotes the average bubble velocity
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X. Wang et al. / Flow Measurement and Instrumentation 27 (2012) 81–91
(a) Fr = 9.9, Re = 62 310.
(b) Fr = 8.0, Re = 50 330.
(c) Fr = 7.0, Re = 43 140. Fig. 18. Distributions of the bubble velocity along the liquid slug (h/D = 0.2).
(a) Fr = 6.7, Re = 74 760.
(b) Fr = 5.3, Re = 59 430.
(c) Fr = 4.3, Re = 47 930. Fig. 19. Distributions of the bubble velocity along the liquid slug (h/D = 0.3).
over the cross section of the liquid slug which is calculated from the same method as Cmean . Fig. 20 compares Qgc with the gas flowrate Qg measured by the gas flowmeter. It is found that the calculated flowrates are far greater than that of measured in the mixing region. In this region, large numbers of gas bubbles were trapped and moved not only in the axial direction but also in the radial and the circular direction due to the strong turbulent vortex and the recirculation flow. Therefore the calculated gas flowrate from the probe was higher than the measurement of the gas flowmeter. With the distance into the slug increasing, the turbulent intensity decreased and Qgc was gradually equal to Qg when the flow was fully developed. Fig. 21 shows a comparison of Qgc and Qg in the fully developed zone. It was found that the agreement is well and the deviations are lower than 20%. The result demonstrated that the measured void fraction and bubble
velocity by double-sensor conductivity probe are credible and the processing methods of average parameters over the cross section of the slug are reasonable. Fig. 21 also shows that the threshold of 50% used in Section 2.2 is reasonable. 4. Conclusion An experimental test rig was constructed to maintain a stationary liquid slug in horizontal acrylic pipe for studying the gas entrainment phenomenon. Air and water were used as the operated fluids. The double-sensor conductivity probes were designed and manufactured to measure the local flow parameters in a stationary slug. The gates used in the experiments were h/D = 0.2 and h/D = 0.3 respectively.
X. Wang et al. / Flow Measurement and Instrumentation 27 (2012) 81–91
(a) h/D = 0.2.
91
(b) h/D = 0.3.
Fig. 20. Comparison of the calculated gas flowrate from the conductivity probe with the measurement from the flowmeter.
References
Fig. 21. Comparison of calculated gas flowrate from the conductivity probe with that measured from the flowmeter in the fully developed region.
It is found that both the profiles of void fraction and bubble frequency have peaks at the lower part of the cross section within a short distance into the slug, which indicates the existence of a turbulent shear layer in the mixing region of the stationary slug. The vertical radial distribution of void fraction in the turbulent shear layer is agreement with the Gaussian distribution. With the distance into the slug increasing, the thickness of the turbulent shear layer increases but the intensity decreases; the radial distributions of void fraction and bubble frequency tend to be linear and the flow becomes fully developed. The average void fraction over cross section decreases quickly and then tends to be a relatively stable value as Px increases. The maximum bubble velocity in the cross section is located at the lower part of the pipe when the flow is in the mixing region. With the distance into the slug increasing, the bubble velocity is fully developed and the calculated gas flowrate from the conductivity probe in this region is well in agreement with the measurement of the gas flowmeter. Acknowledgments This work was financially supported by the National Natural Science Foundation of China (50806083), Shandong Province Natural Science Foundation (ZR2011EEM029), the Fundamental Research Funds for the Central Universities and the State Key Laboratory of Multiphase Flow (Xi’an Jiaotong University).
[1] Dukler A, Hubbard M. A model for gas–liquid slug flow in horizontal and near horizontal tubes. Industrial and Engineering Chemistry Fundamentals 1975; 14:337–47. [2] Taitel Y, Barnea D. Effect of gas compressibility on a slug tracking model. Chemical Engineering Science 1998;53:2089–97. [3] Brauner N, Ullmann A. Modelling of gas entrainment from Taylor bubbles. Part A: slug flow. International Journal of Multiphase Flow 2004;30:239–72. [4] Bonizzi M, Issa R. A model for simulating gas bubble entrainment in twophase horizontal slug flow. International Journal of Multiphase Flow 2003;29: 1685–717. [5] Issa R, Bonizzi M, Barbeau S. Improved closure models for gas entrainment and interfacial shear for slug flow modelling in horizontal pipes. International Journal of Multiphase Flow 2006;32(10–11):1287–93. [6] Gregory G, Nicholson M, Aziz K. Correlation of liquid volume fraction in slug for horizontal gas–liquid slug flow. International Journal of Multiphase Flow 1978;4(1):33–9. [7] Gomez L, Shoham O, Taitel Y. Prediction of slug liquid holdup: horizontal to upward vertical flow. International Journal of Multiphase Flow 2000;26: 517–21. [8] Barnea D, Brauner N. Holdup of the liquid slug in two-phase intermittent flow. International Journal of Multiphase Flow 1985;11:43–9. [9] Chen X, Cai X, Brill J. A general model for transition to dispersed bubble flow. Chemical Engineering Science 1997;52:4373–80. [10] Zhang Hong-Quan, Wang Qian, Sarica Cem, Brill JamesP. A unified mechanistic model for slug liquid holdup and transition between slug and dispersed bubble flows. International Journal of Multiphase Flow 2003;29:97–107. [11] Kvernvold O, Vindoy V, Sontvedt T, Saasen A, Selmer-Olsen S. Velocity distribution in horizontal slug flow. International Journal of Multiphase Flow 1984;10(4):441–57. [12] Jepson W. The flow characteristics in horizontal slug flow. In: 3rd international conference on multiphase flow; 1987. No. 187. [13] Gomez H, Fabre J. An experimental study of the hydrodynamics of a stationary air–water slug. In: 4th international conference on multiphase flow; 2001. [14] Gomez H, Fabre J, Ngoc Hien Ha. Influence of the velocity distribution on the motion of long bubbles in tube. In: 5th international conference on multiphase flow; 2004. No. 191. [15] Maley L, Jepson W. Liquid holdup in large-diameter horizontal multiphase pipelines. Journal of Energy Resources Technology 1998;120:185–92. [16] Julshamn J. Hydraulic jumps in horizontal two-phase pipe flow. Ph.D. Thesis. Norwegian University of Science and Technology; 2006. [17] Delfos R. Experiments on air entrainment from a stationary slug bubble in a vertical tube. Ph.D. Thesis. Delft University of Technology; 1996. [18] Su Chaoguang. Gas entrainment at the bottom of a Taylor bubble in vertical gas–liquid slug flows. Ph.D. Thesis. University of Houston; 1995. [19] Kockx J, Nieuwstadt F, Oliemans R, Delfos R. Gas entrainment by a liquid film falling around a stationary Taylor bubble in a vertical tube. International Journal of Multiphase Flow 2005;31:1–24. [20] Chanson H, Cummings PD. Air–water interface area in supercritical flow down small-slope chutes. Report No. CE 151. The University of Queensland; 1996. ISBN: 0 86776 635 2. [21] Murzyn F, Chanson H. Free surface, bubbly flow and turbulence measurements in hydraulic jumps. Report No. CE 63/07. The University of Queensland; 2007. ISBN: 9781864998917. [22] Hibiki T, Hogsett S, Ishii M. Local measurement of interfacial area, interfacial velocity and liquid turbulence in two-phase flow. Nuclear Engineering and Design 1998;184:287–304. [23] Chanson H. Air bubble entrainment in free-surface turbulent flows. Experimental investigations. Report No. CE 46/95. The University of Queensland; 1995. ISBN: 0 86776 611 5.
Contents lists available at SciVerse ScienceDirect
Flow Measurement and Instrumentation journal homepage: www.elsevier.com/locate/flowmeasinst
Measurement of gas entrainment from stationary liquid slug in horizontal tube with double-sensor conductivity probe Xin Wang a,b,∗ , Tongji Wang a , Limin He a a
College of Pipeline and Civil Engineering, China University of Petroleum, Qingdao 266555, China
b
State Key Laboratory of Multiphase Flow, Xi’an Jiaotong University, Xi’an 710049, China
article
info
abstract
Keywords: Multiphase flow Slug flow Gas entrainment Interfacial structure
Slug flow is encountered frequently in oil and gas pipelines. Stationary liquid slug was constructed in horizontal pipe to study the process of gas entrainment in a slug front and the two-phase flow parameters of liquid slug were measured by a double-sensor conductivity probe. It was found that the gas entrainment flowrate increases as the Froude number and Reynolds number of the liquid film ahead of the slug front increases. A turbulent shear layer exists in the mixing region and the radial distributions of void fraction and bubble frequency have peaks in the layer. As the distance into the slug increases, the void fraction and bubble frequency decrease and tend to be linearly distributed. The radial distribution of the bubble velocity indicates that the velocity gradient is high in the velocity boundary layer near the bottom of the pipe at the mixing region. The velocity profile agrees well with 1/7-th power law in the fully developed zone of the liquid slug. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction
et al. [2] developed a slug tracking model to predict the evolution of slug length in the pipeline. Brauner and Ullmann [3] proposed a model of vertical slug flow which considered the gas entrainment process from the tail of Taylor bubble to liquid slug and announced that the bubble broken was connected with the turbulent kinetic energy loss when liquid film was injected into the liquid slug. Bonizzi and Issa [4] proposed a one-dimensional transient twofluid model which can capture the formation and evolution of liquid slug in horizontal and inclined pipes. On the basis of Brauner and Ullmann’s model, Issa and Bonizzi [5] proposed a model which can predict the liquid holdup well. Liquid holdup of liquid slug is a necessary correlation to close the slug flow model, which could be found in different forms developed from experimental data or some mechanisms in the literatures. The early research of liquid holdup focused on the development of purely empirical correlations from experimental data. For example, Gregory [6] proposed a widely used correlation and the liquid holdup could be expressed as a function of mixture velocity. Gomez [7] discussed the influence of inclination of the pipeline and put forward a general correlation suitable for 0–90° inclination pipe. These empirical correlations can be expressed in simple form, but cannot be used in the other operation conditions. Some researchers proposed mechanical models which were more complex but more accurate. Barnea and Brauner [8] proposed a mechanism model to predict the liquid holdup which presumed the bubbles were balanced by the force induced by the turbulence, the buoyancy and the surface tension. Chen [9] proposed a model to predict the transition from slug flow to bubbly flow and the
Slug flow is encountered frequently in long distance multiphase pipeline of the offshore petroleum industry. In horizontal or inclined pipeline, slug flow is characterized by alternating of elongated bubbles moving above liquid films and liquid slugs containing small dispersed bubbles. The parameters such as pressure drop and slug length are important for design and operation of the multiphase transport and separation system. In fact, the flow characteristics of liquid slug are affected seriously by the gas entrainment process at the slug front due to the breakup of the tail of the upstream elongated bubble. Recent studies showed that the mechanism of the gas entrainment process is very important for improving the prediction accuracy of slug flow parameters such as the liquid holdup, the slug length and the translational velocity of slug. It is difficult to get a clear idea of the physical mechanisms of the gas entrainment process because the turbulent eddies exist in the liquid slug and also large number of dispersed bubbles coalesce and break continuously. To understand this process, some theoretical and experimental works had been done although most research focused on the macroscopic and average parameters. Based on the unit cell model proposed by Dukler and Hubbard [1], Taitel
∗ Corresponding author at: College of Pipeline and Civil Engineering, China University of Petroleum, Qingdao 266555, China. Fax: +86 532 86981822. E-mail address: [email protected] (X. Wang). 0955-5986/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.flowmeasinst.2012.07.002
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Fig. 1. Schematic diagram of the experimental facility.
principle was based on the balance between turbulent kinetic energy of liquid and the surface free energy of dispersed bubbles. Zhang [10] adopted this model in his research and provided a new correlation to predict the liquid holdup. However the distribution of local void fraction in liquid slug has not been well studied until nowadays. The average velocity of the liquid slug can be calculated from the existing models if the liquid superficial velocity, the gas superficial velocity and the liquid holdup are known, but the velocity distribution in the liquid slug has not been understood thoroughly. Kvernvold [11] measured the velocity distribution in the liquid film zone and the slug zone with the LDV method and an optical probe. He found that the velocity of the liquid slug front was larger than that of the liquid film, the velocity decreased slowly with increasing distance into the slug. Because the slug and the long bubble move quickly in the pipeline, direct measurement of the local parameters is very difficult. Some researchers used stationary slug to study this entrainment process. Jepson [12] found that the gas entrainment phenomenon in the moving slug was similar to that in the stationary slug and also the local velocity distribution in the liquid slug zone was affected by the distribution of void fractions. Gomez [13] constructed two stationary long bubbles in the inclined pipe and measured the velocity field with a two dimensional laser doppler velocity tester. Gomez [14] found that the translational velocity of the long bubble depends not only on the velocity of the previous liquid slug but also on the distribution of the local velocity. Maley and Jepson [15] constructed stationary slug in horizontal pipe and studied the influence of the Froude number of liquid film on the distribution of liquid holdup with the isokinetic sample method. Julshamn [16] measured the gas entrainment flowrate in stationary slug in horizontal pipe and found that the gas entrainment flowrate is proportional to the liquid film Froude number. Delfos [17] constructed stationary slug in vertical pipe and found that the disturbance of the downward flow liquid film caused the gas entrainment, which was similar to the jet stream. Su [18] and Kockx [19] found the gas entrainment flowrate increases with an increasing of the length of the Taylor bubble in the experiments of stationary slug in vertical pipe respectively. But the study of gas entrainment in horizontal or inclined pipe is limited and further experimental work is needed to understand the gas entrainment mechanism and the distribution of the interface parameters in liquid slug. In this paper, an experimental test rig was built to study the process of gas entrainment in the slug front by a stationary water
jump in horizontal pipe and the two-phase flow properties of liquid slug were studied by a double-sensor conductivity probe. The air–water interface parameters were investigated in terms of the distributions of void fraction, bubble frequency and bubble velocity. 2. Experimental facility and measurement techniques The main purpose of this paper is to study the gas entrainment phenomenon in horizontal slug flow. A stationary slug experimental system was constructed to facilitate the measurement of local parameters in the slug zone. The main measurement method was a double-sensor conductivity probe. This section describes the details of the stationary slug experimental system, the corresponding data acquisition system, the double-sensor conductivity probe and the calculation methods of local parameters. 2.1. Flow loop and data acquisition system The experiments were performed in the facility shown in Fig. 1. The test section is 6.3 m long and made of 5 cm i.d. acrylic pipe for observation. It is supported by a steel beam which can be set at different inclination angles between −5 and 5°. Water is stored in a 1 m3 stainless steel tank which is pumped by a centrifugal pump and measured with an electromagnetic flowmeter. Oil is stored in a 2 m3 stainless steel tank which is supplied by a screw pump and measured with a Coriolis mass flowmeter. Air is compressed by a screw compressor into a buffer vessel and then measured with an orifice plate flowmeter or a rotameter. The air continuously injects into the test section through a 15 mm o.d. stainless steel tube. At the end of this tube there is a gate. Water and oil flows through a T -junction into the test section and flows under the gate to produce a liquid film. The air is released above the liquid film and forms an elongated bubble. At the end of the long bubble, a hydraulic jump is formed and the gas in the bubble is entrained into the liquid slug downstream of the long bubble. The mixture flows into the gas–liquid separator after the test section and then gas evacuates to the atmosphere. Water and oil flows into the water tank and oil tank respectively. In this study, air and tap water were chosen as the operated fluids and the test section is horizontal. The surface tension of tap water in room temperature is 72.7 mN/m. Two kinds of gates were used and the ratio of h (the height of the open area under the gate) to D (i.d. of the pipe) is 0.2 and 0.3 respectively.
X. Wang et al. / Flow Measurement and Instrumentation 27 (2012) 81–91
83
Fig. 2. Schematic diagram of the test section.
The detailed description of the test section is shown in Fig. 2. Regulating the flowrates of both gas and liquid carefully, the liquid slug could be stabilized at a fixed axial location while the gas entrainment rate at the slug front is equal to the air flowrate. The intersection of the mixture layer and the liquid film at the nose of the slug front is defined as the impingement point. The gas in the long bubble is entrained into the liquid slug at the impingement point and then is broken into a large number of small bubbles due to the turbulent eddies in the slug. The twophase flow properties in the stationary slug were measured by the conductivity probe measurement system which consisted of a double-sensor conductivity probe, an electrical circuit, a high-speed acquisition board and the software used for signal processing. In this study a high speed NI PCI-6143 acquisition board was adopted and Labview 8.5 software installed on a personal computer was used for the conductivity probe signal acquisition. The sampling frequency was set at 40 kHz for each sensor and the sampling time was 80 s. The double-sensor conductivity probe is fixed at a specified axial location and the measurement system is assembled with a mechanical traverser which can adjust the vertical height of the double-sensor conductivity probe in the pipe. The displacement is measured by a vernier caliper which has an accuracy of 0.02 mm. The small diameter gas injection tube which perforates the gate can be moved along the pipe so that the axial location of the liquid slug can be adjusted expediently. In this manner, the local parameters of different axial and radial locations in the liquid slug were measured by the conductivity probe.
Fig. 3. Double-sensor conductivity probe.
2.2. Double-sensor conductivity probe As shown in Fig. 3, the probe consists of two sensors which are made of nickel chromium alloy wire with a diameter of 0.2 mm. The sensors have a sharp needle tip in one end and they are covered with insulated paint film, except the tiny region of the needle tip, where the length of the exposed tip is about 40–80 µm. Two sensors are inserted into an i.d. 0.9 mm, o.d. 1 mm stainless steel tube and the axial distance between two tips 1X is about 2 mm and the lateral distance between two tips 1Z is about 0.5 mm. The measurement principle of the double-sensor conductivity probe relies on the difference of the electrical resistance between air and water. The electrical resistance of air is about 1000 times higher than that of water; therefore the two sensors can distinguish the interface of the gas bubble clearly. The end of the stainless steel tube together with the sensors was bent into a 90° elbow and then it was put into the two-phase flow while the sensor tips were oriented toward the direction of upstream flow. When the sensor tips contact with water, the output voltage is high level and when the sensor tips pierce into a bubble, the output voltage is low level. There is a time delay between the two signals because
Fig. 4. Output signals of two sensors.
the two sensors work simultaneously and a certain distance exists between the two tips, as shown in Fig. 4. The row signals are not strictly square, because the size of the sensor tips are finitude and the electrical system needs some response time. Therefore a signal processing method should be adopted. Firstly, the signals were normalized and signal values set between 0 and 1. Then a threshold should be determined to translate the normalized signals to square signals. A single threshold is always adopted when measuring the air–water two phase flow parameters with a double-sensor conductivity probe. If the signal value is greater than the threshold, set it to 1 and if the signal value is less than the threshold, set it to 0. In the
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Fig. 6. Comparison of vertical radial distribution of void fraction measured by the upstream and downstream probe sensors.
Fig. 5. Comparison of raw signal, normalized signal and square signal.
research of open channel hydraulic jump measurement with a double-sensor conductivity probe, 50% of the signal range was commonly used as the threshold. Chanson and Cummings [20] used 50%, Murzyn and Chanson [21] used 45%–55% of the signal range as the threshold respectively in the research of air–water hydraulic jump. In the present work, the threshold value suggested by Chanson and Cummings [20] was used to regenerate the squarewave signal. The row signal, normalized signal and square signal of the upstream sensor in 0.2 s time intervals are shown in Fig. 5. A higher threshold value would generate a larger void fraction and bubble frequency because noise in the signals would be treated as gas bubbles. On the other hand, a smaller threshold value would generate a smaller void fraction and bubble frequency because some small size bubbles might be missed. Fig. 7. Comparison of vertical radial distribution of bubble frequency measured by the upstream and downstream probe sensors.
2.3. Hydrodynamic parameters calculation The signals of both upstream and downstream sensors are processed and the void fraction C , the bubble frequency F and the bubble velocity Vb could be calculated. Void fraction is defined as the ratio between the total time that the upstream probe sensor is in the gas phase and the sampling time, which can be expressed as: 1
(tTF − tTR )j .
T
(1)
j
Here T denotes the sampling time; Nb denotes the total number of bubbles pierced by the upstream probe sensor or the number of low levels in the upstream signal curve. (tTF − tTR )j denotes the low level duration time of the jth bubble. Bubble frequency is defined as the number of bubbles pierced by the upstream sensor of the probe in one second which can be expressed as: F =
Nb T
.
Fr = Re =
Nb
C =
tip and the head of the stationary slug Px = 6 cm. Here Fr and Re can be expressed as [15]:
(2)
The void fraction and bubble frequency could also be calculated from the downstream sensor signal. Figs. 6 and 7 show the vertical radial distribution of the void fraction and the bubble frequency measured from the upstream and downstream sensors respectively when the gate opening was h/D = 0.3, liquid film Froude number Fr = 6.7, liquid film Reynolds number Re = 74 760, the axial distance between the conductivity probe sensor
v
(3)
ghef
4v Alf
µS L
.
(4)
Here v denotes the average velocity of the liquid film; hef denotes the superficial height of the liquid film and can be expressed as hef = Alf /Lf ; Alf denotes the sectional area of the liquid film; SL denotes the wetted perimeter of the liquid film; µ is the dynamic viscosity of water. Fig. 8 shows the schematic diagram of the pipe cross section. From Figs. 6 and 7, it can be seen that the shape of the curves of both the void fraction and the bubble frequency between the upstream and downstream sensors are almost the same, except for some deviation in the upper region in the pipe which may be related to the eddy structure existing in that region. This verified the reasonableness of the probe and the signal processing method. The void fraction and bubble frequency mentioned below were all measured from the upstream sensor signal. There are two methods to calculate the bubble velocity: Hibiki [22] adopted the effective bubble method and Murzyn and Chanson [21] used the cross-correlation method. In this study, the latter method was chosen and the time delay between the upstream and downstream sensors is calculated from the
X. Wang et al. / Flow Measurement and Instrumentation 27 (2012) 81–91
Fig. 8. Schematic diagram of the pipe cross section. Table 1 Experimental matrix. Gate height
QL (m3 /h)
Fr
Re
Qg (m3 /h)
Px (cm)
h/D = 0.2
1.85 2.1 2.6
7 8 9.9
43 140 50 330 62 310
0.15 0.19 0.245
6, 12, 18, 24 6, 12, 18, 24 6, 12, 18, 24, 30
h/D = 0.3
2.5 3.1 3.9
4.3 5.3 6.7
47 930 59 430 74 760
0.05 0.12 0.19
6, 11, 18 6, 12, 18, 24 6, 12, 22
cross-correlation function and the velocity can be expressed as:
1X (5) 1t where 1X denotes the axial distance between the two sensor tips and 1t denotes the time delay between the two sensor signals
Vb =
determined by the cross-correlation. In this study two gates were adopted. Three liquid flowrates were performed in both gate openings. Table 1 gives the cases performed in this study. In every case the local flow parameters were measured along the radial direction with an interval of 2–3 mm at each specified axial location (Px). The data acquisition lasted 80 s for each experiment and the parameters mentioned above were averaged from the whole acquisition period time. 3. Results and discussion 3.1. Void fraction While the stationary slug is produced in the test section, it is observed that the stationary liquid slug in horizontal pipe is composed of four zones as shown in Fig. 9. The mixing region of the liquid slug comprises the recirculation zone and the turbulent shear layer. There is a free surface at the recirculation zone and the pipe section is filled partially and intermittently by the air–water flow, which is very similar to the water jump in open channel flow.
85
The pipe section in the rear part of the mixing region is full of liquid with high void fraction and high turbulence intensity. The gas pockets in the turbulent shear layer are broken up and the small bubbles leave in pulses to the shedding zone. After the shedding zone, it is the fully developed zone where the small bubbles have an approximately uniform distribution in the upper part of the pipe section. While the gas bubbles move downstream and rise upwards due to the buoyancy force, it is found that the bubbles congregate and coalesce into large bubbles in the middle and upper part of the pipe section from the visual observation from the side face of the pipe. At the end of the liquid slug, the large bubbles coalesce and transform to plug flow or stratified flow eventually. In experiments the location of the slug front along the pipe could be easily adjusted by moving the gas injection tube together with the gate and a specified axial location (Px) of the conductivity probe is reached. At every Px, the bubble parameters were measured at about 24 different vertical heights (Y ) on the vertical centerline across the pipe section. Here Y denotes the radial height of the conductivity probe from the pipe bottom. Fig. 10(a) shows the profiles of void fraction at five different axial locations for a film Froude number of 9.9 when h/D = 0.2. For a short axial distance away from the slug front (Px = 6 cm), the profile shows that the liquid layer near the bottom is free of gas bubbles and there is almost no liquid flow at the upper part of the pipe cross section. Visual observation showed that the air–water mixture partially filled the cross section of the pipe near the slug front and a layer of mixture flowed turbulently on the liquid film. There is a peak of void fraction at Y = 17.2 mm in the profile. Photographs and visual observations show that most of the gas is entrained at the intersection of the mixture layer and the liquid film at the nose of the slug front. After the impingement point, the entrained gas pockets are broken up into small bubbles in a high shear stress layer and then a great number of small bubbles are dispersed and advected in this turbulent shear layer at the lower part of the cross section, as indicated by the peaks of void fraction profiles at Px = 6, 12 cm in Fig. 10(a). Above this layer, the upper part is the recirculation zone which is observed with high turbulent bubble flow, large eddies, splashes and even reverse flow near the top of the pipe. Both zones compose the mixing region of the liquid slug. With increasing axial distance into the slug, the peak value of the void fraction profile decreases whereas the height corresponding to the peak rises. No obvious peak could be found in the void fraction profile while the axial distance is long enough. It reveals that with increasing distance into the slug, the thickness of the turbulent shear layer increases while the turbulent intensity decreases until this layer could not be identified. At Px = 24 cm, the flow is close to fully developed and the void fraction is near to linear distribution along the centerline. In this pipe section, the turbulent shear layer almost disappears. With the distance into the slug increasing, the small bubbles float upwards and coalesce into large bubbles. As shown at Px = 30 cm in Fig. 10(a), there is a rapid increase of void fraction near the top of the pipe. Compared with Fig. 10(a), Fig. 10(b)–(c) show similar void fraction profiles with a smaller liquid film Froude number. As shown in Table 1, the gas entrainment flowrate decreases as
Fig. 9. Schematic diagram of the stationary liquid slug.
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(a) Fr = 9.9, Re = 62 310.
(b) Fr = 8.0, Re = 50 330.
(c) Fr = 7.0, Re = 43 140. Fig. 10. Distributions of the void fraction along the liquid slug (h/D = 0.2).
the Froude number and Reynolds number of the liquid film ahead of the slug front decrease. Also with the film Froude number decreasing, the peak of the void fraction profile becomes indistinctive and also the axial length of the mixing region decreases. The flow reaches full development at a shorter axial distance (Px) which indicates that the turbulent intensity and the axial influence of the turbulent shear layer decreases as the film Froude number decreases. Chanson [23] concluded that the radial distribution of the void fraction profiles in the turbulent shear layer in the open channel flow is in agreement with Gaussian distribution and proposed a correlation. Fig. 10 shows that the experimental data correlated by Gaussian distribution in dash lines are compared with the Chanson’s correlation in solid lines in the turbulent shear layer zone. The results show that the deviation is small while the axial distance away from the slug front (Px) is short. With the distance into the slug increasing, the deviation is small in the lower part of the pipe section but it increases as the radial height increases, because the bubbles are affected not only by the turbulent force but also by the buoyancy force. In addition, the measurement error may increase because the lateral movement of bubbles and reverse flow are evident in this region. Fig. 11 shows the profiles of void fraction along the vertical centerline across the pipe section at different axial locations for three film Froude numbers when h/D = 0.3. It is seen that the distributions of void fraction are similar to Fig. 10. There are peaks in some radial distribution curves, confirming the existence of a turbulent shear layer. The radial heights corresponding to the peaks when h/D = 0.3 are generally higher than that of h/D = 0.2. The reason is that the radial height of the turbulent shear layer is related to the thickness of liquid film which is different for both gates. The initial thickness of the liquid film is 10 mm for h/D = 0.2 and 15 mm for h/D = 0.3 respectively. It is found that the vertical radial height of the void fraction peak in the region downstream of the impingement point corresponds with the film thickness and is slightly greater than it. The pipe cross-sectional average void fraction could be calculated from the data of local void fraction in different radial heights at every axial location measured by the double sensor conductivity probe. Because the distribution of local void fraction is not symmetrical relative to the pipe axis in horizontal slug flow,
the circle integral method proposed by Su [18] is not applicable in this study. A new method to calculate the cross-sectional average void fraction in horizontal pipe is presented. The sketch of the pipe section is shown in Fig. 12. The point along the vertical centerline represents the void fraction which is measured at the position. The pipe cross-section was divided into a number of sub-areas according to the radial measurement positions and two representative sub-areas are given in Fig. 12. While the average void fraction in each sub-area was calculated, an average void fraction over the cross-section of the liquid slug was then calculated by the following equation: Cmean =
1 A
D
Ci dAi
(6)
0
where A is the area of the pipe, Ci denotes the average void fraction of the ith sub-area and dAi denotes the area of the ith sub-area. However the void fraction in the sub-area may be not uniformly distributed in the horizontal direction, therefore an experiment was conducted to measure the distribution of the void fraction along the horizontal centerline of the pipe as shown in Fig. 12. This experiment was easily carried out by rotating the test section 90° and the radial distributions of the void fraction at three axial locations are presented in Fig. 13. It shows that there was maximum of the void fraction located at the center of the pipe cross section when the axial location of the measurement was a short distance from the slug head (Px = 6 cm). Then the void fraction decreased and equaled zero at the near-wall region. In the section at a longer axial distance from the slug head (Px = 22 cm), the radial distribution of the void fraction is nearly uniform. Therefore the liquid slug could be divided into two regions in the axial direction according to the influence of the turbulent shear layer. Firstly, the influence region of the turbulent shear layer is characterized so that the radial distribution of void fractions in the horizontal direction has maximum and is agreement with a parabolic curve. Hence the average void fraction of the sub-area in this region was calculated by the following equation: 2 Cmax i (7) 3 where Cmax i denotes the void fraction measured at the vertical centerline of the pipe section by the conductivity probe. Ci =
X. Wang et al. / Flow Measurement and Instrumentation 27 (2012) 81–91
(a) Fr = 6.7, Re = 74 760.
87
(b) Fr = 5.3, Re = 59 430.
(c) Fr = 4.3, Re = 47 930. Fig. 11. Distributions of the void fraction along the liquid slug (h/D = 0.3).
Secondly, the fully developed zone is characterized that the radial distribution of void fraction in horizontal direction could be assumed uniform and the average void fraction of the sub-area was equal to Cmax i . That is: Ci = Cmax i .
Fig. 12. Sketch of the pipe for calculation of average void fraction.
(8)
Then the average void fraction over the cross-section of the liquid slug at each axial location was calculated by Eq. (6). Fig. 14 shows the distribution of the average void fraction over the cross-section of the pipe along the liquid slug for all experiments. With the distance into the slug (Px) increasing, the average void fraction decreases quickly and then tends to be a relatively stable value. Maley and Jepson [15] reported that the length of the mixed region can be determined by the profile of the average void fraction. While it becomes constant with the increasing of Px, the end of the mixing region is passed and the flow is fully developed. The lengths of the mixing regions for every experiment are estimated and it is found that they increase with the film Froude number increasing. Also it shows that the average void fraction at the end of the mixing region increases with increasing of the liquid film Froude number, which is agreement with the higher gas entrainment rate for larger film Froude number. After the mixing region, the average void fraction increases with increasing of the distance into the slug, because the small bubbles coalesce into large bubbles and then they collect at the top of pipe and transform into plug flow or stratified flow finally. 3.2. Bubble frequency
Fig. 13. The horizontal distribution of void fraction at three axial locations (h/D = 0.3, QL = 3.9 m3 /h).
Fig. 15 shows the profiles of bubble frequency along the vertical centerline across the pipe section with the same condition of Fig. 10. It shows that the vertical radial distribution of the bubble frequency also has peaks within a certain axial distance into the slug. This distance is approximately equal to the length of the mixing zone determined by the axial distribution of the average void fraction over the cross-section of the pipe. The vertical radial height of the peak corresponds to the position of the turbulent shear layer in the mixing region. This indicated that the entrained gas pockets are broken up into a large number of small bubbles by the strong turbulence in this zone. Due to the strong vortex
88
X. Wang et al. / Flow Measurement and Instrumentation 27 (2012) 81–91
(a) h/D = 0.2.
(b) h/D = 0.3. Fig. 14. Distributions of the average void fraction along the liquid slug.
(a) Fr = 9.9, Re = 62 310.
(b) Fr = 8.0, Re = 50 330.
(c) Fr = 7.0, Re = 43 140. Fig. 15. Distributions of the bubble frequency along the liquid slug (h/D = 0.2).
and reverse flow existing in the turbulent shear layer, many small bubbles are trapped in this region and a high bubble frequency is measured. With the distance into the slug increasing, the bubble frequency peak tends to decrease and the vertical radial height of the peak tends to rise. It indicated that the thickness of the turbulent shear layer increases but the turbulent intensity decreases and the numbers of small bubbles in the cross section tend to have a linear distribution. While entering into the fully developed zone, most bubbles floated upward, only few bubbles could be detected in the lower part of the pipe, as shown in Fig. 15. With the Froude number of liquid film decreasing, the peak of bubble frequency at the same axial location decreases and the flow reaches the fully developed zone a short distance from the slug front, which indicated that the region of the turbulent shear layer decreases. Fig. 16 shows the profiles of bubble frequency along the vertical centerline across the pipe section when h/D = 0.3. It demonstrates that the profiles are similar to Fig. 15 of h/D = 0.2. Within a certain axial distance into the liquid slug there also exists a peak in the radial distribution of the bubble frequency. The vertical height of the bubble frequency peak for h/D = 0.3 was generally higher than that of h/D = 0.2.
Fig. 17 compares the vertical radial height of the peak of void fraction and bubble frequency in the turbulent shear layer for all experiments. It is shown that the vertical height of the peak of void fraction (YCmax ) was higher than that of the peak of bubble frequency (YFmax ) for most cases. This is consistent with the report by Murzyn and Chanson [21] from the experiment on the turbulent shear layer of hydraulic jump in open channel flow. They argued that the phenomenon may be associated with a double diffusion process where the vorticity and the air bubbles diffuse at a different rate and in a different manner downstream of the impingement point. At the same axial location, both the vertical height of the peak of void fraction and the bubble frequency increase with the decreasing of film Froude number. The reason is that the film Froude number decreasing results in a smaller turbulent intensity; the flow develops more quickly and the thickness of the turbulent shear layer is higher at the same axial location of the liquid slug. 3.3. Bubble velocity The bubble velocity is defined as the axial velocity of the bubble at a certain local position which is calculated by the crosscorrelation of the signals measured by the upstream sensor and the
X. Wang et al. / Flow Measurement and Instrumentation 27 (2012) 81–91
(a) Fr = 6.7, Re = 74 760.
89
(b) Fr = 5.3, Re = 59 430.
(c) Fr = 4.3, Re = 47 930. Fig. 16. Distributions of the bubble frequency along the liquid slug (h/D = 0.3).
Fig. 17. Comparison of the vertical radial height of the peak of void fraction and that of bubble frequency in the turbulence shear layer.
downstream sensor of the conductivity probe respectively. Fig. 18 shows the profiles of bubble velocity along the vertical centerline across the pipe section with the same condition of Fig. 10. The maximum of the bubble velocity in the cross section is located in the lower part of the pipe when the flow is in the mixing region. Bubble velocity decreases with high gradient when it is near to the pipe wall that indicates the existence of a velocity boundary layer. As the vertical radial position rises, the velocity decreases quickly above the maximum of the profile. These profiles demonstrate that the liquid film extended into the slug in the lower part of the pipe with high inertia. However above the liquid film there is a turbulent shear layer characterized by gas bubble flow with great turbulence intensity, in which the vortexes trap bubbles and reduce the axial velocity. Also above the turbulent shear layer there is the recirculation zone with high turbulent bubble flow, large eddies, splashes and even reverse flow near the top of the pipe. Hence the bubble velocity disturbance exists in this region. The sampling duration was 80 s for each measured point in the experiment. The raw signals were evenly divided into 40 segments and each segment lasted 2 s. The axial bubble velocity in each segment was calculated by cross-correlation of both signals
from the upstream and downstream sensors and then the bubble velocity in this measurement point was calculated by averaging all the 40 segments. It was noticed that some backflow might exist in the recirculation zone, but most of the calculated bubble velocities had good repeatability and only few bubble velocities of some segments were unreasonable and deleted in the averaging process. With the distance into the slug increasing, not only the maximum bubble velocity in the pipe section but also the fluctuation of the velocity decreases. The vertical radial height of the bubble velocity maximum tends to move up and the velocity reaches developed distribution slowly. In the recirculation zone of the slug head region, gas bubbles move slowly and even are detained in this region. However, the liquid as well as the small bubbles move fast in the narrow turbulent shear layer and the region below this layer. While the thickness of the turbulent shear layer increases with the axial distance into the slug increasing, the flow area expands and the liquid velocity decreases owing to continuity. In the fully developed region, it is found that the profile of bubble velocity changes little with an increasing of Px and the maximum of the bubble velocity in the cross section is located near the pipe cross-section center. Some researchers concluded that the velocity distribution of the turbulent boundary layer in the liquidphase pipe flow agree with 1/N-th power law while the flow is fully developed. The fully developed radial distributions of bubble velocity measured were compared with the velocity profiles of 1/7-th power law in Fig. 18(a)–(c) and the agreements were very well when the drifting velocity of the gas bubble was ignored. From Fig. 18, it is shown that the bubble velocity disturbance increases as the radial position moving downwards in the developed region. The reason is that fewer bubbles can be detected in the lower part of the pipe than that of the upper part. Fig. 19 shows the profiles of bubble velocity along the vertical centerline across the pipe section for h/D = 0.3 and can be compared with Fig. 18 for h/D = 0.2. At a given axial location Px, the gas flowrate of the cross section Qgc can be calculated from the measured data as: Qgc = Cmean Vmean A
(9)
where Cmean denotes the average void fraction over the cross section of the liquid slug; Vmean denotes the average bubble velocity
90
X. Wang et al. / Flow Measurement and Instrumentation 27 (2012) 81–91
(a) Fr = 9.9, Re = 62 310.
(b) Fr = 8.0, Re = 50 330.
(c) Fr = 7.0, Re = 43 140. Fig. 18. Distributions of the bubble velocity along the liquid slug (h/D = 0.2).
(a) Fr = 6.7, Re = 74 760.
(b) Fr = 5.3, Re = 59 430.
(c) Fr = 4.3, Re = 47 930. Fig. 19. Distributions of the bubble velocity along the liquid slug (h/D = 0.3).
over the cross section of the liquid slug which is calculated from the same method as Cmean . Fig. 20 compares Qgc with the gas flowrate Qg measured by the gas flowmeter. It is found that the calculated flowrates are far greater than that of measured in the mixing region. In this region, large numbers of gas bubbles were trapped and moved not only in the axial direction but also in the radial and the circular direction due to the strong turbulent vortex and the recirculation flow. Therefore the calculated gas flowrate from the probe was higher than the measurement of the gas flowmeter. With the distance into the slug increasing, the turbulent intensity decreased and Qgc was gradually equal to Qg when the flow was fully developed. Fig. 21 shows a comparison of Qgc and Qg in the fully developed zone. It was found that the agreement is well and the deviations are lower than 20%. The result demonstrated that the measured void fraction and bubble
velocity by double-sensor conductivity probe are credible and the processing methods of average parameters over the cross section of the slug are reasonable. Fig. 21 also shows that the threshold of 50% used in Section 2.2 is reasonable. 4. Conclusion An experimental test rig was constructed to maintain a stationary liquid slug in horizontal acrylic pipe for studying the gas entrainment phenomenon. Air and water were used as the operated fluids. The double-sensor conductivity probes were designed and manufactured to measure the local flow parameters in a stationary slug. The gates used in the experiments were h/D = 0.2 and h/D = 0.3 respectively.
X. Wang et al. / Flow Measurement and Instrumentation 27 (2012) 81–91
(a) h/D = 0.2.
91
(b) h/D = 0.3.
Fig. 20. Comparison of the calculated gas flowrate from the conductivity probe with the measurement from the flowmeter.
References
Fig. 21. Comparison of calculated gas flowrate from the conductivity probe with that measured from the flowmeter in the fully developed region.
It is found that both the profiles of void fraction and bubble frequency have peaks at the lower part of the cross section within a short distance into the slug, which indicates the existence of a turbulent shear layer in the mixing region of the stationary slug. The vertical radial distribution of void fraction in the turbulent shear layer is agreement with the Gaussian distribution. With the distance into the slug increasing, the thickness of the turbulent shear layer increases but the intensity decreases; the radial distributions of void fraction and bubble frequency tend to be linear and the flow becomes fully developed. The average void fraction over cross section decreases quickly and then tends to be a relatively stable value as Px increases. The maximum bubble velocity in the cross section is located at the lower part of the pipe when the flow is in the mixing region. With the distance into the slug increasing, the bubble velocity is fully developed and the calculated gas flowrate from the conductivity probe in this region is well in agreement with the measurement of the gas flowmeter. Acknowledgments This work was financially supported by the National Natural Science Foundation of China (50806083), Shandong Province Natural Science Foundation (ZR2011EEM029), the Fundamental Research Funds for the Central Universities and the State Key Laboratory of Multiphase Flow (Xi’an Jiaotong University).
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