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Experimental study of interfacial characteristics of vertical upward air-water two-phase flow in 25.4 mm ID round pipe
International Journal of Heat and Mass Transfer 108 (2017) 1825–1838
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Experimental study of interfacial characteristics of vertical upward air-water two-phase flow in 25.4 mm ID round pipe Zhuoran Dang a, Guanyi Wang a, Peng Ju a, Xiaohong Yang a, Robert Bean a, Mamoru Ishii a,⇑, Stephen Bajorek b, Matthew Bernard b a b
School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907, USA U.S. Nuclear Regulatory Commission, Rockville, MD 20852, USA
a r t i c l e
i n f o
Article history: Received 17 October 2016 Received in revised form 3 January 2017 Accepted 13 January 2017
Keywords: Local measurement Interfacial characteristics Two-phase flow Four-sensor conductivity probe Pipe flow
a b s t r a c t An adiabatic upward air-water flow experiment was performed on a vertical pipe with 25.4 mm inner diameter to investigate the interface structure and characteristics. Local experiment parameters, including time-averaged void fraction, interfacial area concentration, bubble interfacial velocity and Sauter mean diameter were measured using a four-sensor conductivity probe with a data acquisition frequency of 100 kHz. Experiment data for 19 flow conditions was collected at 3 axial locations (z/D = 15, 78, and 141) and 13 radial positions from r/R = 0.84 to 0.7. In the experimental study, the measuring range of superficial liquid and gas velocity were from 0.3 to 1.0 m/s and 0.03 to 11.0 m/s, respectively. The flow regimes ranged from bubbly flow to the transition of churn-turbulent to annular flow. The local measurement result agreed well with the drift flux model by Ishii (1977) and Kataoka (1987). The different interfacial structures in different flow regimes and two group bubble interfacial transfer were observed from the experiment result. This data will be used for the evaluation and extension of the current interfacial area transport equation. Ó 2017 Published by Elsevier Ltd.
1. Introduction The characteristics of air-water two-phase flow are important in various engineering systems such as power systems, transport systems and biological systems. Thus, accurate prediction of the two-phase flow structure development is necessary. Unlike single phase flow, the physical properties of two-phase flow are not constant so modeling work is difficult. The interfacial area transport equation (IATE) proposed by Ishii and Kocamustafaogullari [2,3] is considered as a reliable model. It is a general balance equation derived from Boltzmann transport equation and it models the transport phenomena of interfacial area in two-phase flow mechanistically and dynamically. In the IATE, source and sink terms of interfacial area concentration are important because their function describes bubble transport behaviors and mechanisms. In order to model these terms, complete and reliable database is required. Kataoka and Ishii [4] proved that local interfacial area concentration is inversely proportional to interfacial velocity in the direction normal to the interface. This observation allows for the creation of an experimental method to obtain interfacial area
⇑ Corresponding author. E-mail address: [email protected] (M. Ishii). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.01.040 0017-9310/Ó 2017 Published by Elsevier Ltd.
concentration. Based on this theory, Kim et al. [5] developed the miniature four-sensor conductivity probe and benchmarked it by images from a high speed camera. The invention of the miniature four-sensor conductivity probe provides an efficient way to measure the interfacial area concentration in relatively small channels. Bernard et al. [6] recently improved the signal processing method and studied the influence of data acquisition frequency on measurement results. He found that acquisition frequency has a nonnegligible effect on the measurement of bubble frequency and interfacial area concentration. In order to reduce the error caused by acquisition frequency, a 100 kHz or higher frequency should be applied in data acquisition. Exceptional efforts on database development for two-phase flow in vertical small diameter pipe were made during last twenty-five years [8–23]. However, most of the former database are focused on bubbly flow and slug flow. The database for the churn-turbulent to annular transient region is sparse. Besides the capability of conductivity probe, the reason for this is that the data acquisition frequencies applied in the past experiments were only up to 30 kHz, which would introduce an error of more than 10% [6]. In current research, the experiment was performed at a high sampling frequency 100 kHz, which instrumentally increased the data accuracy. The current experiment covered ranged from bubbly
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Nomenclature ai C0 D Ddist Dsm g j L N p R t u V z
interfacial area concentration[1/m] distribution parameter [–] diameter [m] maximum distorted bubble diameter [m] Sauter mean diameter [mm] gravitational acceleration [m/s2] mixture volumetric flux [m/s] length [m] non-dimensional number [–] pressure [Pa] pipe radius [m] time [s] velocity [m/s] volume [m3] axial location [m]
flow to the transition of churn-turbulent and annular flow using the miniature four-sensor conductivity probe. The objective of this study is to develop a rigorous database for one-inch vertical pipes with two-group bubble categories covering flow regimes from bubbly flow to churn-turbulent to annular flow, which can be used for benchmarking of the two-group IATE for one-inch pipes.
2. Experimental setup 2.1. Four-sensor conductivity probe Four-sensor conductivity probe is used to measure local parameters in this experiment. The schematic of the probe is given in Fig. 1 [7]. The basic idea of a four-sensor conductivity probe to be applied for measuring interfaces is that the conductivities of water and air are different. When a sensor tip touches interface from water to air (or air to water), the resistance of the closing electrical loop formed by sensor tip and electrical ground will change and electrical signal transferred will also change. The change of signal gives one way to distinguish interfaces between air and water. The four-sensor conductivity probe consists of four
Greek characters void fraction [–] attenuation coefficient [m1] density [kg/m3] surface tension [N/m]
a l q r
Sub/superscripts f quantity for liquid phase g quantity for gas phase m mixture value Mathematical symbols hi area-averaged quantity hh ii void fraction weighted-mean quantity
sensors: one leading sensor and three trailing sensors. The distances between the tip of the leading sensor to tips of the other three trailing sensors are approximately 2 mm. A more detailed description of the design and measurement uncertainty of the four-sensor conductivity probe can be found in the work of Kim et al. [5]. The local parameters measured in this study are void fraction (a), interfacial area concentration (IAC, ai), interfacial velocity (ub), and Sauter mean diameter (Dsm). The time-averaged void fraction a is obtained by using the accumulated time when the sensor touches gas phase divided by the total acquisition time, thus only the signal of leading sensor is used for time-averaged void fraction. The measurement principles for interfacial area concentration and bubble interfacial velocity are given by Kataoka and Ishii [4]. Sauter mean diameter is calculated using measured void fraction and interfacial area concentration and it is expressed as
Dsm ¼
6a ai
ð1Þ
where Dsm , a and ai are Sauter mean diameter, time-averaged void fraction and interfacial area concentration, respectively.
Fig. 1. Diagram of four-sensor conductivity probe [7].
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The measured bubbles are divided into two groups based on the maximum distorted bubble size and its diameter is expressed as
rffiffiffiffiffiffiffiffiffiffi Ddistort ¼ 4
r
g Dq
ð2Þ
For air-water two phase system with atmospheric pressure, the maximum distorted bubble diameter is around 10 mm. Bubble smaller than this size is defined as group 1 bubble, while bubble with diameter larger than this value is defined as group 2 bubble. The uncertainty of four-sensor conductivity probe has the following major factors. The first one is the uncertainty induced by the probe structure (including the probe geometry and the distance between each sensor) and the distortion of bubble surface when contacting with the probe. From former study [5,24] that used same type of conductivity probe, this uncertainty is 10.3%. The second uncertainty factor comes from the locating of the probe. This uncertainty should be considered since a small flow channel is utilized in this experiment. Considering the locating instruments (i.e. calipers) and human factor, this uncertainty is about 6%. After error propagation, the total instrumentation uncertainty is obtained as 11.9%. In this experiment, the results from four-sensor probe will be verified using gamma densitometer and rotameters to verify its accuracy. 2.2. Two-phase flow experiment The experiment was performed in a 25.4 mm inner diameter air–water co-current upward two-phase loop, as shown schematically in Fig. 2. The test section is made of acrylic, providing a view of flow structure during the experiment. The total length of test section is 3.81 m, which is z/D = 150. The water flow is supplied by a 25 hp centrifugal pump, the flow rate of which can be controlled accurately. The water flow rate is measured by electromagnetic liquid flow meters with an accuracy of ±1%. The air is supplied by an external air compressor and measured by 3 rotameters with different ranges. The accuracy of each rotameter is within ±2% of the full scale. The air and water are mixed in the injection unit. The two-phase flow mixture injection system injects the air and water mixture into the test section at the bottom of test section. The operating temperature was room temperature (25 ± 0.4 °C) and the operating pressure was near atmospheric pressure. The four-sensor conductivity probes were placed at each of the three measurement ports (z/D = 15, 78, 141). At each measurement port, the probe was traversing through the test cross section in radial direction. The local interfacial parameters were measured at 13 radial positions for each axial location. The detailed measurement locations are listed in Table 1. Assumption is made when determining the measurement radial locations that flow distribution is symmetric around the pipe center. Thus measurement locations are not symmetric in order to get more data points along the radial direction. For each measuring location, the data acquisition time is 120 s and acquisition frequency is 100 kHz, which is high enough to avoid missing interfacial changes in high mass flow [6]. An injection system is used in this experiment for water/air mixing and injecting. The injection unit is detailed in Fig. 3. Water is pumped into the lower buffer tank where it is divided into primary water flow and secondary water flow. Air is injected at the bottom of the lower sparger, flows through the porous metal element and mixes with the secondary water flow. Primary water flow is injected into the remaining injector space around the annuli and mixes with the two-phase flow at the test section inlet. 19 experimental flow conditions in total were measured in this experiment. The test flow conditions are shown in Fig. 4 and Table 2. The flow regime map was developed by Mishima and Ishii
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[22]. From Fig. 3, the range of experimental flow conditions covers all the types of flow regimes. Table 2 gives the detailed information of the area-averaged superficial liquid and gas velocity hjfi and hjgi, area averaged void fraction hai, and averaged interfacial area concentration haii for each flow condition. In the following section, the local parameters measured will be discussed based on the result of selected flow conditions. 3. Results and discussions In two phase flow development, bubble interaction is a key factor for the development of interfacial structure. These mechanisms are (1) bubble coalescence as a result of random collision driven by turbulent eddies; (2) entrainment of the bubbles following in the wake of the preceding bubbles; (3) bubble breakup due to turbulent impact; (4) surface instability for large bubbles; (5) small bubble shearing-off at the rim of large bubbles [25]. In this experiment, these mechanisms were observed through measurement result and the detail is shown below. 3.1. Data verification Local measurement result was evaluated using different measurement methods to ensure its accuracy. Specifically, the local void fraction at each axial location was integrated over the pipe radial cross section to obtain the area-averaged void fraction. Gamma densitometer was installed on each measuring axial location, measuring the global void fraction across the pipe. The obtained area-averaged total void fraction are compared with each other. Local superficial gas velocity hjgi1 is compared with hjgi2 from rotameters and differential pressure gauge. The local hjgi1 is calculated by integrating and area-averaging the multiplication of local void fraction and local bubble interfacial velocity over the pipe radial cross section, which is havgi. Besides, the gas flow rate read from rotameter is converted into local gas flow rate using the local absolute pressure, then hjgi2 is obtained by local gas flow rate divided by test section cross area. The two independent groups of local hjgi are also compared. The comparison result is shown in Fig. 5. The result shows relatively good agreement in general. The average relative difference is 15.02%, 12.27%, 7.82% for superficial velocity in respect to z/ D = 15 to z/D = 141 and 11.85%, 8.22%, 9.43% for void fraction respect to z/D = 15 to z/D = 141. It should be mentioned that the result of port1 in Run1 is relatively small. This is due to the fact that the bubble number and size is so small especially at inlet position (z/D = 15). Thus it becomes much difficult for probe sensors to capture interfaces and convert them into voltage signals, resulting in relatively lower void fraction and IAC. 3.2. Void fraction 3.2.1. Bubbly flow In order to present better local parameter distribution and transport characteristics, the results of bubbly flow test condition Run 3 is selected. The time-averaged local parameters profiles at all three axial locations are given in Fig. 6. Each column from left to right represents time-averaged void fraction, interfacial area concentration, bubble velocity, and group 1 Sauter mean diameter, respectively. Each row from top to bottom represents the result at z/D = 15, 78, and 141, respectively. Group 2 Sauter mean diameter is not included in this analysis because group 2 bubbles are highly distorted and their shape cannot be represented by Sauter mean diameter. For the figures, the local profiles show good symmetry. In Run 3, the void distribution experiences a change process of wall
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Fig. 2. Schematic of test facility.
Table 1 Radial measurement locations for four-sensor conductivity probe. Measurement sequence
1
2
3
4
5
6
7
Real location (mm) Radial location (r/R)
3.81 0.7
5.08 0.6
6.35 0.5
7.62 0.4
8.89 0.3
10.16 0.2
11.43 0.1
Measurement sequence
8
9
10
11
12
13
Real location (mm) Radial location (r/R)
12.70 0
15.24 0.2
17.78 0.4
20.32 0.6
22.86 0.8
23.37 0.84
peak (z/D = 15) – transition (flat) (z/D = 78) – center peak (z/ D = 141). (It should be note that the void distribution classification follows the work of Serizawa and Kataoka [8].) This is explained by the change of bubble size. At inlet position (z/D = 15), bubbles are relatively small and forced towards wall by lift force, resulting wall peak void distribution. As bubbles grow bigger along the flow direction due to the coalescence and expansion, lift force direction changes and drives bubbles towards pipe center. The bubble growth can be seen from the result of Sauter mean diameter. Hibiki and Ishii [12] used the same round pipe diameter (ID: 25.4 mm) as current study, they found in their experiment that when Sauter mean diameter (Dsm) is less than 3.5 mm, the void distribution is wall peak. As Sauter mean diameter is more than 4 mm, bubbles are more likely to coalesce into larger bubbles and move towards
the pipe center. This finding matches this measurement result in general and it means that this phenomenon is repeatable. From the experiment, as as hjg,0i increases to some extent, this transient phenomenon happens earlier, which means at location closer to inlet. With the bubbles coalesce and move to the pipe center, group 2 bubbles appear at z/D = 141 in Run 3, causing total Sauter mean diameter (not group 1 Sauter mean diameter shown in the figure) to increase rapidly and center peak distribution to form. It should be noted that the group 2 bubbles shown in Run 3 are cap bubbles. They are still relatively small and cannot cover the entire pipe cross section like slug bubbles. Another observation from the void fraction result is the intergroup void transfer at the location between z/D = 78 and z/
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diameter pipe. This explains the significant decreasing of group 1 void fraction. 3.2.2. Slug flow The local profiles of Run 16 and Run 6 is given in Figs. 7 and 8. From the void fraction profiles, group 2 bubble becomes dominant in this regime. Moreover, the void distributions of group 1 and group 2 are quite different: group 2 bubbles are center peak distributed, and group 1 bubbles are wall peak distributed yet its significance is reduced as the flow develops. When flow is fully developed, the major bubble shape of group 2 bubble is slug and they cover the entire flow channel in this flow condition. Thus, group 2 void distribution matches the shape of a slug bubble. The group 1 void distribution is affected by slug bubbles that small group 1 bubbles follows the slug bubbles, distributing in the slug bubbles’ wake regions. Besides, the effect of shear off mechanism start to contribute the amount of group 1 bubbles near wall region. According to shear off mechanism, when slug bubbles are large enough, they are sheared at the rim and many small bubbles show up. This could lead group 1 void fraction increase near the wall. At the same time, Sauter mean diameter near the wall is decreased, which is shown at z/D = 78 in the Fig. 6. This proves that many small bubbles exist here.
Fig. 3. Close-up view of air-water injection annulus.
3.2.3. Churn-turbulent flow Figs. 9 and 10 gives the local profile of Run 7 and Run 19. Run 7 is dotted on the slug flow region, yet it is more close to churn flow from the experiment observation. From the figure, gas almost completely occupies the center part of the flow channel. At this flow condition, hjfi or hjg,0i is not sensitive to the dominant situation for gas at center of the pipe. The difference of inlet conditions could only be observed near wall. At this test condition, almost all the intergroup transfer will happen near the wall yet it is very small. Besides, the group 1 bubble are so small at this test condition, even at near wall region, the void fraction a1 and interfacial area concentration ai are less than 1% and 10 m1. The change of Group 1 terms are small as the flow develops In terms of distribution, group 1 void fraction at center part almost goes to zero. Most of group 1 void fraction is distributed near wall and it is mainly due to two reasons: the first reason is the group 2 bubble shear-off mechanism. The relative velocity between gas and liquid is so high that more small bubbles are created at the rim of large bubbles than in Slug flow. The second reason is the group 1 void distribution is affected by group 2 bubbles that obstruct small group 1 bubbles. Thus the group 1 bubbles are stagnant near wall region.
Fig. 4. Test conditions on flow regime map.
Table 2 Experimental flow conditions. Run No.
hjfi [m/s]
hjg,0i [m/s]
Run No.
hjfi [m/s]
hjg,0i [m/s]
1 2 3 4 5 6 7 8 9 10
1 1 1 1 1 1 1 1 0.5 0.5
0.03 0.1 0.2 0.5 2.2 4 10 11 0.2 0.5
11 12 13 14 15 16 17 18 19
0.5 0.5 0.5 0.5 0.3 0.3 0.3 0.3 0.3
2.2 4 7 10 0.2 0.5 4 7 10
D = 141. Significant amount change of void fraction of group 1 and group 2 is shown. This indicates strong intergroup void transfer happens as the flow developing, resulting the significant decrease of group 1 void fraction. This can be explained by bubble interaction mechanism. Since it is easier for large bubbles to cover the entire flow channel in small diameter pipe, wake entrainment mechanism is more significant. Small bubbles are more likely to follow and coalesce with the preceding large bubble than in large
3.3. Bubble frequency The result of area-averaged bubble frequency for all flow conditions is presented in Fig. 11. Bubble numbers measured at each local position using four-sensor conductivity probe are integrated over the pipe cross section to obtain the area-averaged quantity. The result is plotted separately according to the flow regime: bubbly flow (upper), slug flow (center), and churn-turbulent flow (lower). The left three subfigures give the group 1 bubble frequency change along the flow direction, while the right three subfigures show the group 2 bubble frequency. From the result of Run 2 and 3, the intergroup transfer at z/D = 78 and z/D = 141 is observed. For Run 2 and 3, group 1 bubble coalesces and become group 2 bubbles. Thus from z/D = 78 to z/D = 141, group 1 bubble number is decreasing while group 2 bubble number is increasing. For Run 4 that has higher hjgi, the intergroup transfer comes earlier and the group 1 and group 2 bubble frequencies experience sudden changes between z/D = 15 and z/D = 78. This significant changes of group 1 and group 2 bubble frequency (number) is caused by wake
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Fig. 5. Data verification result.
entrainment. The effect of wake entrainment is enhanced by the narrow flow channel, which leads to the strong intergroup changes. In terms of slug flow with Run 5, 6, and 11, significant decreasing of group 2 bubbles from z/D = 15 to z/D = 78 is shown in the fig-
ure. As mentioned in Section 3.2.2, small group 2 bubbles continue coalescing into slug bubbles, resulting in the decreasing of group 2 bubble number. It is noticed that most of the decreasing rate of group 2 bubble frequency between z/D = 78 and z/D = 141 is slower than that between z/D = 15 and z/D = 78. This indicates that bubble
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Fig. 6. Local profiles for Run 3, hjfi = 1.0 m/s, hjg,0i = 0.2 m/s.
shear off mechanism at z/D = 78 and z/D = 141 is not as strong as that at z/D = 15. Almost all the bubbles at z/D = 15 are sheared off by liquid flow because of the turbulent flow, thus large number of group 1 and small group 2 bubbles exists at z/D = 15. As the flow becomes less turbulent, shear off mechanism becomes less strong. The number of small bubbles decreases at z/D = 78 due to the coalescence and there is no significant decreasing between z/D = 78 and z/D = 141. As for the churn-turbulent flow, the group 2 bubble number is much larger than the group 1 bubble number in the same condition, and they are both decreasing along the flow. This means bubbles coalesce and start to occupy the flow channel as a larger unit. It is predictable that as hjgi continuing increasing, there will be almost no interface at the center of the flow channel and annular flow will show up. 3.4. Interfacial area concentration For group 1 bubble in bubbly flow, the interfacial area concentration (IAC) distribution is similar to void fraction distribu-
tion. This is because most of the small bubbles are close to spherical shape and the bubble size is nearly uniform across the flow channel, thus IAC distribution is similar with void fraction distribution. This can be checked from the local IAC result of Run 3. From the result, the value of total IAC is approximately unchanged during the flow development when group 1 bubble dominates. However, total IAC decreases significantly as group 2 bubble shows up at z/D = 141. This is reasonable because for certain void fraction, larger bubbles have smaller surface area than smaller bubbles. The local IAC distribution for Run 16 is shown in Fig. 7. It can be seen that the group 1 IAC distribution of Run 10 also follows the void distribution as wall peak shape. The distribution shape is more significant at z/D = 78 comparing with that at z/D = 15 where flow is turbulent and the lift force driving bubbles towards wall is insignificant. As flow develops, the significance of lift force shows up. As flow develops and reach z/D = 141, many small bubbles transfer into group 2 due to wake entrainment and coalescence and group 1 IAC is decreased.
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Fig. 7. Local profiles for Run 16, hjfi = 0.3 m/s, hjg,0i = 0.5 m/s.
The group 2 IAC distribution in slug flow should be analyzed with the geometry of the group 2 bubble in this flow regime. Based on the surface distribution of a typical slug, most of interfaces should be near the wall. Thus, wall peak IAC distribution should be seen in fully developed flow. It is easy to conclude that as flow develops, the significance of the wall peak distribution of group 2 IAC should increase since slug bubbles are getting bigger. Given the large size of our four-sensor probe compared with the flow channel, the interfaces which are very close to the wall cannot be measured. Therefore, some IAC profiles that should be wall peak distribution is actually not shown as they should be. Four-sensor probe with smaller geometry is recommended to be used for this flow channel. The IAC profile of Run 19 is given in Fig. 10. From these churnturbulent flow conditions, the group 1 IAC appears only at offcenter area(r/R > 0.7) when flow is fully developed. The group 2 IAC distribution is wall peak at all axial locations. This is reasonable since the center area of the flow channel is almost completely occupied by gas, the interface between gas and liquid should be
small. Compared with center area, smaller group 2 bubbles are likely to exist at off-center area since liquid and gas are mixed in this area and IAC should be high here. 3.5. Bubble interfacial velocity Hibiki et al. [1] indicated that the interfacial velocity for bubbly flow is distributed corresponding to the single phase velocity profile. The introduction of gas will make the liquid velocity profile flattened. From the result, bubble velocity is distributed approximately in the same trend of a power law profile. The value of bubble velocity is approximately equal to the sum of superficial velocities. This is significant at slug and churn-turbulent flow, since the amount of gas injected is large and the flow is highly turbulent. Thus the velocity profile follows the single phase turbulent flow velocity profile and is in general uniformly distributed at center part. Besides, since large group 2 bubble occupies the flow channel and the velocity of a large unit should be nearly of the same, the group 2 velocity profile should be nearly uniform.
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Fig. 8. Local profiles for Run 6, hjfi = 1.0 m/s, hjg,0i = 4.0 m/s.
3.6. Sauter mean diameter The result of group 1 Sauter mean diameter is discussed in this section and shown in Figs. 6 and 7. These results are chosen to analyze the group 1 Sauter mean diameter distribution for bubbly and slug flow in radial positions. Sauter mean diameter
depends on both void fraction and interfacial area concentration, and the result presented here is calculated using these two measurement parameters. The result of churn-turbulent flow is not shown and discussed here because group 1 bubble is not a dominant group and its behavior is largely influenced by group 2 bubble.
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Fig. 9. Local profiles for Run 7, hjfi = 1.0 m/s, hjg,0i = 10.0 m/s.
Fig. 12 shows the axial development of area averaged Sauter mean diameter for all test conditions. These test conditions are separately plotted based on their flow regimes. From the Run 3, Sauter mean diameter is almost uniformly distributed at z/D = 15 and is around 3 mm in average. However when it comes to z/ D = 78 and z/D = 141, Sauter mean diameter is center peak distributed. This is because as flow develops, small group 1 bubbles
coalesce and get larger. Large group 1 bubbles tend to move into the center part due to the lift force, resulting the increasing of Sauter mean diameter at center part. As for slug flow, group 1 Sauter mean diameter distribution is much related to the behavior of large group 2 bubbles. From the result of Run 16, as flow is well developed, Sauter mean diameter at center of the flow channel is less than that at off-center part. This is mainly due to the wake
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Fig. 10. Local profiles for Run 19, hjfi = 0.3 m/s, hjg,0i = 10.0 m/s.
entrainment that small bubble follows closely with the preceding large slugs. In terms of axial development shown, the group 1 Sauter mean diameter is increasing with the increase of z/D at bubbly flow regime because of the local pressure decreasing and bubble expansion and coalescing. However, once bubbles become large
enough and transfer into group 2 bubble, the group 1 Sauter mean diameter would not increase. In slug flow regime, it is observed that the group 1 Sauter mean diameter remains below 3.5 mm in z/D = 78 and z/D = 141, indicating intragroup void transfer (bubble coalescing) happens when slug flow is well developed.
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Fig. 11. Axial development of area averaged bubble frequency.
3.7. Evaluation using drift flux model Drift flux model was used to evaluate the measurement result from the four-sensor conductivity probe. The one-dimensional drift flux model is given as follows (Ishii, 1977):
hhv g ii ¼
hjg i ¼ C 0 hji þ V gj hai
ð3Þ
where v g , jg , a, and j represent gas velocity, superficial gas velocity, void fraction and mixture volumetric flux, respectively. hhii and hi
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Fig. 12. Axial development of area averaged Sauter mean diameter.
are void fraction weighted-mean quantity and area-averaged quantity, respectively. C 0 is distribution parameter and V gj is drift velocity. The expression of them are given as
C0 ¼
haji haihji
ð4Þ
V gj ¼
hav gj i hai
ð5Þ
The distribution parameter depends on Reynold number and two-phase density ratio (Ishii, 1977), and it can be expressed as
sffiffiffiffiffiffi
C 0 ¼ C 1 ðReÞ ½C 1 ðReÞ 1
qg qf
ð6Þ
Ishii (1977) approximated C1 to be 1.2 and the expression above simplifies as
qffiffiffiffiffiffiffiffiffiffiffiffiffi C 0 ¼ 1:2 0:2 qg =qf
ð7Þ
The drift velocity in various two-phase flow regimes for small diameter pipes was proposed by Ishii (Ishii, 1977). Given the fact that the difference between each type of drift velocities is small, this study use drift velocity for churn flow for its simplicity, which is expressed as
pffiffiffi V gj ¼ 2
DH DH ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r=g Dq
ð12Þ
V gj 0:25
V gj ¼
ð13Þ
rg Dq q2f
Nlf ¼
qf r
lf
qffiffiffiffiffiffi0:5
Fig. 13 gives the result of drift flux model comparison. The plot uses log-log scale in order to show clearly the results with low superficial mixture velocity hji. Experimental data when flow is fully developed (z/D = 141) is included in the comparison. From the figure, the two types of drift flux model used have very similar results. Therefore, their results is arithmetically averaged into one result. For flow conditions with superficial mixture velocity and low gas velocity, the measurement itself is more challenged, since void fraction is so low in these flow conditions and errors including measurement and signal processing will make total relative result error (appears in the figure) larger while the absolute result error remains small. Thus the data at superficial mixture velocity and
!0:25
r g Dq q2f
ð8Þ
Kataoka and Ishii (Kataoka, 1987) proposed drift velocity for pool conditions and is given as For N lf 6 2:25 103
V gj ¼ 0:0019DH
V gj
qg ¼ 0:030 qf
0:809
qg qf
!0:157 N0:562 for DH 6 30 lf
ð9Þ
!0:157 N0:562 lf
for DH P 30
ð10Þ
For Nlf > 2:25 103
V gj
qg ¼ 0:92 qf
!0:157
ð11Þ
where DH , V gj , Nlf are non-dimensional hydraulic diameter, drift velocity, and viscous number, respectively. They are defined as
ð14Þ
r g Dq
Fig. 13. Drift flux model comparison result.
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low gas velocity looks deviated from models. For all the flow conditions, the relative difference between area-averaged local data and drift flux model at z/D = 141 is 17.79%. It must be noted that the drift velocity V gj used for all the flow conditions here is for churn flow since it is much simpler and easy to calculate. Considering that the drift flux model applied is simplified, the four-sensor conductivity probe is acceptable in this experiment.
warranty, expressed or implied, or assumes any legal liability or responsibility for any third party’s use, or the results of such use, of any information, apparatus, product, or process disclosed in this report, or represents that its use by such third party would not infringe privately owned rights. The views expressed in this paper are not necessarily those of the U.S. Nuclear Regulatory Commission.
4. Conclusion
References
Experiment on local interfacial parameters for vertical one-inch pipe was performed in this study. Four-sensor conductivity probe was used for the measurement of 19 flow conditions in total, which covers from bubbly flow to churn-turbulent and annular flow transition area. The local parameters included are time-averaged void fraction, interfacial area concentration, bubble interfacial velocity, and bubble Sauter mean diameter. A higher data acquisition frequency of 100 kHz was applied to reduce the error, especially for measuring bubble frequency and interfacial area concentration. The results for this experiment are as below: (1) Gamma densitometer and rotameter were utilized for measurement result verification. The relative difference between results from four-sensor conductivity probe and these two measurement methods are less than 15%. Given the fact that relative difference tend to be high statistically at low void fraction conditions, the result strongly supports the accuracy of the local measurement result. (2) From the local experiment result, the mechanisms for radial and axial profiles development of interfacial area were observed and discussed in detail. The differences of local parameter distribution related to the inlet conditions were observed in all flow regimes. They were caused by the bubble interaction mechanisms. These observations matched previous study. (3) Strong intergroup transfer was observed in certain bubbly flow conditions, which was not shown in previous similar experiments. The significant changes of group 1 and group 2 fractions is due to the strong wake entrainment mechanism happened in this certain flow conditions. (4) Drift flux model (Ishii, 1977; Kataoka, 1987) was introduced for the evaluation of local experimental result and relative difference is 17.79%. Considering the model used here is simplified that the drift velocity for churn flow are used for all flow conditions, the disagreement between drift flux model and four-sensor conductivity probe results is acceptable. By introducing more information about flow channel geometry, fluid properties, and void distribution and its development, Drift flux model can be more specific and accurate.
Acknowledgement This work was performed at Purdue University under the auspices of the U.S. Nuclear Regulatory Commission (NRC), Office of Nuclear Regulatory Research, through the Institute of ThermalHydraulics. The authors would like to express their gratitude to technical staff of the NRC for their support on this project. This paper was prepared as an account of work sponsored by an agency of the U.S. Government. Neither the U.S. Government nor any agency thereof, nor any of their employees, makes any
[1] T. Hibiki, M. Ishii, Z. Xiao, Axial interfacial area transport of vertical bubbly flows, Int. J. Heat Mass Transf. 44 (10) (2001) 1869–1888. [2] M. Ishii, G. Kojasoy, Interfacial Area Transport Equation and Preliminary Considerations for Closure Relations Technical Report, PU-NE-93/6, School of Nuclear Engineering, Purdue University, West Lafayette, IN, USA, 1993. [3] G. Kocamustafaogullari, M. Ishii, Foundation of the interfacial area transport equation and its closure relations, Int. J. Heat Mass Transf. 38 (3) (1995) 481– 493. [4] I. Kataoka, M. Ishii, A. Serizawa, Local formulation and measurements of interfacial area concentration in two-phase flow, Int. J. Multiph. Flow 12 (4) (1986) 505–529. [5] S. Kim, X.Y. Fu, X. Wang, M. Ishii, Development of the miniaturized four-sensor conductivity probe and the signal processing scheme, Int. J. Heat Mass Transf. 43 (22) (2000) 4101–4118. [6] M. Bernard, T.E.D. Worosz, S. Kim, C. Hoxie, Considerations in the practical application of the multisensor conductivity probe for two-phase flow, Nucl. Technol. 190 (2015) 225–235. [7] X. Yang, J.P. Schlegel, Y. Liu, S. Paranjape, T. Hibiki, M. Ishii, Measurement and modeling of two-phase flow parameters in scaled 8 8 BWR rod bundle, Int. J. Heat Fluid Flow 34 (2012) 85–97. [8] A. Serizawa, I. Kataoka, I. Michiyoshi, Experimental data set No. 24: phase distribution in bubbly flow, Multiphase Sci. Technol. 6 (1992) 257–301. [9] T.J. Liu, S.G. Bankoff, Structure of air-water bubbly flow in a vertical pipe-II. Void fraction, bubble velocity and bubble size distribution, Int. J. Heat Mass Transf. 36 (4) (1993) 1061–1072. [10] W.H. Leung, S.T. Revankar, Y. Ishii, M. Ishii, Axial development of interfacial area and void concentration profiles measured by double-sensor probe method, Int. J. Heat Mass Transf. 38 (1995) 445–453. [11] T. Hibiki, M. Ishii, Effect of flow-induced vibration on local flow parameters of two-phase flow, Nucl. Eng. Des. 185 (1998) 113–125. [12] T. Hibiki, M. Ishii, Experimental study on interfacial area transport in bubbly two-phase flow, Int. J. Heat Mass Transf. 42 (1999) 3019–3035. [13] S. Kim, X. Fu, X. Wang, M. Ishii, Study on interfacial structures in slug flows using a miniaturized four-sensor conductivity probe, Nucl. Eng. Des. 204 (2001) 45–55. [14] T. Hibiki, T. Takamasa, M. Ishii, Interfacial area transport of bubbly flow in a small diameter pipe, J. Nucl. Sci. Technol. 38 (8) (2001) 614–620. [15] T. Hibiki, H. Goda, S. Kim, M. Ishii, J. Uhle, Experimental study on interfacial area transport in bubbly two-phase flows, Exp. Fluids 35 (16) (2003) 100–111. [16] X. Sun, T.R. Smith, S. Kim, M. Ishii, J. Uhle, Interfacial structure of air-water two-phase flow in a relatively large pipe, Exp. Fluids 34 (2003) 206–219. [17] T. Takamasa, T. Goto, T. Hibiki, M. Ishii, Experimental study of interfacial area transport of bubbly flow in small-diameter tube, Int. J. Multiph. Flow 29 (2003) 395–409. [18] M. Ishii, S.S. Paranjape, S. Kim, X. Sun, Interfacial structures and interfacial area transport in download two-phase bubbly flow, Int. J. Multiph. Flow 30 (2004) 779–801. [19] T. Hibiki, H. Goda, S.J. Kim, M. Ishii, J. Uhle, Axial development of interfacial structure of vertical downward bubbly flow, Int. J. Heat Mass Transf. 48 (3–4) (2005) 749–764. [20] T. Hibiki, T. Hazuku, T. Takamasa, M. Ishii, Some characteristics of developing bubbly flow in a vertical mini pipe, Int. J. Heat Fluid Flow 28 (2007) 1034– 1048. [21] A. Manera, B. Ozar, M. Paranjape, M. Ishii, H.M. Prasser, Comparison between wire-mesh sensors and conductive needle-probes for measurements of twophase flow parameters, Nucl. Eng. Des. 239 (2009) 1718–1724. [22] T.R. Smith, J.P. Schlegel, T. Hibiki, M. Ishii, Two-phase structure in large diameter pipes, Int. J. Heat Fluid Flow 33 (2012) 156–167. [23] X.Z. Shen, T. Hibiki, H. Nakamura, Developing structure of two-phase flow in a large diameter pipe at low liquid flow rates, Int. J. Heat Fluid Flow 34 (2012) 70–84. [24] J.P. Schlegel, S. Miwa, S. Chen, T. Hibiki, M. Ishii, Experimental study of twophase flow structure in large diameter pipes, Exp. Thermal Fluid Sci. 41 (2012) 12–22. [25] Y. Liu, Three-dimensional Interfacial Area Transport in Gas-Dispersed Twophase flow up to Churn-annular Flow Transition Ph.D. Thesis, Purdue University, West Lafayette, IN, 2008.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Experimental study of interfacial characteristics of vertical upward air-water two-phase flow in 25.4 mm ID round pipe Zhuoran Dang a, Guanyi Wang a, Peng Ju a, Xiaohong Yang a, Robert Bean a, Mamoru Ishii a,⇑, Stephen Bajorek b, Matthew Bernard b a b
School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907, USA U.S. Nuclear Regulatory Commission, Rockville, MD 20852, USA
a r t i c l e
i n f o
Article history: Received 17 October 2016 Received in revised form 3 January 2017 Accepted 13 January 2017
Keywords: Local measurement Interfacial characteristics Two-phase flow Four-sensor conductivity probe Pipe flow
a b s t r a c t An adiabatic upward air-water flow experiment was performed on a vertical pipe with 25.4 mm inner diameter to investigate the interface structure and characteristics. Local experiment parameters, including time-averaged void fraction, interfacial area concentration, bubble interfacial velocity and Sauter mean diameter were measured using a four-sensor conductivity probe with a data acquisition frequency of 100 kHz. Experiment data for 19 flow conditions was collected at 3 axial locations (z/D = 15, 78, and 141) and 13 radial positions from r/R = 0.84 to 0.7. In the experimental study, the measuring range of superficial liquid and gas velocity were from 0.3 to 1.0 m/s and 0.03 to 11.0 m/s, respectively. The flow regimes ranged from bubbly flow to the transition of churn-turbulent to annular flow. The local measurement result agreed well with the drift flux model by Ishii (1977) and Kataoka (1987). The different interfacial structures in different flow regimes and two group bubble interfacial transfer were observed from the experiment result. This data will be used for the evaluation and extension of the current interfacial area transport equation. Ó 2017 Published by Elsevier Ltd.
1. Introduction The characteristics of air-water two-phase flow are important in various engineering systems such as power systems, transport systems and biological systems. Thus, accurate prediction of the two-phase flow structure development is necessary. Unlike single phase flow, the physical properties of two-phase flow are not constant so modeling work is difficult. The interfacial area transport equation (IATE) proposed by Ishii and Kocamustafaogullari [2,3] is considered as a reliable model. It is a general balance equation derived from Boltzmann transport equation and it models the transport phenomena of interfacial area in two-phase flow mechanistically and dynamically. In the IATE, source and sink terms of interfacial area concentration are important because their function describes bubble transport behaviors and mechanisms. In order to model these terms, complete and reliable database is required. Kataoka and Ishii [4] proved that local interfacial area concentration is inversely proportional to interfacial velocity in the direction normal to the interface. This observation allows for the creation of an experimental method to obtain interfacial area
⇑ Corresponding author. E-mail address: [email protected] (M. Ishii). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2017.01.040 0017-9310/Ó 2017 Published by Elsevier Ltd.
concentration. Based on this theory, Kim et al. [5] developed the miniature four-sensor conductivity probe and benchmarked it by images from a high speed camera. The invention of the miniature four-sensor conductivity probe provides an efficient way to measure the interfacial area concentration in relatively small channels. Bernard et al. [6] recently improved the signal processing method and studied the influence of data acquisition frequency on measurement results. He found that acquisition frequency has a nonnegligible effect on the measurement of bubble frequency and interfacial area concentration. In order to reduce the error caused by acquisition frequency, a 100 kHz or higher frequency should be applied in data acquisition. Exceptional efforts on database development for two-phase flow in vertical small diameter pipe were made during last twenty-five years [8–23]. However, most of the former database are focused on bubbly flow and slug flow. The database for the churn-turbulent to annular transient region is sparse. Besides the capability of conductivity probe, the reason for this is that the data acquisition frequencies applied in the past experiments were only up to 30 kHz, which would introduce an error of more than 10% [6]. In current research, the experiment was performed at a high sampling frequency 100 kHz, which instrumentally increased the data accuracy. The current experiment covered ranged from bubbly
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Nomenclature ai C0 D Ddist Dsm g j L N p R t u V z
interfacial area concentration[1/m] distribution parameter [–] diameter [m] maximum distorted bubble diameter [m] Sauter mean diameter [mm] gravitational acceleration [m/s2] mixture volumetric flux [m/s] length [m] non-dimensional number [–] pressure [Pa] pipe radius [m] time [s] velocity [m/s] volume [m3] axial location [m]
flow to the transition of churn-turbulent and annular flow using the miniature four-sensor conductivity probe. The objective of this study is to develop a rigorous database for one-inch vertical pipes with two-group bubble categories covering flow regimes from bubbly flow to churn-turbulent to annular flow, which can be used for benchmarking of the two-group IATE for one-inch pipes.
2. Experimental setup 2.1. Four-sensor conductivity probe Four-sensor conductivity probe is used to measure local parameters in this experiment. The schematic of the probe is given in Fig. 1 [7]. The basic idea of a four-sensor conductivity probe to be applied for measuring interfaces is that the conductivities of water and air are different. When a sensor tip touches interface from water to air (or air to water), the resistance of the closing electrical loop formed by sensor tip and electrical ground will change and electrical signal transferred will also change. The change of signal gives one way to distinguish interfaces between air and water. The four-sensor conductivity probe consists of four
Greek characters void fraction [–] attenuation coefficient [m1] density [kg/m3] surface tension [N/m]
a l q r
Sub/superscripts f quantity for liquid phase g quantity for gas phase m mixture value Mathematical symbols hi area-averaged quantity hh ii void fraction weighted-mean quantity
sensors: one leading sensor and three trailing sensors. The distances between the tip of the leading sensor to tips of the other three trailing sensors are approximately 2 mm. A more detailed description of the design and measurement uncertainty of the four-sensor conductivity probe can be found in the work of Kim et al. [5]. The local parameters measured in this study are void fraction (a), interfacial area concentration (IAC, ai), interfacial velocity (ub), and Sauter mean diameter (Dsm). The time-averaged void fraction a is obtained by using the accumulated time when the sensor touches gas phase divided by the total acquisition time, thus only the signal of leading sensor is used for time-averaged void fraction. The measurement principles for interfacial area concentration and bubble interfacial velocity are given by Kataoka and Ishii [4]. Sauter mean diameter is calculated using measured void fraction and interfacial area concentration and it is expressed as
Dsm ¼
6a ai
ð1Þ
where Dsm , a and ai are Sauter mean diameter, time-averaged void fraction and interfacial area concentration, respectively.
Fig. 1. Diagram of four-sensor conductivity probe [7].
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The measured bubbles are divided into two groups based on the maximum distorted bubble size and its diameter is expressed as
rffiffiffiffiffiffiffiffiffiffi Ddistort ¼ 4
r
g Dq
ð2Þ
For air-water two phase system with atmospheric pressure, the maximum distorted bubble diameter is around 10 mm. Bubble smaller than this size is defined as group 1 bubble, while bubble with diameter larger than this value is defined as group 2 bubble. The uncertainty of four-sensor conductivity probe has the following major factors. The first one is the uncertainty induced by the probe structure (including the probe geometry and the distance between each sensor) and the distortion of bubble surface when contacting with the probe. From former study [5,24] that used same type of conductivity probe, this uncertainty is 10.3%. The second uncertainty factor comes from the locating of the probe. This uncertainty should be considered since a small flow channel is utilized in this experiment. Considering the locating instruments (i.e. calipers) and human factor, this uncertainty is about 6%. After error propagation, the total instrumentation uncertainty is obtained as 11.9%. In this experiment, the results from four-sensor probe will be verified using gamma densitometer and rotameters to verify its accuracy. 2.2. Two-phase flow experiment The experiment was performed in a 25.4 mm inner diameter air–water co-current upward two-phase loop, as shown schematically in Fig. 2. The test section is made of acrylic, providing a view of flow structure during the experiment. The total length of test section is 3.81 m, which is z/D = 150. The water flow is supplied by a 25 hp centrifugal pump, the flow rate of which can be controlled accurately. The water flow rate is measured by electromagnetic liquid flow meters with an accuracy of ±1%. The air is supplied by an external air compressor and measured by 3 rotameters with different ranges. The accuracy of each rotameter is within ±2% of the full scale. The air and water are mixed in the injection unit. The two-phase flow mixture injection system injects the air and water mixture into the test section at the bottom of test section. The operating temperature was room temperature (25 ± 0.4 °C) and the operating pressure was near atmospheric pressure. The four-sensor conductivity probes were placed at each of the three measurement ports (z/D = 15, 78, 141). At each measurement port, the probe was traversing through the test cross section in radial direction. The local interfacial parameters were measured at 13 radial positions for each axial location. The detailed measurement locations are listed in Table 1. Assumption is made when determining the measurement radial locations that flow distribution is symmetric around the pipe center. Thus measurement locations are not symmetric in order to get more data points along the radial direction. For each measuring location, the data acquisition time is 120 s and acquisition frequency is 100 kHz, which is high enough to avoid missing interfacial changes in high mass flow [6]. An injection system is used in this experiment for water/air mixing and injecting. The injection unit is detailed in Fig. 3. Water is pumped into the lower buffer tank where it is divided into primary water flow and secondary water flow. Air is injected at the bottom of the lower sparger, flows through the porous metal element and mixes with the secondary water flow. Primary water flow is injected into the remaining injector space around the annuli and mixes with the two-phase flow at the test section inlet. 19 experimental flow conditions in total were measured in this experiment. The test flow conditions are shown in Fig. 4 and Table 2. The flow regime map was developed by Mishima and Ishii
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[22]. From Fig. 3, the range of experimental flow conditions covers all the types of flow regimes. Table 2 gives the detailed information of the area-averaged superficial liquid and gas velocity hjfi and hjgi, area averaged void fraction hai, and averaged interfacial area concentration haii for each flow condition. In the following section, the local parameters measured will be discussed based on the result of selected flow conditions. 3. Results and discussions In two phase flow development, bubble interaction is a key factor for the development of interfacial structure. These mechanisms are (1) bubble coalescence as a result of random collision driven by turbulent eddies; (2) entrainment of the bubbles following in the wake of the preceding bubbles; (3) bubble breakup due to turbulent impact; (4) surface instability for large bubbles; (5) small bubble shearing-off at the rim of large bubbles [25]. In this experiment, these mechanisms were observed through measurement result and the detail is shown below. 3.1. Data verification Local measurement result was evaluated using different measurement methods to ensure its accuracy. Specifically, the local void fraction at each axial location was integrated over the pipe radial cross section to obtain the area-averaged void fraction. Gamma densitometer was installed on each measuring axial location, measuring the global void fraction across the pipe. The obtained area-averaged total void fraction are compared with each other. Local superficial gas velocity hjgi1 is compared with hjgi2 from rotameters and differential pressure gauge. The local hjgi1 is calculated by integrating and area-averaging the multiplication of local void fraction and local bubble interfacial velocity over the pipe radial cross section, which is havgi. Besides, the gas flow rate read from rotameter is converted into local gas flow rate using the local absolute pressure, then hjgi2 is obtained by local gas flow rate divided by test section cross area. The two independent groups of local hjgi are also compared. The comparison result is shown in Fig. 5. The result shows relatively good agreement in general. The average relative difference is 15.02%, 12.27%, 7.82% for superficial velocity in respect to z/ D = 15 to z/D = 141 and 11.85%, 8.22%, 9.43% for void fraction respect to z/D = 15 to z/D = 141. It should be mentioned that the result of port1 in Run1 is relatively small. This is due to the fact that the bubble number and size is so small especially at inlet position (z/D = 15). Thus it becomes much difficult for probe sensors to capture interfaces and convert them into voltage signals, resulting in relatively lower void fraction and IAC. 3.2. Void fraction 3.2.1. Bubbly flow In order to present better local parameter distribution and transport characteristics, the results of bubbly flow test condition Run 3 is selected. The time-averaged local parameters profiles at all three axial locations are given in Fig. 6. Each column from left to right represents time-averaged void fraction, interfacial area concentration, bubble velocity, and group 1 Sauter mean diameter, respectively. Each row from top to bottom represents the result at z/D = 15, 78, and 141, respectively. Group 2 Sauter mean diameter is not included in this analysis because group 2 bubbles are highly distorted and their shape cannot be represented by Sauter mean diameter. For the figures, the local profiles show good symmetry. In Run 3, the void distribution experiences a change process of wall
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Fig. 2. Schematic of test facility.
Table 1 Radial measurement locations for four-sensor conductivity probe. Measurement sequence
1
2
3
4
5
6
7
Real location (mm) Radial location (r/R)
3.81 0.7
5.08 0.6
6.35 0.5
7.62 0.4
8.89 0.3
10.16 0.2
11.43 0.1
Measurement sequence
8
9
10
11
12
13
Real location (mm) Radial location (r/R)
12.70 0
15.24 0.2
17.78 0.4
20.32 0.6
22.86 0.8
23.37 0.84
peak (z/D = 15) – transition (flat) (z/D = 78) – center peak (z/ D = 141). (It should be note that the void distribution classification follows the work of Serizawa and Kataoka [8].) This is explained by the change of bubble size. At inlet position (z/D = 15), bubbles are relatively small and forced towards wall by lift force, resulting wall peak void distribution. As bubbles grow bigger along the flow direction due to the coalescence and expansion, lift force direction changes and drives bubbles towards pipe center. The bubble growth can be seen from the result of Sauter mean diameter. Hibiki and Ishii [12] used the same round pipe diameter (ID: 25.4 mm) as current study, they found in their experiment that when Sauter mean diameter (Dsm) is less than 3.5 mm, the void distribution is wall peak. As Sauter mean diameter is more than 4 mm, bubbles are more likely to coalesce into larger bubbles and move towards
the pipe center. This finding matches this measurement result in general and it means that this phenomenon is repeatable. From the experiment, as as hjg,0i increases to some extent, this transient phenomenon happens earlier, which means at location closer to inlet. With the bubbles coalesce and move to the pipe center, group 2 bubbles appear at z/D = 141 in Run 3, causing total Sauter mean diameter (not group 1 Sauter mean diameter shown in the figure) to increase rapidly and center peak distribution to form. It should be noted that the group 2 bubbles shown in Run 3 are cap bubbles. They are still relatively small and cannot cover the entire pipe cross section like slug bubbles. Another observation from the void fraction result is the intergroup void transfer at the location between z/D = 78 and z/
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diameter pipe. This explains the significant decreasing of group 1 void fraction. 3.2.2. Slug flow The local profiles of Run 16 and Run 6 is given in Figs. 7 and 8. From the void fraction profiles, group 2 bubble becomes dominant in this regime. Moreover, the void distributions of group 1 and group 2 are quite different: group 2 bubbles are center peak distributed, and group 1 bubbles are wall peak distributed yet its significance is reduced as the flow develops. When flow is fully developed, the major bubble shape of group 2 bubble is slug and they cover the entire flow channel in this flow condition. Thus, group 2 void distribution matches the shape of a slug bubble. The group 1 void distribution is affected by slug bubbles that small group 1 bubbles follows the slug bubbles, distributing in the slug bubbles’ wake regions. Besides, the effect of shear off mechanism start to contribute the amount of group 1 bubbles near wall region. According to shear off mechanism, when slug bubbles are large enough, they are sheared at the rim and many small bubbles show up. This could lead group 1 void fraction increase near the wall. At the same time, Sauter mean diameter near the wall is decreased, which is shown at z/D = 78 in the Fig. 6. This proves that many small bubbles exist here.
Fig. 3. Close-up view of air-water injection annulus.
3.2.3. Churn-turbulent flow Figs. 9 and 10 gives the local profile of Run 7 and Run 19. Run 7 is dotted on the slug flow region, yet it is more close to churn flow from the experiment observation. From the figure, gas almost completely occupies the center part of the flow channel. At this flow condition, hjfi or hjg,0i is not sensitive to the dominant situation for gas at center of the pipe. The difference of inlet conditions could only be observed near wall. At this test condition, almost all the intergroup transfer will happen near the wall yet it is very small. Besides, the group 1 bubble are so small at this test condition, even at near wall region, the void fraction a1 and interfacial area concentration ai are less than 1% and 10 m1. The change of Group 1 terms are small as the flow develops In terms of distribution, group 1 void fraction at center part almost goes to zero. Most of group 1 void fraction is distributed near wall and it is mainly due to two reasons: the first reason is the group 2 bubble shear-off mechanism. The relative velocity between gas and liquid is so high that more small bubbles are created at the rim of large bubbles than in Slug flow. The second reason is the group 1 void distribution is affected by group 2 bubbles that obstruct small group 1 bubbles. Thus the group 1 bubbles are stagnant near wall region.
Fig. 4. Test conditions on flow regime map.
Table 2 Experimental flow conditions. Run No.
hjfi [m/s]
hjg,0i [m/s]
Run No.
hjfi [m/s]
hjg,0i [m/s]
1 2 3 4 5 6 7 8 9 10
1 1 1 1 1 1 1 1 0.5 0.5
0.03 0.1 0.2 0.5 2.2 4 10 11 0.2 0.5
11 12 13 14 15 16 17 18 19
0.5 0.5 0.5 0.5 0.3 0.3 0.3 0.3 0.3
2.2 4 7 10 0.2 0.5 4 7 10
D = 141. Significant amount change of void fraction of group 1 and group 2 is shown. This indicates strong intergroup void transfer happens as the flow developing, resulting the significant decrease of group 1 void fraction. This can be explained by bubble interaction mechanism. Since it is easier for large bubbles to cover the entire flow channel in small diameter pipe, wake entrainment mechanism is more significant. Small bubbles are more likely to follow and coalesce with the preceding large bubble than in large
3.3. Bubble frequency The result of area-averaged bubble frequency for all flow conditions is presented in Fig. 11. Bubble numbers measured at each local position using four-sensor conductivity probe are integrated over the pipe cross section to obtain the area-averaged quantity. The result is plotted separately according to the flow regime: bubbly flow (upper), slug flow (center), and churn-turbulent flow (lower). The left three subfigures give the group 1 bubble frequency change along the flow direction, while the right three subfigures show the group 2 bubble frequency. From the result of Run 2 and 3, the intergroup transfer at z/D = 78 and z/D = 141 is observed. For Run 2 and 3, group 1 bubble coalesces and become group 2 bubbles. Thus from z/D = 78 to z/D = 141, group 1 bubble number is decreasing while group 2 bubble number is increasing. For Run 4 that has higher hjgi, the intergroup transfer comes earlier and the group 1 and group 2 bubble frequencies experience sudden changes between z/D = 15 and z/D = 78. This significant changes of group 1 and group 2 bubble frequency (number) is caused by wake
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Fig. 5. Data verification result.
entrainment. The effect of wake entrainment is enhanced by the narrow flow channel, which leads to the strong intergroup changes. In terms of slug flow with Run 5, 6, and 11, significant decreasing of group 2 bubbles from z/D = 15 to z/D = 78 is shown in the fig-
ure. As mentioned in Section 3.2.2, small group 2 bubbles continue coalescing into slug bubbles, resulting in the decreasing of group 2 bubble number. It is noticed that most of the decreasing rate of group 2 bubble frequency between z/D = 78 and z/D = 141 is slower than that between z/D = 15 and z/D = 78. This indicates that bubble
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Fig. 6. Local profiles for Run 3, hjfi = 1.0 m/s, hjg,0i = 0.2 m/s.
shear off mechanism at z/D = 78 and z/D = 141 is not as strong as that at z/D = 15. Almost all the bubbles at z/D = 15 are sheared off by liquid flow because of the turbulent flow, thus large number of group 1 and small group 2 bubbles exists at z/D = 15. As the flow becomes less turbulent, shear off mechanism becomes less strong. The number of small bubbles decreases at z/D = 78 due to the coalescence and there is no significant decreasing between z/D = 78 and z/D = 141. As for the churn-turbulent flow, the group 2 bubble number is much larger than the group 1 bubble number in the same condition, and they are both decreasing along the flow. This means bubbles coalesce and start to occupy the flow channel as a larger unit. It is predictable that as hjgi continuing increasing, there will be almost no interface at the center of the flow channel and annular flow will show up. 3.4. Interfacial area concentration For group 1 bubble in bubbly flow, the interfacial area concentration (IAC) distribution is similar to void fraction distribu-
tion. This is because most of the small bubbles are close to spherical shape and the bubble size is nearly uniform across the flow channel, thus IAC distribution is similar with void fraction distribution. This can be checked from the local IAC result of Run 3. From the result, the value of total IAC is approximately unchanged during the flow development when group 1 bubble dominates. However, total IAC decreases significantly as group 2 bubble shows up at z/D = 141. This is reasonable because for certain void fraction, larger bubbles have smaller surface area than smaller bubbles. The local IAC distribution for Run 16 is shown in Fig. 7. It can be seen that the group 1 IAC distribution of Run 10 also follows the void distribution as wall peak shape. The distribution shape is more significant at z/D = 78 comparing with that at z/D = 15 where flow is turbulent and the lift force driving bubbles towards wall is insignificant. As flow develops, the significance of lift force shows up. As flow develops and reach z/D = 141, many small bubbles transfer into group 2 due to wake entrainment and coalescence and group 1 IAC is decreased.
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Fig. 7. Local profiles for Run 16, hjfi = 0.3 m/s, hjg,0i = 0.5 m/s.
The group 2 IAC distribution in slug flow should be analyzed with the geometry of the group 2 bubble in this flow regime. Based on the surface distribution of a typical slug, most of interfaces should be near the wall. Thus, wall peak IAC distribution should be seen in fully developed flow. It is easy to conclude that as flow develops, the significance of the wall peak distribution of group 2 IAC should increase since slug bubbles are getting bigger. Given the large size of our four-sensor probe compared with the flow channel, the interfaces which are very close to the wall cannot be measured. Therefore, some IAC profiles that should be wall peak distribution is actually not shown as they should be. Four-sensor probe with smaller geometry is recommended to be used for this flow channel. The IAC profile of Run 19 is given in Fig. 10. From these churnturbulent flow conditions, the group 1 IAC appears only at offcenter area(r/R > 0.7) when flow is fully developed. The group 2 IAC distribution is wall peak at all axial locations. This is reasonable since the center area of the flow channel is almost completely occupied by gas, the interface between gas and liquid should be
small. Compared with center area, smaller group 2 bubbles are likely to exist at off-center area since liquid and gas are mixed in this area and IAC should be high here. 3.5. Bubble interfacial velocity Hibiki et al. [1] indicated that the interfacial velocity for bubbly flow is distributed corresponding to the single phase velocity profile. The introduction of gas will make the liquid velocity profile flattened. From the result, bubble velocity is distributed approximately in the same trend of a power law profile. The value of bubble velocity is approximately equal to the sum of superficial velocities. This is significant at slug and churn-turbulent flow, since the amount of gas injected is large and the flow is highly turbulent. Thus the velocity profile follows the single phase turbulent flow velocity profile and is in general uniformly distributed at center part. Besides, since large group 2 bubble occupies the flow channel and the velocity of a large unit should be nearly of the same, the group 2 velocity profile should be nearly uniform.
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Fig. 8. Local profiles for Run 6, hjfi = 1.0 m/s, hjg,0i = 4.0 m/s.
3.6. Sauter mean diameter The result of group 1 Sauter mean diameter is discussed in this section and shown in Figs. 6 and 7. These results are chosen to analyze the group 1 Sauter mean diameter distribution for bubbly and slug flow in radial positions. Sauter mean diameter
depends on both void fraction and interfacial area concentration, and the result presented here is calculated using these two measurement parameters. The result of churn-turbulent flow is not shown and discussed here because group 1 bubble is not a dominant group and its behavior is largely influenced by group 2 bubble.
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Fig. 9. Local profiles for Run 7, hjfi = 1.0 m/s, hjg,0i = 10.0 m/s.
Fig. 12 shows the axial development of area averaged Sauter mean diameter for all test conditions. These test conditions are separately plotted based on their flow regimes. From the Run 3, Sauter mean diameter is almost uniformly distributed at z/D = 15 and is around 3 mm in average. However when it comes to z/ D = 78 and z/D = 141, Sauter mean diameter is center peak distributed. This is because as flow develops, small group 1 bubbles
coalesce and get larger. Large group 1 bubbles tend to move into the center part due to the lift force, resulting the increasing of Sauter mean diameter at center part. As for slug flow, group 1 Sauter mean diameter distribution is much related to the behavior of large group 2 bubbles. From the result of Run 16, as flow is well developed, Sauter mean diameter at center of the flow channel is less than that at off-center part. This is mainly due to the wake
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Fig. 10. Local profiles for Run 19, hjfi = 0.3 m/s, hjg,0i = 10.0 m/s.
entrainment that small bubble follows closely with the preceding large slugs. In terms of axial development shown, the group 1 Sauter mean diameter is increasing with the increase of z/D at bubbly flow regime because of the local pressure decreasing and bubble expansion and coalescing. However, once bubbles become large
enough and transfer into group 2 bubble, the group 1 Sauter mean diameter would not increase. In slug flow regime, it is observed that the group 1 Sauter mean diameter remains below 3.5 mm in z/D = 78 and z/D = 141, indicating intragroup void transfer (bubble coalescing) happens when slug flow is well developed.
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Fig. 11. Axial development of area averaged bubble frequency.
3.7. Evaluation using drift flux model Drift flux model was used to evaluate the measurement result from the four-sensor conductivity probe. The one-dimensional drift flux model is given as follows (Ishii, 1977):
hhv g ii ¼
hjg i ¼ C 0 hji þ V gj hai
ð3Þ
where v g , jg , a, and j represent gas velocity, superficial gas velocity, void fraction and mixture volumetric flux, respectively. hhii and hi
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Fig. 12. Axial development of area averaged Sauter mean diameter.
are void fraction weighted-mean quantity and area-averaged quantity, respectively. C 0 is distribution parameter and V gj is drift velocity. The expression of them are given as
C0 ¼
haji haihji
ð4Þ
V gj ¼
hav gj i hai
ð5Þ
The distribution parameter depends on Reynold number and two-phase density ratio (Ishii, 1977), and it can be expressed as
sffiffiffiffiffiffi
C 0 ¼ C 1 ðReÞ ½C 1 ðReÞ 1
qg qf
ð6Þ
Ishii (1977) approximated C1 to be 1.2 and the expression above simplifies as
qffiffiffiffiffiffiffiffiffiffiffiffiffi C 0 ¼ 1:2 0:2 qg =qf
ð7Þ
The drift velocity in various two-phase flow regimes for small diameter pipes was proposed by Ishii (Ishii, 1977). Given the fact that the difference between each type of drift velocities is small, this study use drift velocity for churn flow for its simplicity, which is expressed as
pffiffiffi V gj ¼ 2
DH DH ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r=g Dq
ð12Þ
V gj 0:25
V gj ¼
ð13Þ
rg Dq q2f
Nlf ¼
qf r
lf
qffiffiffiffiffiffi0:5
Fig. 13 gives the result of drift flux model comparison. The plot uses log-log scale in order to show clearly the results with low superficial mixture velocity hji. Experimental data when flow is fully developed (z/D = 141) is included in the comparison. From the figure, the two types of drift flux model used have very similar results. Therefore, their results is arithmetically averaged into one result. For flow conditions with superficial mixture velocity and low gas velocity, the measurement itself is more challenged, since void fraction is so low in these flow conditions and errors including measurement and signal processing will make total relative result error (appears in the figure) larger while the absolute result error remains small. Thus the data at superficial mixture velocity and
!0:25
r g Dq q2f
ð8Þ
Kataoka and Ishii (Kataoka, 1987) proposed drift velocity for pool conditions and is given as For N lf 6 2:25 103
V gj ¼ 0:0019DH
V gj
qg ¼ 0:030 qf
0:809
qg qf
!0:157 N0:562 for DH 6 30 lf
ð9Þ
!0:157 N0:562 lf
for DH P 30
ð10Þ
For Nlf > 2:25 103
V gj
qg ¼ 0:92 qf
!0:157
ð11Þ
where DH , V gj , Nlf are non-dimensional hydraulic diameter, drift velocity, and viscous number, respectively. They are defined as
ð14Þ
r g Dq
Fig. 13. Drift flux model comparison result.
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low gas velocity looks deviated from models. For all the flow conditions, the relative difference between area-averaged local data and drift flux model at z/D = 141 is 17.79%. It must be noted that the drift velocity V gj used for all the flow conditions here is for churn flow since it is much simpler and easy to calculate. Considering that the drift flux model applied is simplified, the four-sensor conductivity probe is acceptable in this experiment.
warranty, expressed or implied, or assumes any legal liability or responsibility for any third party’s use, or the results of such use, of any information, apparatus, product, or process disclosed in this report, or represents that its use by such third party would not infringe privately owned rights. The views expressed in this paper are not necessarily those of the U.S. Nuclear Regulatory Commission.
4. Conclusion
References
Experiment on local interfacial parameters for vertical one-inch pipe was performed in this study. Four-sensor conductivity probe was used for the measurement of 19 flow conditions in total, which covers from bubbly flow to churn-turbulent and annular flow transition area. The local parameters included are time-averaged void fraction, interfacial area concentration, bubble interfacial velocity, and bubble Sauter mean diameter. A higher data acquisition frequency of 100 kHz was applied to reduce the error, especially for measuring bubble frequency and interfacial area concentration. The results for this experiment are as below: (1) Gamma densitometer and rotameter were utilized for measurement result verification. The relative difference between results from four-sensor conductivity probe and these two measurement methods are less than 15%. Given the fact that relative difference tend to be high statistically at low void fraction conditions, the result strongly supports the accuracy of the local measurement result. (2) From the local experiment result, the mechanisms for radial and axial profiles development of interfacial area were observed and discussed in detail. The differences of local parameter distribution related to the inlet conditions were observed in all flow regimes. They were caused by the bubble interaction mechanisms. These observations matched previous study. (3) Strong intergroup transfer was observed in certain bubbly flow conditions, which was not shown in previous similar experiments. The significant changes of group 1 and group 2 fractions is due to the strong wake entrainment mechanism happened in this certain flow conditions. (4) Drift flux model (Ishii, 1977; Kataoka, 1987) was introduced for the evaluation of local experimental result and relative difference is 17.79%. Considering the model used here is simplified that the drift velocity for churn flow are used for all flow conditions, the disagreement between drift flux model and four-sensor conductivity probe results is acceptable. By introducing more information about flow channel geometry, fluid properties, and void distribution and its development, Drift flux model can be more specific and accurate.
Acknowledgement This work was performed at Purdue University under the auspices of the U.S. Nuclear Regulatory Commission (NRC), Office of Nuclear Regulatory Research, through the Institute of ThermalHydraulics. The authors would like to express their gratitude to technical staff of the NRC for their support on this project. This paper was prepared as an account of work sponsored by an agency of the U.S. Government. Neither the U.S. Government nor any agency thereof, nor any of their employees, makes any
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