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Distribution parameter and drift velocity for two-phase flow in a large diameter pipe
Nuclear Engineering and Design 240 (2010) 3991–4000
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Distribution parameter and drift velocity for two-phase flow in a large diameter pipe Xiuzhong Shen a,∗ , Ryota Matsui a , Kaichiro Mishima a , Hideo Nakamura b a b
Research Reactor Institute, Kyoto University, West Asashiro 2-1010, Kumatori-cho, Sennan-gun, Osaka 590-0494, Japan Nuclear Safety Research Center, Japan Atomic Energy Agency, Tokai-mura, Ibaraki 319-1195, Japan
a r t i c l e
i n f o
Article history: Received 31 August 2009 Received in revised form 21 December 2009 Accepted 13 January 2010
a b s t r a c t In view of practical importance of the drift flux model for two-phase flow analysis in general, and in the analysis of nuclear reactor transients and accidents in particular, the distribution parameter, and the drift velocity have been studied for two-phase flow in a vertical large diameter pipe. In this, study, local measurements were performed on flow parameters, such as void fraction, gas velocity and, liquid velocity in a vertical upward air–water two-phase flow in a pipe of 200 mm inner diameter and, 25 m in height by using the local sensor techniques such as hot-film probes, optical multi-sensor, probes and differential pressure gauges. Two-phase flow regimes in a vertical large diameter pipe, were classified into bubbly, churn and slug flows according to the visual observation. The values of the, distribution parameter and the mean drift velocity were determined directly by their definition using experiment data of the local flow parameters in a two-phase flow in a large diameter pipe. Various existing drift flux correlations were compared with the present experimental results and experimental data obtained by other researchers. A detailed discussion on the problems of these correlations was presented in this paper. Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved.
1. Introduction Since the motions of two phases are strongly coupled in a bubbly flow in a large diameter pipe, the drift flux model is appropriate in the analysis of flow characteristics. An extensive number of experimental and theoretical works have been performed for the distribution parameter and the drift velocity in a flow in a large diameter pipe. It should be mentioned here that the distribution parameter and the drift velocity used in the development of the existing drift flux models are obtained indirectly from the slope and the intercept of the line, respectively, in a plot of jg /˛ versus j. However, the two-phase flow in a large diameter pipe may not be fully developed and their flow patterns may vary remarkably with the flow development, especially at low flow rate. Since the distribution parameter and the drift velocity are closely linked with the flow pattern, their values determined from such plots, in some cases, may not reflect the true values of the flow. So the existing correlations may be approximate drift flux correlations. Recent development of local probe techniques enables the measurement of local flow parameters such as void fraction, and gas and liquid velocities. The values of the distribution parameter and the drift
∗ Corresponding author. Tel.: +81 72 451 2456; fax: +81 72 451 2620. E-mail address: [email protected] (X. Shen).
velocity can be obtained directly from their definition by using the local experimental data of two-phase flow. Further development of detailed and more rigorous drift flux correlations becomes possible. The purposes of this study are (1) to experimentally investigate on the characteristics of air–water two-phase flow in a vertical large diameter pipe, (2) to directly measure the distribution parameter and drift velocity from their definition by using the local experimental data of two-phase flow and establish a large diameter pipe database, (3) to re-estimate existing constitutive equations for the drift flux model in a large diameter pipe, and (4) to make a preparation for developing a new drift flux correlation applicable to two-phase flow in a large diameter pipe. Therefore, the authors conducted local measurements of flow parameters (void fraction, gas velocity and liquid velocity) in a vertical upward air–water two-phase flow in a pipe of 200 mm inner diameter and 25 m in height by using the local sensor techniques and established a database for local parameters for a two-phase flow in a large diameter pipe. Two-phase flow characteristics in a large diameter pipe are analyzed on the basis of these experimental results. The database is further expanded by including the experimental data obtained by other researchers. Various existing drift flux correlations were compared with our newly established experimental database. Their existing problems were carefully studied in the present paper.
0029-5493/$ – see front matter. Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2010.01.004
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Nomenclature C0 j jg jl Re
vA,eff vB,eff vg Vgj
vgj Vgj,B Vgj,P
vl
distribution parameter mixture volumetric flux (m/s) superficial gas velocity (m/s) superficial liquid velocity (m/s) Reynolds number effective velocity of the sensor “A” (m/s) effective velocity of the sensor “B” (m/s) time-averaged rising velocity of gas phase (m/s) void-fraction-weighted mean drift velocity (m/s) drift velocity of gas phase (m/s) mean drift velocity for bubbly flow predicted by Ishii (1977) (m/s) mean drift velocity for pool system predicted by Kataoka and Ishii (1987) (m/s) rising velocity of liquid phase, or time-averaged rising velocity of liquid phase (m/s)
Greek Letters ˛ void fraction kinematic viscosity (m/s) Subscripts g gas phase l liquid phase
2. Experimental 2.1. Experimental rig The present study was carried out by using the Large Scale Test Facility (LSTF) of the adiabatic air–water two-phase flow in the Japan Atomic Energy Agency (JAEA). Fig. 1 shows the experimental facility layout. Purified water was used in the experimental loop and renewed every day during the experimental period to maintain the water quality. Water was kept in the lower reservoir tank, and was pumped with a positive displacement, centrifugal pump, capable of providing a constant head with minimum pressure oscillation. For adiabatic air–water flow experiments, porous sinter tubes with grain size of 40 m were used as air injectors. The water, which flowed through one Venturi flow meter, was divided into four separate flows and then mixed with air in the center of the mixer, while the water, which flowed through the other Venturi flow meter, was divided into two separate flows and then mixed with the former mixed air–water flow before they were injected into the test section. The two-phase mixture flowed out of the test section to enter a separator, namely, the open upper reservoir tank. The air was discharged there and the water was circulated through the loop. The water temperature was kept at a constant temperature within the deviation of ±1 ◦ C during each experimental period. Due to the high pressure in the lower part of the facility, the test section was made of stainless steel round pipe in the low part for its solidity and the transparent acrylic resin round pipes in the upper part to enable flow observation. All the pipes used for the test section were 200 mm in inner diameter. The overall height of the test section, not including the height of the upper reservoir tank, was about 25 m. 2.2. Instrumentation and data acquisition system The inlet water flow rate and water pressure were measured by using Venturi flow meters (25 and 50 mm in inner diameters, respectively) and a pressure gauge, respectively. The inlet
Fig. 1. Schematic diagram of the experimental loop.
gas flow rate and gas pressure were measured by using orifice flow meters: FE-H11-GAS (nominal flow rate: 73.8 Nm3 /h) and FEH12-GAS (nominal flow rate: 47.5 Nm3 /h), and a mass flow meter: FE-H20-GAS (nominal flow rate: 2 Nm3 /h) and a pressure gauge, respectively. The accuracies of the liquid Venturi flow meters and the gas orifice flow meters are ±0.1% FS (full scale) and ±0.5% FS respectively at ambient temperature of 0–55 ◦ C. The measurable range of the pressure gauge is 0–5 kg/cm2 and its maximum measurement error is 1% FS. The pressure distribution along the flow was obtained by using differential pressure gauges, whose maximum uncertainties were estimated as ±0.1 kPa/m. Optical multi-sensor probes, i.e. flat-tip optical four-sensor probes (Shen et al., 2005, 2008a,b) were installed at 3 axial locations of z/D = 41.5, 82.8 and 113 to obtain the void fraction and gas velocity. Measurements in each axial location were made at 11 radial locations, i.e. r/R = 0, 0.2, 0.4, 0.5, 0.6, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, to obtain local flow parameters of adiabatic air–water two-phase flow. The WE7000 control data acquisition system of Yokogawa Electric Corporation was used together with optical probes at a sampling frequency of 10 kHz for 300 s. After optical multi-sensor probe measurements, Dantec 55R61 X-hot film probe with over heat ratio of 0.1 was used to measure the vertical and circumferential turbulent velocities in two-phase flow. The hot-film probes were traversed in the radial direction in
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the same way as the optical probes. Measured data were acquired using a NI PCI/AT-MIO-16E-1 A/D board at a sampling frequency of 10 kHz for 200 s. The hot-film probe method was calibrated based on the centerline velocity of single-phase flow of water in the flow loop, assuming a 1/n-power law for the turbulent velocity profile (where n = 2.95Re0.0805 ) (Schlichting, 1979). 2.3. Brief introduction of optical four-sensor probe and X-type hot-film probe methods To facilitate reading, the working principles of the optical foursensor probe (Shen et al., 2005, 2008a,b) and X-type hot-film probe (Liu and Bankoff, 1993a,b; Bruun, 1995) are introduced briefly here. The working principle of an optical probe is based on the refraction and reflection laws in the optical fiber. A liquid–gas interface passing by the tip of the probe causes the laser light to change from one reflection state to another. Thus, the existence of liquid or gas around the optical fiber tip can be distinguished in a two-phase flow. The time-averaged local void fraction is measured by using the ratio of the accumulated time when an optical fiber tip is in gas phase to the total sampling period. A four-sensor probe consists of one front sensor and three rear sensors. There exist 3 pairs of double-sensor probe, which composes of the front sensor and one rear sensor. The time-averaged void fraction of the front sensor is usually used as the representative value of the four-sensor probe. By assuming that (1) the gas phase velocity equals the interfacial velocity and (2) the bubbles flow parallel to the four-sensor probe direction, viz., the axial main flow direction, we can approximate the interfacial velocity by using the ratio of two sensor tip separation to the time difference when the interface is passing the two sensor tips in each double-sensor probe. Finally the average value of the interfacial velocities from the 3 pairs or available pairs (when the bubble misses one or two rear sensors) is taken as the measured gas velocity of the four-sensor probe. As a result of that, we know that the measured gas velocity is not reliable, when the lateral bubbly flow prevails in the two-phase flow. The hot-film anemometer measures fluid velocity by sensing the change in heat transfer from a small, electrically heated element (namely, sensor) exposed to the fluid. In the CTA (constant temperature anemometer), the cooling effect caused by the flow passing the element is balanced by the electrical current to the element so that the element is held at a constant temperature. The change in current due to a change in flow velocity shows up as a voltage at the anemometer output. In two-phase flow, the void fraction is calculated on basis of the probe signal level that is markedly different in the gas and liquid phases. The X-type hot-film probe positions two sensors in an “X” configuration, for measuring two components of flow. If the two sensors are further aligned so that the angle between them is 45◦ and the velocity component normal to the plane formed by the two sensors is negligible, the axial velocity component (viz. the main flow) is expressed by
vl =
vA,eff + vB,eff . √ 2
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ing from 0.0016 to 0.093 m/s, and the superficial liquid velocity, jl from 0.0501 to 0.311 m/s. Their corresponding ranges of singlephase Reynolds numbers, Reg (=jg × D/g ) and Rel (=jl × D/l ) are 20–1175 for gas phase and 11,224–69,675 for liquid phase respectively. The upper range for liquid phase is limited by the centrifugal pump and that for gas phase is by X-type hot-film probe and optical multi-sensor probe. The superficial gas velocity, jg , shown here and in Figs. 2–4 is used for representing the gas flow condition and estimated based on the normal condition (1 atm and 0 ◦ C). The jg values in Figs. 7 and 10–18 are determined by their corresponding local pressure and temperature. 3. Experimental result 3.1. Optical multi-sensor probe measurement In optical multi-sensor probe measurement, we obtained the time-averaged local void fraction and the time-averaged local rising gas velocity. Typical radial distributions of measured timeaveraged local void fraction (at jl = 0.311 m/s) are shown in Fig. 2. The figure shows that the radial distributions of void fraction change from a slight wall-peak shape to a core-peak one or grow in the core-peak height as the gas flow rate increases at a given superficial liquid velocity. Radial profile of void fraction with a slight wall-peak shape was observed commonly in the low void fraction region. The radial void fraction profiles vary from a slight wall-peak shape to a core-peak shape or change the core-peak shape to be steeper with the flow development in the axial direction. As result of that, it is difficult for the flow to develop into a fully developed flow even in the large z/D (=41.5–113) region. This phenomenon could be attributed mainly to the expansion of gas phase caused by local pressure reduction along the flow direction. Typical radial distributions of time-averaged rising gas velocity (i.e. local mean gas velocity), vg , obtained at jl = 0.311 m/s are
(1)
where vA,eff and vB,eff are, respectively, the effective velocities of the two sensor “A” and “B”, which are obtained from the outputs of the two sensors and the calibration curves. Since the radial and circumferential components of the velocity vector are small in comparison to the axial component, it is possible for us to measure the axial velocity component, viz. the rising liquid velocity, in present experimental range. 2.4. Experimental ranges The adiabatic air–water flow experiments were performed under the flow conditions of the superficial gas velocity, jg rang-
Fig. 2. Radial distribution of time-averaged void fraction at jl = 0.311 m/s.
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shown in Fig. 3. From this figure, the local mean gas velocity profile shows a fairly uniform distribution in the upstream flow region. As the flow develops or the gas flow increases at a constant liquid flow rate, the local mean gas velocity increases and its profile becomes steeper. This trend in the profile of local mean gas velocity can be attributed to the bubble expansion and coalescence with increasing gas flow rate. 3.2. X-type hot-film probe measurement
Fig. 3. Radial distribution of time-averaged rising gas velocity at jl = 0.311 m/s.
The analysis of hot-film signals leads to evaluation of void fraction and the velocity of continuous-phase, i.e. liquid phase in the present case. Since we can obtain the void fraction using the optical multi-sensor probe method, the void fraction measured by the hotfilm probe method was not used in the following drift flux model calculation, but was compared with the results from the other measurement methods. The time-averaged rising liquid velocity, vl , is obtained by removing both the bubble and the meniscusaffected portions from the signals. Typical radial distributions for the time-averaged rising liquid velocity measured at jl = 0.311 m/s are shown in Fig. 4. As the void fraction increases from zero (jg = 0 m/s) to a certain non-zero small value (jg = 0.018 m/s) at a low gas flow rate condition, the radial profile of rising liquid velocity changes from the normal turbulent velocity profile, i.e. following the 1/n-power law, to an approximately flat profile. When the gas flow rate is significantly increased, the profile changes from an approximately flat shape to a core-peaked shape. The approximately flat profile of rising liquid velocity may be due to the turbulence modification by densely concentrated bubbles near the wall. The rising liquid velocity gradually increases in the pipe core region and its radial profile becomes steeper along the flow direction. The increase of rising liquid velocity may be explained by the core-peak phase distribution and the bubble size increase in the flow direction. Due to the significant radial and circumferential motions of the bubbles in high jg flow region, the local measurements using hot-film anemometry were limited within bubbly flow and part of churn flow in the present experiments. 3.3. Result verification In order to verify the accuracy of local measurements by the optical multi-sensor and X-type hot-film probes, we compared the area-averaged void fractions obtained by integrating the timeaveraged local void fractions along the pipe radius with the void fraction measured by the differential pressure (DP) gauges. Since frictional pressure drop is much smaller than gravitational pressure drop in the present low flow rate region, it was neglected in the void fraction measurement by DP. The comparison between optical multi-sensor probe and DP gauges was illustrated in Fig. 5(a) and that between X-type hot-film probe and DP gauges in Fig. 5(b). Reasonably good agreements were obtained among the area-averaged void fractions measured by the local probes and those measured by the DP gauges. The maximum measurement errors in both comparisons are about 10%. The cross-sectional area-averaged superficial liquid velocity can be obtained from its definition: jl =
Fig. 4. Radial distribution of time-averaged rising liquid velocity at jl = 0.311 m/s.
1 A
(1 − ˛)vl dA,
(2)
A
where the void fraction, ˛, and the liquid velocity, vl , are measured with optical multi-sensor probe and X-type hot-film probe, respectively. The superficial liquid velocity jl can also be measured by the calibrated water Venturi flow meter. Thus we can check the local probe measurement against the flow meter measurement. The comparisons were illustrated in Fig. 6. The agreement between the
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Fig. 7. jg from air orifice flow meter versus jg from optical probes.
superficial gas velocity defined by 1 jg = A
˛vg dA.
(3)
A
The superficial gas velocity jg can also be directly measured by the calibrated air orifice flow meter. Thus we can compare the local probe measurement with the flow meter measurement. The comparisons were illustrated in Fig. 7. The agreement between the two measurements is good with a maximum measurement error of about 10%. 3.4. Flow regimes
Fig. 5. Area-averaged void fraction comparison among optical multi-sensor probes, hot-film probes and DP gauges: (a) optical multi-sensor probes and DP gauges and (b) hot-film probes and DP gauges.
two measurements is good with a maximum measurement error of about 16%. From the locally measured ˛ and vg by using an optical multisensor probe, we can calculate the cross-sectional area-averaged
Fig. 6. jl from water Venturi flow meter versus jl from optical probes and hot-film probes.
Ohnuki and Akimoto (2000) investigated experimentally the flow regimes and phase distributions in an upward air–water two-phase flow along a vertical large diameter pipe (D = 0.2 m, z/D = 61.5) based on visual observations. They delineated five types of flow regimes, namely, undisturbed bubbly, agitated bubbly, churn bubbly, churn slug and churn froth. Sawant et al. (2008) pointed out, however, that the flow regime identification by Ohnuki and Akimoto (2000) is highly subjective. The present study shows that the dominant two-phase flow regimes in a vertical large diameter pipe were classified, under the present experimental conditions, into three, namely bubbly flow, churn flow and slug flow as illustrated in Figs. 8 and 9. The bubbly flow regime was observed at low superficial gas velocity or high superficial liquid velocity conditions and it is always developing in the main flow direction. The bubbly flow regime is characterized by small-dispersed bubbles moving upward along the main flow with or without significant local chaotic bubbly motions. Since the difference in characteristic between the undisturbed and agitated bubbly flow regimes in the experiment by Ohnuki and Akimoto (2000) is not important, they can be combined into one group, namely the bubbly flow in this study. The churn flow regime was observed to start forming in the entrance region of the test section at relative high superficial gas and low superficial liquid velocities. The churn flow regime is characterized by the existence of relatively large deformed bubbles agitating the flow and producing strong local turbulence and secondary flow. The slug flow regime appeared at high superficial gas velocity conditions and developed from the bubbly flow and the churn flow in the upstream flow region. The slug flow regime is characterized by the existence of large coalescent cap bubbles (greater than 100 mm in either the cross-sectional diameter or bubble length). They flow upward intermittently, accompanied by numerous small bubbles. These satellite small bubbles sweep the large cap bubble from its nose to the tail and sometimes stagnate. Bubbles ahead of a large cap
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Fig. 8. Dominant flow regimes in the large diameter pipe: (a) bubbly flow, (b) churn flow, and (c) slug flow.
bubble move upward without significant agitation. Bubbles in the wake of the large cap bubble are highly agitated and run quickly after the large cap bubble passing. The flow between two successive large cap bubbles is relatively stable like an upward bubbly flow. The dominant flow regime map based on the high speed video observation is presented in Fig. 10 in terms of the superficial liquid and gas velocities, jl and jg , respectively. The transition from bubbly to slug flow and the phase distribution pattern map, as predicted by Mishima and Ishii (1984) and Serizawa and Kataoka (1988), respectively, are superimposed on the present data in Fig. 10. Since the cap bubble size cannot increase beyond some limiting size due to the surface instability (Kataoka and Ishii, 1987), clear Taylor bubble that almost fully occupies the pipe cross-section was not observed in the present experiment. It can be seen that the bubblyslug transition boundary by Mishima and Ishii (1984) lies between the bubbly flow and the slug flow in the present flow regime map, while the phase distribution pattern map of Serizawa and Kataoka (1988) can predict well the wall-peak phase distribution in bubbly flow and the core-peak phase distribution in slug flow.
Fig. 10. Flow regime map.
4. Drift flux model 4.1. Basic drift flux model The drift–flux model is one of the most practical and accurate models for two-phase-flow analysis. The model takes into account both the effects of non-uniform flow and void fraction profiles as well as the effect of the local relative velocity between phases. It has been utilized to solve many engineering problems involving two-phase-flow dynamics. The one-dimensional drift–flux model
Fig. 9. Photos of dominant flow regimes: (a) bubbly flow, (b) churn flow, and (c) slug flow.
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(Zuber and Findlay, 1965) is given as jg = C0 j + Vgj ˛
(4)
where denotes the area average over the cross-sectional area of the flow path, the distribution parameter, C0 and the mean drift velocity, Vgj are defined by the following equations: C0 = Vgj =
˛j ˛j vgj ˛ ˛
(5) (6)
where vgj is the local drift velocity of gas phase defined as
vgj = vgj − j = (1 − ˛)(vg − vl ).
(7)
Since the effects of non-uniform flow and void fraction profiles are taken into account by the distribution parameter and the effect of the local relative velocity between phases is accounted for by the mean drift velocity, these two quantities are closely linked with flow regimes. 4.2. Distribution parameter and drift velocity One-dimensional drift flux model (Eq. (4)) shows that the distribution parameter C0 and the mean drift velocity Vgj are obtained by using a graph, i.e. the slope and the intercept, respectively, of the line for a plot of jg /˛ versus j. This method has been used commonly in the development of the constitutive equations for those two quantities in a fully developed flow. Since two-phase flow in a large diameter pipe is multi-dimensional and developing, the distribution parameter and the drift velocity obtained by the graphical method may not reflect the reality of the flow. Based on the definitions of the distribution parameter, C0 and the average drift velocity, Vgj in Eqs. (5) and (6), respectively, it is possible to obtain the local C0 and the Vgj from the radial distribution of void fraction, ˛, gas velocity, vg and liquid velocity vl measured by using multi-sensor and hot-film probes, respectively. Shawkat et al. (2008) also experimentally investigated the bubble and liquid turbulence characteristics of air–water bubbly flow in a 200 mm diameter vertical pipe. They measured the time-averaged void fraction and rising gas velocity by using a dual optical probe and the time-averaged liquid-phase turbulent velocity by using the hot-film anemometry. Their measurements were performed at six liquid superficial velocities in the range of 0.2–0.68 m/s and gas superficial velocity from 0.005 to 0.18 m/s, corresponding to an area average void fraction from 1.2% to 15.4%. Based on the local data taken by the present experiments and those by the experiments of Shawkat et al. (2008), we established a database for the C0 and the Vgj in the two-phase flow in a large diameter pipe. According to our visual observation of two-phase flow in a large diameter pipe, flow regimes were classified into three, i.e. bubbly flow, churn flow and slug flow. In order to clearly show the changes in the distribution parameter, C0 and the mean drift velocity, Vgj , in these various flow regimes, we illustrated C0 in Figs. 11 and 12 and Vgj in Figs. 13 and 14, respectively, according to the bubbly flow and churn flow (no data is available for slug flow due to the limitation of local probe techniques). Figs. 11(a) and 13(a) are based on present experimental data and Figs. 11(b) and 13(b) are based on the experimental data of Shawkat et al. (2008). In order to compare the distribution parameter, C0 , and the mean drift velocity, Vgj , measured by graphical method with those by using their definition, we illustrate the plot of jg /˛ versus j for bubbly flow in present experiments in Fig. 15. The experimental data points were fitted by a straight line. Thus, C0 = 0.8886 and Vgj = 0.341 m/s were obtained from the slope and the intercept of
Fig. 11. Distribution parameter, C0 in bubbly flow: (a) present data and (b) Shawkat et al. (2008) data.
the line respectively. By comparing the C0 in Fig. 11(a) and the Vgj in Fig. 13(a), we know that the distribution parameter, C0 , and the mean drift velocity, Vgj , from graphical method differ from those from the method using their definition. The graphical method can get a rough approximation of the C0 and the Vgj only.
Fig. 12. Distribution parameter, C0 in churn flow.
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Fig. 15. Plot of jl /˛ versus j in bubbly flow.
4.3. Comparison between experimental data and predictions of various drift flux correlations
Fig. 13. Mean drift velocity, Vgj in bubbly flow: (a) present data and (b) Shawkat et al. (2008) data.
Fig. 14. Mean drift velocity, Vgj in churn flow.
A literature survey was performed on the major constitutive equations for the drift flux model for upward two-phase flow in a vertical large diameter pipe. The survey results are tabulated in Table 1. Existing constitutive equations for distribution parameter, C0 , from Clark and Flemmer (1986), Ishii (1977) and Hibiki and Ishii (2003) were compared with experimental data in Figs. 11 and 12. The former two equations can predict neither present data nor the experimental data of Shawkat et al. (2008) in both bubbly flow and churn flow. The latter equation of Hibiki and Ishii (2003) can predict distribution parameter, C0 in bubbly flow very well, but over-predict in churn flow when jg /j is between 0.2 and 0.35. Existing constitutive equations for drift velocity, Vgj from Clark and Flemmer (1986), Ishii (1977), Kataoka and Ishii (1987) and Hibiki and Ishii (2003) were compared with the experimental data in Figs. 13 and 14. The predictions by the equations of Clark and Flemmer (1986) and Ishii (1977) (which is for churn flow) lie at the bottom of present database, while the prediction by the equation of Kataoka and Ishii (1987) at the top. The constitutive equation of Hibiki and Ishii (2003) developed by using the interpolation between the equations of Ishii (1977) and Kataoka and Ishii (1987) does not predict well the drift velocity, Vgj in bubbly flow in Fig. 13(a) and (b), when jg /j ranges from 0 to 0.1. Clift et al. (1978) pointed out that the bubble terminal velocity in bounded fluid is less than that in infinite fluid due to the wall effect. Since the constitutive equation developed by Kataoka and Ishii (1987) is based on the experimental data taken in a pool, in which the wall effect is negligible and the bubbles are able to rise freely, their equation predicts the drift velocity, Vgj , to be in its maximum value region. On the other hand, the equations by Clark and Flemmer (1986) and Ishii (1977) are based on the experimental data taken in a relatively small diameter pipe, in which no large bubble was formed or the ratio of the bubble diameter to pipe is relatively large and the wall effect significantly reduces its bubble terminal velocity. So their equations predict the drift velocity, Vgj , to be in its low value region. When the jg takes a very small value and the jg /j ranges from 0 to 0.1, the bubbles in present bubbly flow are able to move freely like in a pool and some bubbles grow readily in size. So their mean drift velocity, Vgj , shows a large value in Fig. 13. Although Hibiki and Ishii (2003) included the wall effect by using the equation of Ishii (1977), they did not take into account of the low void fraction case in which the freely moving of
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Table 1 Constitutive equations for drift flux model related to large diameter pipes. Researchers
Classification
Ishii (1977)
Bubbly flow
C0
Vgj Vgj = √
g
Churn flow
C0 = 1.2 − 0.2
Clark and Flemmer (1986)
(D = 0.1 m)
C0 = 0.93
Kataoka and Ishii (1987)
Nl ≤ 2.25 × 10−3 ∗ DH ≥ 30
C0 = 1.2 − 0.2
−3
Nl ≤ 2.25 × 10 ∗ DH ≥ 30
Hibiki and Ishii (2003)
Uniformly dispersed bubbly flow (˛ > 0.3)
jl j
2
g 2 l
Vgj =
l
√
g
jg j
Vgj =
l
l
g
1.75
1/4
2
g −0.157 g(l −g ) 0.25 l
2 l
Vgj =
−0.562 Nl
g −0.157 g(l −g ) 0.25
0.92
g
2
(1 − (˛))
Vgj = 0.25
Ishii (1977)
exp
l
+ 1.95
0.030
C0 =
1/4
jg 1.69
0.475
for 0 ≤
j jg j
1−
g l
l
Vgj = +
2 l
Vgj,B exp
−1.39jg
g
l
≤ 0.9,
1 − exp
Vgj,P
−0.25 +
2
−1.39jg
g
−0.25
2 l
(D = 0.102 m)
C0 =
−2.88
g l
jg j
for 0.9 ≤
+ 4.08 jg j
≤1
1−
g l
Vgj,B = +
√
2
g 2
1/4
1.75
(1 − (˛))
l
Vgj,p : Kataoka and Ishii (1987) equation
the bubbles helps some bubbles to grow in size and the mean drift velocity is resultantly increased. These bubbles, moving freely like in a pool, should have a large drift velocity value, Vgj,P , but the drift velocity equation of Hibiki and Ishii (2003) lets these bubbles take a small value, Vgj,B . As a result of that, it is difficult for the drift veloc-
Fig. 16. Comparison of Hibiki and Ishii prediction with present experiment data.
ity equation of Hibiki and Ishii (2003) to predict the right value in a low void fraction condition. Since a large number of small bubbles, accompanied by some relatively large deformed bubbles, are surging upwardly in the churn flow, the wall-induced reduction of drift velocity depends on the liquid velocity (jl ). When the liquid velocity is large, the wall effect on main flow is weakened and the drift velocity, Vgj , shows a relatively large value. When the liquid velocity is relatively small, the wall effect can be easily transferred to the main flow by the bubble cloud and their drift velocity, Vgj , decreases obviously. We can see this tendency in Fig. 14. In order to re-confirm these points described above, we calculated the void fraction by using the drift flux model with Hibiki and Ishii correlations and compared the calculation results with the present experimental data taken by using differential pressure gauges, and with the experimental data by Shawkat et al. (2008) in Figs. 16 and 17, respectively. Although the calculation results in
Fig. 17. Comparison of Hibiki and Ishii prediction with the experiment data of Shawkat et al. (2008).
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(2003) can predict the right value in bubbly flow, but over-predicts in churn flow when jg /j is between 0.2 and 0.35. (b) None of the existing Vgj correlations can successfully predict the mean drift velocity for the two-phase flow in a large diameter pipe. Acknowledgements The authors are profoundly grateful to Messrs. I. Ohtsu and T. Nishikizawa of JAEA and Mr. Yamada and his group of Nuclear Engineering Co. Ltd. (NECO) for their devoted assistance in the experiments. The work was supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sport and Culture of Japan (Grant No.: 20560774). References
Fig. 18. Comparison of Hibiki and Ishii prediction with the experiment data of Hills (1976).
these two figures colligate the effects of C0 and Vgj , the two figures still show that large differences exist between the Hibiki and Ishii prediction and the experimental data when jg /j is less than 0.1 and jg /j is between 0.2 and 0.35. In Fig. 18, Hibiki and Ishii equation was checked with the air–water experimental data by Hills (1976), which were taken in vertical bubble column with an inner diameter of 0.15 m at superficial gas velocities of 0.07–3.5 m/s and superficial liquid velocities of 0–2.7 m/s. The comparison shows that Hibiki and Ishii correlation is capable of predicting the experimental data well when jl = / 0, but it cannot reasonably predict the experimental data when jl = 0. It may be attributed to the deficiency of the distribution parameter (C0 ) correlation of Hibiki and Ishii (2003), in which C0 does not change with jg (jg /j = 1) at the condition of jl = 0. 5. Conclusions This study can be concluded as follows: (1) we performed local measurements of flow parameters, such as void fraction, gas velocity and liquid velocity, by using hot-film probes, optical multisensor probes and differential pressure gauges in a vertical upward air–water two-phase flow in a large diameter pipe. (2) The dominant flow regimes were carefully investigated and divided into three types, i.e. bubbly flow, churn flow and slug flow in the vertical large diameter. (3) Based on the experiment data of the local flow parameters, we obtained the distribution parameter and the mean drift velocity directly from their definition. (4) The comparison between the predictions by the existing drift flux correlations and the experimental data of the two-phase flow in a large diameter pipe showed that (a) it is not appropriate to predict the distribution parameter, C0 , by using the C0 correlations of Clark and Flemmer (1986) and Ishii (1977) and the C0 correlation of Hibiki and Ishii
Bruun, H.H., 1995. Hot-wire Anemometry: Principles and Signal Analysis. Oxford University Press, New York, NY, USA, pp. 1–445. Clark, N., Flemmer, R., 1986. The effect of varying gas voidage distributions on average holdup in vertical bubble flow. Int. J. Multiphase Flow 12 (2), 299–302. Clift, R., Grace, J.R., Weber, M.E., 1978. Bubbles, Drops and Particles. Academic Press. Hibiki, T., Ishii, M., 2003. One-dimensional drift–flux model for two-phase flow in a large diameter pipe. Int. J. Heat Mass Transfer 40 (10), 1773–1790. Hills, J., 1976. The Operation of a bubble column at high throughputs I. Gas holdup measurement. Chem. Eng. J. 12 (2), 89–99. Ishii, M., 1977. One-dimensional Drift–flux Model and Constitutive Equations for Relative Motion Between Phases in Various Two-phase Flow Regimes, ANL-7747, USA. Kataoka, I., Ishii, M., 1987. Drift–flux model for large diameter pipe and new correlation for pool void fraction. Int. J. Heat Mass Transfer 30 (9), 1927–1939. Liu, T.J., Bankoff, S.G., 1993a. Structure of air–water bubbly flow in a vertical pipe—I. Liquid mean velocity and turbulence measurements. Int. J. Heat Mass Transfer 36 (4), 1049–1060. Liu, T.J., Bankoff, S.G., 1993b. Structure of air–water bubbly flow in a vertical pipe—II. Void fraction. Bubble velocity and bubble size distribution. Int. J. Heat Mass Transfer 36 (4), 1061–1072. Mishima, K., Ishii, M., 1984. Flow regime transition criteria for upward two-phase flow in vertical tubes. Int. J. Heat Mass Transfer 27 (5), 727–737. Ohnuki, A., Akimoto, H., 2000. Experimental study on transition of flow pattern and phase distribution in upward air–water two-phase flow along a large vertical pipe. Int. J. Multiphase Flow 26 (3), 367–386. Sawant, P., Schelegel, J., Paranjape, S., Ozar, B., Hibiki, T., Ishii, M., 2008. Flow regime identification in large diameter pipe. In: The 16th International Conference on Nuclear Engineering, Orlanda, FL, USA, May 11–15, ICONE16-48311. Schlichting, H., 1979. Boundary Layer Theory. McGraw Hill, New York, NY, USA, pp. 1–200. Serizawa, A., Kataoka, I., 1988. Phase distribution in two-phase flow. In: Afgan, N.H. (Ed.), Transient Phenomena in Multiphase Flow. Hemisphere, Washington, DC, pp. 179–224. Shawkat, M., Ching, C., Shoukri, M., 2008. Bubble and liquid turbulence characteristics of bubbly flow in a large diameter vertical pipe. Int. J. Multiphase Flow 34 (8), 767–785. Shen, X., Saito, Y., Mishima, K., Nakamura, H., 2005. Methodological improvement of an intrusive four-sensor probe for the multi-dimensional two-phase flow measurement. Int. J. Multiphase Flow 31 (5), 593–617. Shen, X., Mishima, K., Nakamura, H., 2008a. Error reduction, evaluation and correction for the intrusive optical four-sensor probe measurement in multidimensional two-phase flow. Int. J. Heat Mass Transfer 51 (3–4), 882–895. Shen, X., Mishima, K., Nakamura, H., 2008b. A method for measuring local instantaneous interfacial velocity vector in multi-dimensional two-phase flow. Int. J. Multiphase Flow 34 (5), 502–509. Zuber, N., Findlay, J.A., 1965. Average volumetric concentration in two-phase flow systems. J. Heat Transfer 87, 453–468.
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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Distribution parameter and drift velocity for two-phase flow in a large diameter pipe Xiuzhong Shen a,∗ , Ryota Matsui a , Kaichiro Mishima a , Hideo Nakamura b a b
Research Reactor Institute, Kyoto University, West Asashiro 2-1010, Kumatori-cho, Sennan-gun, Osaka 590-0494, Japan Nuclear Safety Research Center, Japan Atomic Energy Agency, Tokai-mura, Ibaraki 319-1195, Japan
a r t i c l e
i n f o
Article history: Received 31 August 2009 Received in revised form 21 December 2009 Accepted 13 January 2010
a b s t r a c t In view of practical importance of the drift flux model for two-phase flow analysis in general, and in the analysis of nuclear reactor transients and accidents in particular, the distribution parameter, and the drift velocity have been studied for two-phase flow in a vertical large diameter pipe. In this, study, local measurements were performed on flow parameters, such as void fraction, gas velocity and, liquid velocity in a vertical upward air–water two-phase flow in a pipe of 200 mm inner diameter and, 25 m in height by using the local sensor techniques such as hot-film probes, optical multi-sensor, probes and differential pressure gauges. Two-phase flow regimes in a vertical large diameter pipe, were classified into bubbly, churn and slug flows according to the visual observation. The values of the, distribution parameter and the mean drift velocity were determined directly by their definition using experiment data of the local flow parameters in a two-phase flow in a large diameter pipe. Various existing drift flux correlations were compared with the present experimental results and experimental data obtained by other researchers. A detailed discussion on the problems of these correlations was presented in this paper. Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved.
1. Introduction Since the motions of two phases are strongly coupled in a bubbly flow in a large diameter pipe, the drift flux model is appropriate in the analysis of flow characteristics. An extensive number of experimental and theoretical works have been performed for the distribution parameter and the drift velocity in a flow in a large diameter pipe. It should be mentioned here that the distribution parameter and the drift velocity used in the development of the existing drift flux models are obtained indirectly from the slope and the intercept of the line, respectively, in a plot of jg /˛ versus j. However, the two-phase flow in a large diameter pipe may not be fully developed and their flow patterns may vary remarkably with the flow development, especially at low flow rate. Since the distribution parameter and the drift velocity are closely linked with the flow pattern, their values determined from such plots, in some cases, may not reflect the true values of the flow. So the existing correlations may be approximate drift flux correlations. Recent development of local probe techniques enables the measurement of local flow parameters such as void fraction, and gas and liquid velocities. The values of the distribution parameter and the drift
∗ Corresponding author. Tel.: +81 72 451 2456; fax: +81 72 451 2620. E-mail address: [email protected] (X. Shen).
velocity can be obtained directly from their definition by using the local experimental data of two-phase flow. Further development of detailed and more rigorous drift flux correlations becomes possible. The purposes of this study are (1) to experimentally investigate on the characteristics of air–water two-phase flow in a vertical large diameter pipe, (2) to directly measure the distribution parameter and drift velocity from their definition by using the local experimental data of two-phase flow and establish a large diameter pipe database, (3) to re-estimate existing constitutive equations for the drift flux model in a large diameter pipe, and (4) to make a preparation for developing a new drift flux correlation applicable to two-phase flow in a large diameter pipe. Therefore, the authors conducted local measurements of flow parameters (void fraction, gas velocity and liquid velocity) in a vertical upward air–water two-phase flow in a pipe of 200 mm inner diameter and 25 m in height by using the local sensor techniques and established a database for local parameters for a two-phase flow in a large diameter pipe. Two-phase flow characteristics in a large diameter pipe are analyzed on the basis of these experimental results. The database is further expanded by including the experimental data obtained by other researchers. Various existing drift flux correlations were compared with our newly established experimental database. Their existing problems were carefully studied in the present paper.
0029-5493/$ – see front matter. Crown Copyright © 2010 Published by Elsevier B.V. All rights reserved. doi:10.1016/j.nucengdes.2010.01.004
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Nomenclature C0 j jg jl Re
vA,eff vB,eff vg Vgj
vgj Vgj,B Vgj,P
vl
distribution parameter mixture volumetric flux (m/s) superficial gas velocity (m/s) superficial liquid velocity (m/s) Reynolds number effective velocity of the sensor “A” (m/s) effective velocity of the sensor “B” (m/s) time-averaged rising velocity of gas phase (m/s) void-fraction-weighted mean drift velocity (m/s) drift velocity of gas phase (m/s) mean drift velocity for bubbly flow predicted by Ishii (1977) (m/s) mean drift velocity for pool system predicted by Kataoka and Ishii (1987) (m/s) rising velocity of liquid phase, or time-averaged rising velocity of liquid phase (m/s)
Greek Letters ˛ void fraction kinematic viscosity (m/s) Subscripts g gas phase l liquid phase
2. Experimental 2.1. Experimental rig The present study was carried out by using the Large Scale Test Facility (LSTF) of the adiabatic air–water two-phase flow in the Japan Atomic Energy Agency (JAEA). Fig. 1 shows the experimental facility layout. Purified water was used in the experimental loop and renewed every day during the experimental period to maintain the water quality. Water was kept in the lower reservoir tank, and was pumped with a positive displacement, centrifugal pump, capable of providing a constant head with minimum pressure oscillation. For adiabatic air–water flow experiments, porous sinter tubes with grain size of 40 m were used as air injectors. The water, which flowed through one Venturi flow meter, was divided into four separate flows and then mixed with air in the center of the mixer, while the water, which flowed through the other Venturi flow meter, was divided into two separate flows and then mixed with the former mixed air–water flow before they were injected into the test section. The two-phase mixture flowed out of the test section to enter a separator, namely, the open upper reservoir tank. The air was discharged there and the water was circulated through the loop. The water temperature was kept at a constant temperature within the deviation of ±1 ◦ C during each experimental period. Due to the high pressure in the lower part of the facility, the test section was made of stainless steel round pipe in the low part for its solidity and the transparent acrylic resin round pipes in the upper part to enable flow observation. All the pipes used for the test section were 200 mm in inner diameter. The overall height of the test section, not including the height of the upper reservoir tank, was about 25 m. 2.2. Instrumentation and data acquisition system The inlet water flow rate and water pressure were measured by using Venturi flow meters (25 and 50 mm in inner diameters, respectively) and a pressure gauge, respectively. The inlet
Fig. 1. Schematic diagram of the experimental loop.
gas flow rate and gas pressure were measured by using orifice flow meters: FE-H11-GAS (nominal flow rate: 73.8 Nm3 /h) and FEH12-GAS (nominal flow rate: 47.5 Nm3 /h), and a mass flow meter: FE-H20-GAS (nominal flow rate: 2 Nm3 /h) and a pressure gauge, respectively. The accuracies of the liquid Venturi flow meters and the gas orifice flow meters are ±0.1% FS (full scale) and ±0.5% FS respectively at ambient temperature of 0–55 ◦ C. The measurable range of the pressure gauge is 0–5 kg/cm2 and its maximum measurement error is 1% FS. The pressure distribution along the flow was obtained by using differential pressure gauges, whose maximum uncertainties were estimated as ±0.1 kPa/m. Optical multi-sensor probes, i.e. flat-tip optical four-sensor probes (Shen et al., 2005, 2008a,b) were installed at 3 axial locations of z/D = 41.5, 82.8 and 113 to obtain the void fraction and gas velocity. Measurements in each axial location were made at 11 radial locations, i.e. r/R = 0, 0.2, 0.4, 0.5, 0.6, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, to obtain local flow parameters of adiabatic air–water two-phase flow. The WE7000 control data acquisition system of Yokogawa Electric Corporation was used together with optical probes at a sampling frequency of 10 kHz for 300 s. After optical multi-sensor probe measurements, Dantec 55R61 X-hot film probe with over heat ratio of 0.1 was used to measure the vertical and circumferential turbulent velocities in two-phase flow. The hot-film probes were traversed in the radial direction in
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the same way as the optical probes. Measured data were acquired using a NI PCI/AT-MIO-16E-1 A/D board at a sampling frequency of 10 kHz for 200 s. The hot-film probe method was calibrated based on the centerline velocity of single-phase flow of water in the flow loop, assuming a 1/n-power law for the turbulent velocity profile (where n = 2.95Re0.0805 ) (Schlichting, 1979). 2.3. Brief introduction of optical four-sensor probe and X-type hot-film probe methods To facilitate reading, the working principles of the optical foursensor probe (Shen et al., 2005, 2008a,b) and X-type hot-film probe (Liu and Bankoff, 1993a,b; Bruun, 1995) are introduced briefly here. The working principle of an optical probe is based on the refraction and reflection laws in the optical fiber. A liquid–gas interface passing by the tip of the probe causes the laser light to change from one reflection state to another. Thus, the existence of liquid or gas around the optical fiber tip can be distinguished in a two-phase flow. The time-averaged local void fraction is measured by using the ratio of the accumulated time when an optical fiber tip is in gas phase to the total sampling period. A four-sensor probe consists of one front sensor and three rear sensors. There exist 3 pairs of double-sensor probe, which composes of the front sensor and one rear sensor. The time-averaged void fraction of the front sensor is usually used as the representative value of the four-sensor probe. By assuming that (1) the gas phase velocity equals the interfacial velocity and (2) the bubbles flow parallel to the four-sensor probe direction, viz., the axial main flow direction, we can approximate the interfacial velocity by using the ratio of two sensor tip separation to the time difference when the interface is passing the two sensor tips in each double-sensor probe. Finally the average value of the interfacial velocities from the 3 pairs or available pairs (when the bubble misses one or two rear sensors) is taken as the measured gas velocity of the four-sensor probe. As a result of that, we know that the measured gas velocity is not reliable, when the lateral bubbly flow prevails in the two-phase flow. The hot-film anemometer measures fluid velocity by sensing the change in heat transfer from a small, electrically heated element (namely, sensor) exposed to the fluid. In the CTA (constant temperature anemometer), the cooling effect caused by the flow passing the element is balanced by the electrical current to the element so that the element is held at a constant temperature. The change in current due to a change in flow velocity shows up as a voltage at the anemometer output. In two-phase flow, the void fraction is calculated on basis of the probe signal level that is markedly different in the gas and liquid phases. The X-type hot-film probe positions two sensors in an “X” configuration, for measuring two components of flow. If the two sensors are further aligned so that the angle between them is 45◦ and the velocity component normal to the plane formed by the two sensors is negligible, the axial velocity component (viz. the main flow) is expressed by
vl =
vA,eff + vB,eff . √ 2
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ing from 0.0016 to 0.093 m/s, and the superficial liquid velocity, jl from 0.0501 to 0.311 m/s. Their corresponding ranges of singlephase Reynolds numbers, Reg (=jg × D/g ) and Rel (=jl × D/l ) are 20–1175 for gas phase and 11,224–69,675 for liquid phase respectively. The upper range for liquid phase is limited by the centrifugal pump and that for gas phase is by X-type hot-film probe and optical multi-sensor probe. The superficial gas velocity, jg , shown here and in Figs. 2–4 is used for representing the gas flow condition and estimated based on the normal condition (1 atm and 0 ◦ C). The jg values in Figs. 7 and 10–18 are determined by their corresponding local pressure and temperature. 3. Experimental result 3.1. Optical multi-sensor probe measurement In optical multi-sensor probe measurement, we obtained the time-averaged local void fraction and the time-averaged local rising gas velocity. Typical radial distributions of measured timeaveraged local void fraction (at jl = 0.311 m/s) are shown in Fig. 2. The figure shows that the radial distributions of void fraction change from a slight wall-peak shape to a core-peak one or grow in the core-peak height as the gas flow rate increases at a given superficial liquid velocity. Radial profile of void fraction with a slight wall-peak shape was observed commonly in the low void fraction region. The radial void fraction profiles vary from a slight wall-peak shape to a core-peak shape or change the core-peak shape to be steeper with the flow development in the axial direction. As result of that, it is difficult for the flow to develop into a fully developed flow even in the large z/D (=41.5–113) region. This phenomenon could be attributed mainly to the expansion of gas phase caused by local pressure reduction along the flow direction. Typical radial distributions of time-averaged rising gas velocity (i.e. local mean gas velocity), vg , obtained at jl = 0.311 m/s are
(1)
where vA,eff and vB,eff are, respectively, the effective velocities of the two sensor “A” and “B”, which are obtained from the outputs of the two sensors and the calibration curves. Since the radial and circumferential components of the velocity vector are small in comparison to the axial component, it is possible for us to measure the axial velocity component, viz. the rising liquid velocity, in present experimental range. 2.4. Experimental ranges The adiabatic air–water flow experiments were performed under the flow conditions of the superficial gas velocity, jg rang-
Fig. 2. Radial distribution of time-averaged void fraction at jl = 0.311 m/s.
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shown in Fig. 3. From this figure, the local mean gas velocity profile shows a fairly uniform distribution in the upstream flow region. As the flow develops or the gas flow increases at a constant liquid flow rate, the local mean gas velocity increases and its profile becomes steeper. This trend in the profile of local mean gas velocity can be attributed to the bubble expansion and coalescence with increasing gas flow rate. 3.2. X-type hot-film probe measurement
Fig. 3. Radial distribution of time-averaged rising gas velocity at jl = 0.311 m/s.
The analysis of hot-film signals leads to evaluation of void fraction and the velocity of continuous-phase, i.e. liquid phase in the present case. Since we can obtain the void fraction using the optical multi-sensor probe method, the void fraction measured by the hotfilm probe method was not used in the following drift flux model calculation, but was compared with the results from the other measurement methods. The time-averaged rising liquid velocity, vl , is obtained by removing both the bubble and the meniscusaffected portions from the signals. Typical radial distributions for the time-averaged rising liquid velocity measured at jl = 0.311 m/s are shown in Fig. 4. As the void fraction increases from zero (jg = 0 m/s) to a certain non-zero small value (jg = 0.018 m/s) at a low gas flow rate condition, the radial profile of rising liquid velocity changes from the normal turbulent velocity profile, i.e. following the 1/n-power law, to an approximately flat profile. When the gas flow rate is significantly increased, the profile changes from an approximately flat shape to a core-peaked shape. The approximately flat profile of rising liquid velocity may be due to the turbulence modification by densely concentrated bubbles near the wall. The rising liquid velocity gradually increases in the pipe core region and its radial profile becomes steeper along the flow direction. The increase of rising liquid velocity may be explained by the core-peak phase distribution and the bubble size increase in the flow direction. Due to the significant radial and circumferential motions of the bubbles in high jg flow region, the local measurements using hot-film anemometry were limited within bubbly flow and part of churn flow in the present experiments. 3.3. Result verification In order to verify the accuracy of local measurements by the optical multi-sensor and X-type hot-film probes, we compared the area-averaged void fractions obtained by integrating the timeaveraged local void fractions along the pipe radius with the void fraction measured by the differential pressure (DP) gauges. Since frictional pressure drop is much smaller than gravitational pressure drop in the present low flow rate region, it was neglected in the void fraction measurement by DP. The comparison between optical multi-sensor probe and DP gauges was illustrated in Fig. 5(a) and that between X-type hot-film probe and DP gauges in Fig. 5(b). Reasonably good agreements were obtained among the area-averaged void fractions measured by the local probes and those measured by the DP gauges. The maximum measurement errors in both comparisons are about 10%. The cross-sectional area-averaged superficial liquid velocity can be obtained from its definition: jl =
Fig. 4. Radial distribution of time-averaged rising liquid velocity at jl = 0.311 m/s.
1 A
(1 − ˛)vl dA,
(2)
A
where the void fraction, ˛, and the liquid velocity, vl , are measured with optical multi-sensor probe and X-type hot-film probe, respectively. The superficial liquid velocity jl can also be measured by the calibrated water Venturi flow meter. Thus we can check the local probe measurement against the flow meter measurement. The comparisons were illustrated in Fig. 6. The agreement between the
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Fig. 7. jg from air orifice flow meter versus jg from optical probes.
superficial gas velocity defined by 1 jg = A
˛vg dA.
(3)
A
The superficial gas velocity jg can also be directly measured by the calibrated air orifice flow meter. Thus we can compare the local probe measurement with the flow meter measurement. The comparisons were illustrated in Fig. 7. The agreement between the two measurements is good with a maximum measurement error of about 10%. 3.4. Flow regimes
Fig. 5. Area-averaged void fraction comparison among optical multi-sensor probes, hot-film probes and DP gauges: (a) optical multi-sensor probes and DP gauges and (b) hot-film probes and DP gauges.
two measurements is good with a maximum measurement error of about 16%. From the locally measured ˛ and vg by using an optical multisensor probe, we can calculate the cross-sectional area-averaged
Fig. 6. jl from water Venturi flow meter versus jl from optical probes and hot-film probes.
Ohnuki and Akimoto (2000) investigated experimentally the flow regimes and phase distributions in an upward air–water two-phase flow along a vertical large diameter pipe (D = 0.2 m, z/D = 61.5) based on visual observations. They delineated five types of flow regimes, namely, undisturbed bubbly, agitated bubbly, churn bubbly, churn slug and churn froth. Sawant et al. (2008) pointed out, however, that the flow regime identification by Ohnuki and Akimoto (2000) is highly subjective. The present study shows that the dominant two-phase flow regimes in a vertical large diameter pipe were classified, under the present experimental conditions, into three, namely bubbly flow, churn flow and slug flow as illustrated in Figs. 8 and 9. The bubbly flow regime was observed at low superficial gas velocity or high superficial liquid velocity conditions and it is always developing in the main flow direction. The bubbly flow regime is characterized by small-dispersed bubbles moving upward along the main flow with or without significant local chaotic bubbly motions. Since the difference in characteristic between the undisturbed and agitated bubbly flow regimes in the experiment by Ohnuki and Akimoto (2000) is not important, they can be combined into one group, namely the bubbly flow in this study. The churn flow regime was observed to start forming in the entrance region of the test section at relative high superficial gas and low superficial liquid velocities. The churn flow regime is characterized by the existence of relatively large deformed bubbles agitating the flow and producing strong local turbulence and secondary flow. The slug flow regime appeared at high superficial gas velocity conditions and developed from the bubbly flow and the churn flow in the upstream flow region. The slug flow regime is characterized by the existence of large coalescent cap bubbles (greater than 100 mm in either the cross-sectional diameter or bubble length). They flow upward intermittently, accompanied by numerous small bubbles. These satellite small bubbles sweep the large cap bubble from its nose to the tail and sometimes stagnate. Bubbles ahead of a large cap
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Fig. 8. Dominant flow regimes in the large diameter pipe: (a) bubbly flow, (b) churn flow, and (c) slug flow.
bubble move upward without significant agitation. Bubbles in the wake of the large cap bubble are highly agitated and run quickly after the large cap bubble passing. The flow between two successive large cap bubbles is relatively stable like an upward bubbly flow. The dominant flow regime map based on the high speed video observation is presented in Fig. 10 in terms of the superficial liquid and gas velocities, jl and jg , respectively. The transition from bubbly to slug flow and the phase distribution pattern map, as predicted by Mishima and Ishii (1984) and Serizawa and Kataoka (1988), respectively, are superimposed on the present data in Fig. 10. Since the cap bubble size cannot increase beyond some limiting size due to the surface instability (Kataoka and Ishii, 1987), clear Taylor bubble that almost fully occupies the pipe cross-section was not observed in the present experiment. It can be seen that the bubblyslug transition boundary by Mishima and Ishii (1984) lies between the bubbly flow and the slug flow in the present flow regime map, while the phase distribution pattern map of Serizawa and Kataoka (1988) can predict well the wall-peak phase distribution in bubbly flow and the core-peak phase distribution in slug flow.
Fig. 10. Flow regime map.
4. Drift flux model 4.1. Basic drift flux model The drift–flux model is one of the most practical and accurate models for two-phase-flow analysis. The model takes into account both the effects of non-uniform flow and void fraction profiles as well as the effect of the local relative velocity between phases. It has been utilized to solve many engineering problems involving two-phase-flow dynamics. The one-dimensional drift–flux model
Fig. 9. Photos of dominant flow regimes: (a) bubbly flow, (b) churn flow, and (c) slug flow.
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(Zuber and Findlay, 1965) is given as jg = C0 j + Vgj ˛
(4)
where denotes the area average over the cross-sectional area of the flow path, the distribution parameter, C0 and the mean drift velocity, Vgj are defined by the following equations: C0 = Vgj =
˛j ˛j vgj ˛ ˛
(5) (6)
where vgj is the local drift velocity of gas phase defined as
vgj = vgj − j = (1 − ˛)(vg − vl ).
(7)
Since the effects of non-uniform flow and void fraction profiles are taken into account by the distribution parameter and the effect of the local relative velocity between phases is accounted for by the mean drift velocity, these two quantities are closely linked with flow regimes. 4.2. Distribution parameter and drift velocity One-dimensional drift flux model (Eq. (4)) shows that the distribution parameter C0 and the mean drift velocity Vgj are obtained by using a graph, i.e. the slope and the intercept, respectively, of the line for a plot of jg /˛ versus j. This method has been used commonly in the development of the constitutive equations for those two quantities in a fully developed flow. Since two-phase flow in a large diameter pipe is multi-dimensional and developing, the distribution parameter and the drift velocity obtained by the graphical method may not reflect the reality of the flow. Based on the definitions of the distribution parameter, C0 and the average drift velocity, Vgj in Eqs. (5) and (6), respectively, it is possible to obtain the local C0 and the Vgj from the radial distribution of void fraction, ˛, gas velocity, vg and liquid velocity vl measured by using multi-sensor and hot-film probes, respectively. Shawkat et al. (2008) also experimentally investigated the bubble and liquid turbulence characteristics of air–water bubbly flow in a 200 mm diameter vertical pipe. They measured the time-averaged void fraction and rising gas velocity by using a dual optical probe and the time-averaged liquid-phase turbulent velocity by using the hot-film anemometry. Their measurements were performed at six liquid superficial velocities in the range of 0.2–0.68 m/s and gas superficial velocity from 0.005 to 0.18 m/s, corresponding to an area average void fraction from 1.2% to 15.4%. Based on the local data taken by the present experiments and those by the experiments of Shawkat et al. (2008), we established a database for the C0 and the Vgj in the two-phase flow in a large diameter pipe. According to our visual observation of two-phase flow in a large diameter pipe, flow regimes were classified into three, i.e. bubbly flow, churn flow and slug flow. In order to clearly show the changes in the distribution parameter, C0 and the mean drift velocity, Vgj , in these various flow regimes, we illustrated C0 in Figs. 11 and 12 and Vgj in Figs. 13 and 14, respectively, according to the bubbly flow and churn flow (no data is available for slug flow due to the limitation of local probe techniques). Figs. 11(a) and 13(a) are based on present experimental data and Figs. 11(b) and 13(b) are based on the experimental data of Shawkat et al. (2008). In order to compare the distribution parameter, C0 , and the mean drift velocity, Vgj , measured by graphical method with those by using their definition, we illustrate the plot of jg /˛ versus j for bubbly flow in present experiments in Fig. 15. The experimental data points were fitted by a straight line. Thus, C0 = 0.8886 and Vgj = 0.341 m/s were obtained from the slope and the intercept of
Fig. 11. Distribution parameter, C0 in bubbly flow: (a) present data and (b) Shawkat et al. (2008) data.
the line respectively. By comparing the C0 in Fig. 11(a) and the Vgj in Fig. 13(a), we know that the distribution parameter, C0 , and the mean drift velocity, Vgj , from graphical method differ from those from the method using their definition. The graphical method can get a rough approximation of the C0 and the Vgj only.
Fig. 12. Distribution parameter, C0 in churn flow.
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Fig. 15. Plot of jl /˛ versus j in bubbly flow.
4.3. Comparison between experimental data and predictions of various drift flux correlations
Fig. 13. Mean drift velocity, Vgj in bubbly flow: (a) present data and (b) Shawkat et al. (2008) data.
Fig. 14. Mean drift velocity, Vgj in churn flow.
A literature survey was performed on the major constitutive equations for the drift flux model for upward two-phase flow in a vertical large diameter pipe. The survey results are tabulated in Table 1. Existing constitutive equations for distribution parameter, C0 , from Clark and Flemmer (1986), Ishii (1977) and Hibiki and Ishii (2003) were compared with experimental data in Figs. 11 and 12. The former two equations can predict neither present data nor the experimental data of Shawkat et al. (2008) in both bubbly flow and churn flow. The latter equation of Hibiki and Ishii (2003) can predict distribution parameter, C0 in bubbly flow very well, but over-predict in churn flow when jg /j is between 0.2 and 0.35. Existing constitutive equations for drift velocity, Vgj from Clark and Flemmer (1986), Ishii (1977), Kataoka and Ishii (1987) and Hibiki and Ishii (2003) were compared with the experimental data in Figs. 13 and 14. The predictions by the equations of Clark and Flemmer (1986) and Ishii (1977) (which is for churn flow) lie at the bottom of present database, while the prediction by the equation of Kataoka and Ishii (1987) at the top. The constitutive equation of Hibiki and Ishii (2003) developed by using the interpolation between the equations of Ishii (1977) and Kataoka and Ishii (1987) does not predict well the drift velocity, Vgj in bubbly flow in Fig. 13(a) and (b), when jg /j ranges from 0 to 0.1. Clift et al. (1978) pointed out that the bubble terminal velocity in bounded fluid is less than that in infinite fluid due to the wall effect. Since the constitutive equation developed by Kataoka and Ishii (1987) is based on the experimental data taken in a pool, in which the wall effect is negligible and the bubbles are able to rise freely, their equation predicts the drift velocity, Vgj , to be in its maximum value region. On the other hand, the equations by Clark and Flemmer (1986) and Ishii (1977) are based on the experimental data taken in a relatively small diameter pipe, in which no large bubble was formed or the ratio of the bubble diameter to pipe is relatively large and the wall effect significantly reduces its bubble terminal velocity. So their equations predict the drift velocity, Vgj , to be in its low value region. When the jg takes a very small value and the jg /j ranges from 0 to 0.1, the bubbles in present bubbly flow are able to move freely like in a pool and some bubbles grow readily in size. So their mean drift velocity, Vgj , shows a large value in Fig. 13. Although Hibiki and Ishii (2003) included the wall effect by using the equation of Ishii (1977), they did not take into account of the low void fraction case in which the freely moving of
X. Shen et al. / Nuclear Engineering and Design 240 (2010) 3991–4000
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Table 1 Constitutive equations for drift flux model related to large diameter pipes. Researchers
Classification
Ishii (1977)
Bubbly flow
C0
Vgj Vgj = √
g
Churn flow
C0 = 1.2 − 0.2
Clark and Flemmer (1986)
(D = 0.1 m)
C0 = 0.93
Kataoka and Ishii (1987)
Nl ≤ 2.25 × 10−3 ∗ DH ≥ 30
C0 = 1.2 − 0.2
−3
Nl ≤ 2.25 × 10 ∗ DH ≥ 30
Hibiki and Ishii (2003)
Uniformly dispersed bubbly flow (˛ > 0.3)
jl j
2
g 2 l
Vgj =
l
√
g
jg j
Vgj =
l
l
g
1.75
1/4
2
g −0.157 g(l −g ) 0.25 l
2 l
Vgj =
−0.562 Nl
g −0.157 g(l −g ) 0.25
0.92
g
2
(1 − (˛))
Vgj = 0.25
Ishii (1977)
exp
l
+ 1.95
0.030
C0 =
1/4
jg 1.69
0.475
for 0 ≤
j jg j
1−
g l
l
Vgj = +
2 l
Vgj,B exp
−1.39jg
g
l
≤ 0.9,
1 − exp
Vgj,P
−0.25 +
2
−1.39jg
g
−0.25
2 l
(D = 0.102 m)
C0 =
−2.88
g l
jg j
for 0.9 ≤
+ 4.08 jg j
≤1
1−
g l
Vgj,B = +
√
2
g 2
1/4
1.75
(1 − (˛))
l
Vgj,p : Kataoka and Ishii (1987) equation
the bubbles helps some bubbles to grow in size and the mean drift velocity is resultantly increased. These bubbles, moving freely like in a pool, should have a large drift velocity value, Vgj,P , but the drift velocity equation of Hibiki and Ishii (2003) lets these bubbles take a small value, Vgj,B . As a result of that, it is difficult for the drift veloc-
Fig. 16. Comparison of Hibiki and Ishii prediction with present experiment data.
ity equation of Hibiki and Ishii (2003) to predict the right value in a low void fraction condition. Since a large number of small bubbles, accompanied by some relatively large deformed bubbles, are surging upwardly in the churn flow, the wall-induced reduction of drift velocity depends on the liquid velocity (jl ). When the liquid velocity is large, the wall effect on main flow is weakened and the drift velocity, Vgj , shows a relatively large value. When the liquid velocity is relatively small, the wall effect can be easily transferred to the main flow by the bubble cloud and their drift velocity, Vgj , decreases obviously. We can see this tendency in Fig. 14. In order to re-confirm these points described above, we calculated the void fraction by using the drift flux model with Hibiki and Ishii correlations and compared the calculation results with the present experimental data taken by using differential pressure gauges, and with the experimental data by Shawkat et al. (2008) in Figs. 16 and 17, respectively. Although the calculation results in
Fig. 17. Comparison of Hibiki and Ishii prediction with the experiment data of Shawkat et al. (2008).
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(2003) can predict the right value in bubbly flow, but over-predicts in churn flow when jg /j is between 0.2 and 0.35. (b) None of the existing Vgj correlations can successfully predict the mean drift velocity for the two-phase flow in a large diameter pipe. Acknowledgements The authors are profoundly grateful to Messrs. I. Ohtsu and T. Nishikizawa of JAEA and Mr. Yamada and his group of Nuclear Engineering Co. Ltd. (NECO) for their devoted assistance in the experiments. The work was supported by the Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Sport and Culture of Japan (Grant No.: 20560774). References
Fig. 18. Comparison of Hibiki and Ishii prediction with the experiment data of Hills (1976).
these two figures colligate the effects of C0 and Vgj , the two figures still show that large differences exist between the Hibiki and Ishii prediction and the experimental data when jg /j is less than 0.1 and jg /j is between 0.2 and 0.35. In Fig. 18, Hibiki and Ishii equation was checked with the air–water experimental data by Hills (1976), which were taken in vertical bubble column with an inner diameter of 0.15 m at superficial gas velocities of 0.07–3.5 m/s and superficial liquid velocities of 0–2.7 m/s. The comparison shows that Hibiki and Ishii correlation is capable of predicting the experimental data well when jl = / 0, but it cannot reasonably predict the experimental data when jl = 0. It may be attributed to the deficiency of the distribution parameter (C0 ) correlation of Hibiki and Ishii (2003), in which C0 does not change with jg (jg /j = 1) at the condition of jl = 0. 5. Conclusions This study can be concluded as follows: (1) we performed local measurements of flow parameters, such as void fraction, gas velocity and liquid velocity, by using hot-film probes, optical multisensor probes and differential pressure gauges in a vertical upward air–water two-phase flow in a large diameter pipe. (2) The dominant flow regimes were carefully investigated and divided into three types, i.e. bubbly flow, churn flow and slug flow in the vertical large diameter. (3) Based on the experiment data of the local flow parameters, we obtained the distribution parameter and the mean drift velocity directly from their definition. (4) The comparison between the predictions by the existing drift flux correlations and the experimental data of the two-phase flow in a large diameter pipe showed that (a) it is not appropriate to predict the distribution parameter, C0 , by using the C0 correlations of Clark and Flemmer (1986) and Ishii (1977) and the C0 correlation of Hibiki and Ishii
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