- Email: [email protected]
Experimental study of two-phase flow structure in large diameter pipes
Experimental Thermal and Fluid Science 41 (2012) 12–22
Contents lists available at SciVerse ScienceDirect
Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Experimental study of two-phase flow structure in large diameter pipes J.P. Schlegel, S. Miwa, S. Chen, T. Hibiki, M. Ishii ⇑ School of Nuclear Engineering, Purdue University, 400 Central Dr., West Lafayette, IN 47907-2017, United States
a r t i c l e
i n f o
Article history: Received 15 June 2011 Received in revised form 30 November 2011 Accepted 29 January 2012 Available online 15 February 2012 Keywords: Large diameter Interfacial area Two-fluid model Void fraction
a b s t r a c t Current thermal–hydraulic analysis codes use static, flow-regime-dependent empirical models which introduce several sources of error and numerical instability. The interfacial area transport equation offers a more robust, reliable prediction of interfacial area and can allow for dynamic predictions of two-phase flows. In order to develop reliable mechanistic models for interfacial area concentration sources and sinks an extensive database is required, however the current database lacks significant data for pipes larger than 0.1 m diameter and for void fractions above 0.4. To improve and extend the database experiments have been performed in pipes with diameters of 0.152 m and 0.203 m with void fractions of up to 0.7, providing valuable data regarding the local profiles and axial development that can be used to evaluate current interfacial area transport models and assist in the development of new mechanistic models for interfacial area concentration sources and sinks. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction Two phase flows are essential to industrial applications in many fields. In the nuclear industry, fundamental understanding of twophase flows under various conditions is essential for predicting the steady-state behavior of Boiling Water Reactors (BWRs) of all types as well as accident scenarios in both BWRs and Pressurized Water Reactors (PWRs), and even in liquid–metal-cooled reactors. Prediction of behavior in new natural-circulation BWR designs is even more sensitive to the reliability of the models used, as these systems drive natural circulation through the inclusion of a long chimney section above the core to provide sufficient gravity head. This region is extremely sensitive to changes in the flow conditions, and fundamentally sound, accurate models are essential for accurate prediction of the natural circulation flow rate and Reactor Pressure Vessel (RPV) liquid inventory. This region behaves as a large diameter pipe, and indeed many of the flow channels in reactor systems are significantly larger than the transition size,
DH DH ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 40 r=g Dq
ð1Þ
which is about 7 cm under typical BWR conditions, and can therefore be considered as having ‘large diameter.’ Large diameter pipes differ from those considered small diameter because two-phase flows in large pipes can no longer sustain slug bubbles which bridge the entire cross-section of the flow channel, due to Raleigh–Taylor instability. For flow channels larger than the transition value, this interaction of the two types of instability results in large bubbles ⇑ Corresponding author. Tel.: +1 765 494 4587. E-mail address: [email protected] (M. Ishii). 0894-1777/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2012.01.034
being broken into many smaller cap-shaped bubbles. This causes many changes to the hydrodynamics of the flow, producing additional turbulence due to bubble drag, enhancing turbulent diffusion, and producing strong secondary recirculations in the flow. These changes result in very different physical mechanisms behind the transport of gas and liquid, meaning that models typically applied to flows in small-diameter pipes can no longer be guaranteed to predict flows in large-diameter channels accurately [13]. The two-fluid model, sometimes called the six-equation model, is the most-used model in engineering applications today [11]. This model calculates the balance of mass, momentum, and energy for each phase separately. Time-averaging of the equations results in interfacial transfer terms to account for the transfer of these quantities from one phase to the other. While numerical methods such as LES and DNS can provide more accurate results, these types of calculations take much longer than two-fluid model calculations and the two-fluid model can be area-averaged to give a onedimensional form suitable for use in advanced computational codes. The disadvantage to the two-fluid model, and the major challenge facing its implementation, is accurate modeling of the interfacial transfer terms for mass, momentum and energy. The interfacial transfer terms can be expressed as the product of the driving potential for the transfer across the interface (i.e. the interfacial drag for momentum transfer) and a term representing the geometry of the interface, or ‘flow regime.’ This representation of the interfacial geometry is often given as the interfacial area concentration (IAC), ai, which is defined as the amount of surface area per unit volume of the two-phase mixture. The current method used by most advanced system analysis codes is a two-step method. An experimentally determined flow regime map is used to determine the approximate flow geometry
13
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22
Nomenclature Latin characters A area (m2) interfacial area concentration (m1) ai C constant () DH hydraulic diameter (m) g gravitational acceleration (m s2) j superficial velocity (m s1) n normal vector () P pressure (Pa) v velocity (m s1) z axial location (m) Greek characters a void fraction () u interfacial area concentration source or sink (m1 s1) Dq density difference (kg m3)
for a given flow condition, then empirical correlations for the driving force and IAC are used to predict the interfacial transfer. For large pipes, the recommended flow regime map is that given by Schlegel et al. [24], which is supported by other data available in the literature [21]. Using the example of momentum transfer, once the flow regime is determined a drift-flux model such as that developed by Hibiki and Ishii [7] is used to calculate the drag coefficient, then another empirical equation is used to compute the IAC [11]. This approach has two significant problems. The first is the uncertainties in the flow regime boundaries, as the transitions actually occur over a region on the flow regime map and in reality are not abrupt transitions. The second is the error in the empirical models used. These models are developed under steady-state, fully developed conditions and may not be applicable to highly transient conditions such as accident scenarios or reactor startup computations. To mitigate these effects in advanced computational codes, the interfacial area transport equation (IATE) is currently under development [11]. In this approach a transport equation is used to model the change in interfacial area concentration by accounting for the interaction of bubbles given reasonable boundary conditions. This eliminates the requirement for flow regime maps and reduces error and numerical oscillations or bifurcations. The transport equation is also dynamic, allowing the effect of transient conditions to be predicted. Constitutive models for the driving forces are still required, however the ability of the IATE to provide bubble size estimates can also improve the performance of those models. Developing the IATE accurately requires the creation of mechanistic models for IAC sources and sinks due to interactions between bubbles and due to phase change. In order to accomplish this, these models must be developed based on the hydrodynamics of the flow and verified using a database of interfacial area transport measurements. A review of the literature has revealed that while models for flows in small diameter channels are well-developed, the database for flows in large-diameter pipes has significant shortcomings. To remedy this shortcoming, the void fraction, interfacial area concentration, gas velocity and bubble size have been measured at three axial locations in test facilities with diameters of 0.152 m and 0.203 m and at absolute pressures of 180 kPa and 280 kPa. Flow conditions varied widely, with void fractions up to 0.7, much higher than those seen in previous experiments in such large flow channels. 2. Previous work Flows in large pipes and small pipes are very different. These differences are summarized in Table 1. The presence of cap-shaped
r
surface tension (N m) ratio of actual to predicted IAC () time elapsed (s)
n Dt
Sub/superscripts pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ⁄ non-dimensionalized value using r=g Dq 1 group 1 2 group 2 c1 critical value for group 1 f liquid phase g gas phase j measurement or bubble mechanism Operators hi area-averaged quantity void-weighted area-averaged quantity
bubbles also has a strong effect on turbulence in large pipe flows [14]. Along with the lift force and wall lubrication force, turbulence plays an important part in determining the void profiles, i.e. the wall-peaking or center-peaking phenomenon. Increased turbulent diffusion for flows in large diameter pipes can reduce wall-peaking, a phenomenon which has been observed previously by Ohnuki and Akimoto [20,22]. Stronger turbulence can also result in enhanced bubble breakup although these differences may become less significant for higher liquid velocities where the turbulent intensity is already very high [1]. The change in the hydrodynamics can also be noted in various efforts to develop flow regime maps for large pipes and in the differences in the criteria used in small pipe flows and large pipe flows to determine flow regime transitions [21,24]. The major developments related to the development of IATE source and sink terms, a brief review of the status of IATE models in pipes, is given in Table 2. Ishii and Mishima [10] developed the modern formulation of the two-fluid model and developed static IAC correlations for small round pipes. The IATE was first proposed by Kocamustafaogullari and Ishii [16]. It was later modified to account for the expansion and contraction of bubbles due to pressure change [32,5] and has been derived in a two-group form that allows accurate prediction of cap/slug and churn-turbulent flows where two groups of bubbles, small spherical and distorted bubbles and large cap-shaped Taylor bubbles, with very different behaviors exist [5]. These equations can then be area-averaged to develop a onedimensional form that is suitable for inclusion in advanced system analysis codes. This form of the two-group IATE is given as [11]
@hai1 i @ 2 hai1 i @ þ hai1 ihhv i1 ii ¼ CðDc1 Þ2 ha1 ihhv g1 ii @t @z 3 ha1 i @z P þ h/j1 i
ð2Þ
j
@hai2 i @ 2hai2 i @ hai1 i @ þ hai2 ihhv i2 ii ¼ ha2 ihhv g2 ii þ CðDc1 Þ2 @t @z 3ha2 i @z ha1 i @z P ha1 ihhv g1 ii þ h/j2 i j
ð3Þ The meanings of the symbols in these equations can be found in the nomenclature. The boundary between the two bubble groups is defined as the maximum distorted bubble size, which is
Db Db ¼ qffiffiffiffiffiffi ¼ 4: r
g Dq
ð4Þ
14
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22 Table 1 Summary of differences between flows in small and large pipes. Small pipes DH < 2Q
Large pipes DH > 40
Flow structure (Flow regime)
Bubbly, slug, churn-turbulent, annular Mishima and Ishii [19]
Bubbly, cap-turbufent, churn-turbulent, annular Schlegel et al. [24]
Diameter effect
Significant effects Ishii, [8]; Mishima and Ishii [19]
Effect of wall very reduced Kataoka and Ishii [13]; Schlegel et al. [25]
Entrance effect
Injection method insensitive Hibiki and Ishii [5]
Sensitive to injection method Hibiki and Ishii [7]
Recirculation Effects
Insignificant Hibiki and Ishii [5]
Very significant for some flow conditions Kataoka and Ishii [13]
Wall-peaking
Strong for some flow conditions Hibiki and Ishii, [6]
Reduced or eliminated for all flow conditions Ohnuki and Akimoto [20]
Drift-flux model
Available Ishii, [9]; Hibiki and Ishii, 2002
Available Hibiki and Ishii [7]
IAC correlations
Available Hibiki and Ishii, 2002;Hibiki et al. [8]
Available Hibiki et al. [8]
IATE
Available Hibiki and Ishii [5]; Fu and Ishii [3]
Not available
The solution of the IATE requires some changes to the typical two-fluid model. The most significant change is that the continuity equation for the gas phase must be rewritten as two equations, one for each bubble group, with a term added to account for mass transfer between the groups. This term can be computed based on the interfacial area transfer terms. The other major change is appropriate averaging of the momentum equation to account for the differences between the bubble groups. This change is detailed by Sun et al. [31]. Given this form of the IATE, the next necessary step is to develop the source, sink, and inter-group transfer terms which account for bubble interactions. While these interfacial transfer terms have not been well-developed for flows in large diameter pipes, much effort has been devoted to the development of interfacial area transport models for small diameter pipes. One of the most welldeveloped sets of interfacial area transport models was developed by Fu [3,4] for small-diameter pipes. Based on this work, it is possible to determine all of the models which need to be developed for flows in large diameter pipes. In order to develop accurate models for interfacial area transport, an experimental database is needed to aid in determining the relative strengths of each bubble interaction type and to verify the performance of the models which are developed. A review of the literature has found several efforts to measure quantities relevant to interfacial area transport in large pipes which are summarized in Table 3. Fig. 1 illustrates the flow ranges for each of the studies detailed here. As the figure shows, there is a distinct lack of data in the cap/slug and churn-turbulent flow regimes, where
Table 2 Summary of development of IATE for large diameter pipes. Researcher
Significant development
lshii and Mishima [19] Kocamustafaogullari and Ishii [16] Wu et al. [32], Hibiki and Ishii [5] Hibiki and Ishii [5] Sun et al. [31]
Two-fluid model, static IAC correlations Proposal and preliminary formulation of IATE
Fu [3]
Ishii and Hibiki [11]
One-group IATE for small round pipes Two-group IATE forsmall round pipes Modified two-fluid model for use with two p-group IATE Identification of all necessary source and sink models, Updated models for two-group IATE in small round pipes Review of development of IATE and significant models
the two-group form of the IATE is essential to accurately predict two-phase flows. Previously experiments by Smith [29] and Lucas et al. [17] have collected data in this region, however extensive data from Smith [29] has only been collected for pipes of 0.102 m diameter. The data collected by Lucas et al. [17] extends into the churn-turbulent regime and has a similar range of flow conditions to the present study, however it has some limitations. First, the gas is injected from the side of the pipe. This may not mimic the development of typical boiling flows in industrial systems well, as such systems typically have internal heaters. Also, interfacial area concentration measurements are not reported and the current data would be difficult to use for evaluation of interfacial area transport in two-phase systems. Further, the reported data is largely for low void fraction cases. The use of wire mesh sensors presents several possible difficulties. For instance the resolution of the wire mesh sensor is limited to 3 mm, and individual bubble velocities for small bubbles is not directly measured but inferred from cross-correlation of two mesh sensors. Finally, the mesh sensor may distort the bubble interface for large bubbles. Manera et al. [18] showed that for small diameter pipes in the bubbly and slug flow regimes measurements made using wire mesh sensors and local probe techniques agree reasonably well, however this study did not extend to the churn-turbulent flow regime or into pipes with diameters larger than 5.08 cm. Thus the measurements reported in the literature should be confirmed by another measurement method and further expanded for use in evaluation of interfacial area transport models. For that reason it is essential that additional data be collected for pipes of 0.152 m and larger diameter and at higher void fraction conditions in order to facilitate the development and validation of the two-group IATE for flows in large diameter pipes. 3. Experiment Fig. 2 shows a schematic of the facility used in this experiment. The liquid flow rate is measured using a magnetic flow meter with an experimental uncertainty of ±1%, and controlled using a centrifugal pump with a variable frequency drive. Compressed air is supplied by a compressor with a large storage tank and pressure regulator to prevent upstream pressure from having a significant effect on the gas flow rate. The gas flow rate is measured using a Venturi flow meter with uncertainty of ±2%. The air and water are mixed in an injector unit, also shown in Fig. 2, utilizing sintered metal elements surrounded by steel annuli. This configuration
15
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22 Table 3 Summary of experimental research on interfacial area concentration in large pipes. Researcher
Pipe diameter (m)
Void fraction range
Liquid velocity range (m s1)
Instrumentation
Sun et al. [30]
0.102
0.02–0.30
0.00–1.00
Yoneda et al. [33] Shoukri et al. [28] Shen et al. [27] Prasser [23] Shawkat et al. [26] Lucas et al. [17]
0.155 0.200 0.200 0.195 0.200 0.195
0.00–0.20 0.00–0.04 0.00–0.40 0.00–0.30 0.012–0.154 0.01–0.74
0.00–0.60 0.00–0.40 0.14–1.12 1.02 0.2–0.68 0.04–1.6
Four-sensor electrical conductivity probes Dual-sensor optical probes Dual-sensor optical probes Dual-sensor optical probes Wire-mesh sensors Dual-sensor optical probes Wire-mesh sensors
allows the liquid flow rate through the annuli to be controlled so that the initial bubble size can be maintained for a variety of flow conditions. This allows evaluation of the effect of initial bubble size on the properties of the flow, although this analysis is beyond the scope of the current study and in these experiments the liquid velocity in the annuli was held constant so that initial bubble size was approximately constant for all tests. Test sections of 0.152 m and 0.203 m diameter are constructed of clear acrylic to allow flow visualization. Measurements of system pressure and local flow parameters are made at three locations along each test section, at z/D = 11.7, 17.7 and 33.9 in the 0.152 m facility and z/D = 5.4. 9.8 and 26.0 in the 0.203 m facility. Pressure is measured using pressure transducers with measurement uncertainty of ±0.25% of the full range and local flow data is measured at 15 radial locations using four-sensor electrical conductivity probes. Each of these three locations have been staggered around the pipe, so that no measurements are made directly above a lower probe. The four-sensor electrical conductivity probe was developed by Kataoka et al. [12] and miniaturized by Kim et al. [15]. The
Fig. 1. Experimental ranges of previous studies.
Number of flow conditions 6 36 25 10 6 48 48
miniaturized probe can measure bubbles as small as 1 mm in diameter. It uses the conductive properties of air and water to determine when each of the four sensors is surrounded by air or water. By spacing the sensors very closely it is possible to determine the time taken for a bubble interface to move between two sensors, thereby allowing the computation of the interface velocity. The time-averaged interfacial area concentration can then be calculated as
ai ¼
1 P 1 Dt j ~ v j ~nj
ð5Þ
Further, by using the measured interface velocity and bubble residence time, the bubble chord length can be measured. Bubbles are classified as group 1 or group 2 based on whether the measured chord length exceeds the maximum distorted bubble limit given in Eq. (4) [2]. Probe measurements were spaced evenly at 15 radial locations with the first being in the exact center of the pipe and the last being about 2.5 mm from the pipe wall. The measurement uncertainty of conductivity probes can generally be divided into two categories. First is the probe structure, which includes the interface velocity, probe geometry, measurement frequency and response time. These give the uncertainty in the velocity of a single interface based on the uncertainty in the time at which the interface encounters a given sensor. The uncertainty due to this source is 10.3%. The second major source of uncertainty is due to the deformation of bubble surfaces on contact with the probe. This was investigated by Kim et al. [15] by comparing the probe measurement with the results of image processing techniques in a narrow rectangular channel. After accounting for the uncertainty due to probe structure, they noted an additional uncertainty due to deformation of bubble interfaces of approximately 6%. As the probes used in this experiment have similar structure, it can be assumed that deformation of the bubble interface is similar. Further, based on this study, the effect of lateral deflection of bubbles is expected to be negligible due to the very small size of the needle sensors. The use of the four-sensor probe allows measurement of interface velocity in three dimensions, negating the need for bubble shape assumptions that cause flowregime-based uncertainty when using dual-sensor local probes. Thus using error propagation techniques, the conductivity probe method has an experimental uncertainty of 11.9%. The uncertainty in void fraction is partially based on statistical considerations and total measurement time, 60 s. The rise and fall time of the electronic signal also contributes to uncertainty in void fraction due to a small degree of uncertainty in the residence time of each bubble at the probe location. Based on the work of Kim et al. [15], this leads to an uncertainty in the void fraction of 10%. It would also be possible for distortions in the flow field to cause additional uncertainty, however at the measurement location the flow obstruction caused by the probe is due only to the sensor needles and as a result is less than 0.1%. The probe body, located about 5 cm downstream of the measurement location, has a flow obstruction of 2.7% but has very little effect on the measurement. It is expected
16
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22
Fig. 2. Schematic of experimental facility.
that for such small flow obstruction, all effects of the intrusive probe will disappear within one to two pipe diameters downstream, however to ensure that downstream measurement locations are not affected by flow distortions the measurements are made in a staggered fashion so that no measurement is made directly above an upstream probe. Test conditions include liquid velocities of up to 1 m s1 and gas velocities of up to 3 m s1, with tests performed at system pressures of 180 kPa and 280 kPa and void fractions from 0.2 up to 0.7. Fig. 3 shows the test conditions with the flow regime transitions predicted by Schlegel et al. [24]. These tests provide valuable data for the transition from bubbly to cap/slug flow and from cap/ slug to churn-turbulent flow and extend the experimental database for pipes of 0.152 m diameter and larger into regions where data has not been collected previously. In total, this experiment results in 78 new area-averaged data points in the 0.152 m diameter facility and 54 new data points in the 0.203 m diameter facility. 4. Results
turbulent phenomena because of eddies created near bubble skirts. Kataoka and Serizawa [14] showed that transfer of turbulence to bubbles through the interface at small length scales decreases turbulence because of the energy required to move the interface, while the interfacial drag on large bubbles results in the production of turbulence. Experimental data [20] showed that wall-peaking in large pipes is over-predicted when using models developed for small pipes, which indicates that turbulent dispersion forces near the wall are significantly larger than the lift force for flows in large pipes. Additionally, the enhanced turbulence results in additional bubble breakup due to turbulent impact, meaning that average bubble sizes are smaller.
4.1.1. Void fraction The void fraction profiles measured during the experiment are given in Fig. 4. Fig. 4a shows all flow conditions with liquid velocity of 0.40 m s1 in the 0.152 m diameter test facility, collected at an axial location of z/DH = 33.9. Each of the data sets represents a
4.1. Profiles of local measured quantities The local profiles of various quantities can provide very valuable information regarding the flow structure and behavior. For this reason, the measured profiles for several test conditions are presented in Figs. 4–7. These local profiles are very different from those seen in flows in small pipes. Typically data from small pipes shows wall-peaking behavior at lower void fraction and centerpeaking behavior at higher void fractions, but flows in large pipes are typically developing flows while flows in small pipes are generally fully developed. For the current experiment, the L/D of the 0.152 m test section is 33.9, while for the 0.203 m test section it is only 26.0. Significant changes to the bubble size, void fraction, and gas velocity profiles can occur within the first several pipe diameters following the inlet. Thus for large diameter pipes with L/D less than 12–15, flow development may not be negligible when developing predictions for flow behavior. Turbulence in two-phase flows also plays a significant role in the shape of the local profiles. Larger diameter pipes have higher Reynolds number for a given flow condition and therefore show greater turbulence, however very small bubbles and high liquid fluxes may attenuate this effect due to suppression of eddies with similar size to the bubbles [1]. Large group 2 bubbles can enhance
Fig. 3. Flow conditions.
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22
17
different gas velocity, showing the effect of the gas flow rate on the local parameter profiles. It should be noted that group 2 bubbles are present for all of the test conditions shown. This results in nearly flat group 1 void fraction profiles with a peak near the middle range of r/R. This is reasonable given what is known of bubble behavior. The lift force acts to carry small bubbles towards areas of high velocity gradient, i.e. near the wall. Under the conditions in this study however the velocity profile, as indicated in Section 4.1.3, is very flat except near the wall. Additionally, as shown by Ohnuki and Akimoto [22], the turbulent intensity is much higher in large diameter channels than in small diameter channels. In this case, turbulent diffusion overwhelms the lift force, resulting in the much flatter void fraction profiles noted here. Further, the wake structure following large group 2 bubbles may result in limited motion for following group 2 bubbles, leading to the formation of large-scale eddies. The group 1 void fraction does not peak in the center though, because as the group 2 void profile shows the larger bubbles tend to gather in that region, forcing group 1 bubbles away from the center or absorbing them. The effect of varying pipe diameter is shown in Fig. 4b. Three test conditions were selected with varying liquid flow rate and similar gas flow rate. In the 0.152 m diameter test facility, this data was collected at z/D = 33.9. In the 0.203 m diameter test section the data was collected at z/D = 26.0. Thus the profiles should be fully developed for both cases. The colors represent tests at similar flow conditions and the differing symbols represent the two different diameters. As the figure shows, the data from the smaller test section shows lower group 1 void fraction and larger group 2 void fraction. As mentioned previously, turbulence is more significant in flows in larger pipes. This may lead to additional bubble breakup due to turbulence in larger pipe sizes, which results in fewer large bubbles and additional group 1 bubbles. Fig. 4c shows the effect of system pressure on the flow, as well as the effect of liquid velocity. Again, conditions at three liquid velocities and similar gas velocities are shown, with each color representing a flow condition and the different symbols representing pressures of 180 kPa and 280 kPa, respectively. In general, the only significant effect of the system pressure is to affect the density of the gas phase. In the current experiments, the gas volumetric flux rather than mass flow rate is used as the boundary condition, so changes in bubble properties will be small over the observed range of system pressures resulting in nearly immeasurable changes to bubble properties or bubble rise velocity, so only very small differences in the profiles are expected. As the figure shows, neither the liquid velocity over the range studied nor the system pressure over the range studied has any significant effect on the local profiles. The small differences between the profiles at different pressures can easily be accounted for as experimental error and small differences in the test conditions.
4.1.2. Gas velocity The gas velocity profiles are shown in Fig. 5. Fig. 5a shows flow conditions identical to that in 4a, and the data shows that the gas velocity increases as the gas flow rate increases. The gas velocity profiles also show that the velocity for group 1 bubbles is nearly constant across the pipe, with some decrease in the gas velocity near the pipe wall. This can be caused by enhanced turbulent diffusion resulting in significant mixing of the two-phase mixture, as was indicated in previous studies. For group 2 bubbles, the decrease in gas velocity near the pipe wall is somewhat smaller but begins slightly further from the pipe wall than for group 1 bubbles. This is simply because the bubbles are larger, meaning that while the effect of the wall is felt further away, the larger bubble is more resistant to changes in momentum due to the influence of the pipe wall.
Fig. 4. Void fraction profiles.
Fig. 5b, with flow conditions identical to Fig. 4b and measurements shown at z/D = 33.9 in the 0.152 m test section and z/ D = 26.0 in the 0.203 m test section, indicates that the group 1 gas velocity is slightly elevated in the 0.152 m test section when compared to the 0.203 m test section, but that the group 2 gas velocities are reasonably similar and perhaps slightly elevated in the 0.203 m test section. These differences are likely due to the effect of secondary recirculating flow patterns, which develop due to the effect of the large group 2 bubble moving through the mixture.
18
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22
Fig. 6. Comparison of gas flux measurements.
weighted sum. In Fig. 6, the comparison between the gas flux measured using a Venturi mass flow meter and the conductivity probe method is shown. The results show an average difference of 12.1%, while the expected uncertainty based on the velocity, void fraction, and Venturi meter measurement uncertainties is 12.9%. The maximum error for the tests in the 0.152 m diameter test facility is 12.3%, while the maximum error for the tests in the 0.203 m diameter test facility is 15.8%.
Fig. 5. Gas velocity profiles.
The data seems to indicate that the recirculation effects may be more significant in the smaller pipe sizes very close to the boundary between large and small pipes and become less important as the pipe size increases. Fig. 5c shows that the gas velocity has almost no variation due to pressure, which is expected for the flow conditions tested. Some variation in the group 2 velocity measured near the pipe wall is likely due to the small number of large bubbles encountered, which can have a negative effect on the measurement accuracy. To confirm the performance of the conductivity probe measurement technique, the gas flux has been calculated from the measured local gas velocity and void fraction measurements using a
4.1.3. Interfacial area concentration Fig. 7a shows the effect of varying the gas velocity on the interfacial area concentration profiles. The flow conditions shown are identical to those shown in Fig. 4a. Here, the interfacial area concentration profile follows much the same trend as the void fraction profile. These trends are expected as the group 1 bubble size is expected to remain relatively constant. Fig. 7b shows the effect of pipe diameter on the interfacial area concentration profile, again using the same test conditions as Fig. 4b and at the same axial locations. The profile indicates a slightly higher group 1 interfacial area concentration and slightly lower group 2 interfacial area concentration in the larger diameter test section. This is consistent with the previous observations regarding the void fraction and indicates that a larger portion of the void fraction is made up of smaller spherical and distorted bubbles in the 0.203 m test section when compared to the 0.152 m test section. Fig. 7c shows the effect of pressure using the same test conditions as in Fig. 4c, and as in Fig. 4c the pressure effect of pressure over the range measured in this study and the effect of superficial liquid velocity are negligible. 4.1.4. Average bubble size The bubble size in this case is estimated by the Sauter mean diameter, DSm ¼ 6a=ai which is based on the measured volume and surface area of the bubbles. The average bubble size profiles are given in Fig. 8. Fig. 8a shows that the average group 1 bubble size increases as the gas flow rate increases but reaches a maximum of just over 3 mm at roughly the same gas flow rate. Overall the profiles are very flat, but the group 1 bubble size tends to decrease near the pipe wall. This agrees with what is known about the lift force, namely that small bubbles are pulled toward the wall and large bubbles pushed away from the wall. The group 2 profile, however, shows an increase in the average bubble size near the
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22
19
Fig. 7. Interfacial area concentration profiles. Fig. 8. Average bubble diameter profiles.
wall. This may be because only very large group 2 bubbles are able to get near the wall while smaller ones are forced away. This would result in slightly larger measured bubble sizes. Fig. 8b shows that the bubble size is not significantly affected by changes in pressure. Fig. 8b shows that while the group 2 bubble size is not significantly affected by the change in pipe diameter, the group 1 bubble size is slightly increased in the larger channel. This is likely due to the increase in group 1 void fraction, which causes additional coalescence by to random collision of group 1 bubbles. Fig. 8c shows that the bubble size is not significantly affected by changes in pressure.
4.2. Comparison with drift-flux models for large pipes Most analysis codes for thermal–hydraulic systems use the onedimensional formulation of the two-fluid model. Therefore, the area-averaged data is of great interest in developing and validating models for application in such analysis codes. The area averaged data collected in this experiment has therefore been compared to the most up-to-date drift-flux model in large pipes. This model is that of Hibiki and Ishii [7], as determined by Schlegel et al. [25] and detailed in Table 4. Therefore in Figs. 9 and 10 the data is
20
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22
Table 4 Distribution parameter and drift velocity specified by Hibiki and Ishii [7]. Distribution parameter qffiffiffiffi þ 1:69 qffiffiffiffi hj i q q C 0 ¼ exp 0:475 hjgþ i 1 qg þ qg f f qffiffiffiffi n hjþ i o qffiffiffiffi q q C 0 ¼ 2:88 hjgþ i þ 4:08 1 qg þ qg f f qffiffiffiffi qffiffiffiffi q q C 0 ¼ 1:2 expð0:110hjþ i2:22 Þ 1 qg þ qg f f qffiffiffiffi qffiffiffiffi q q C 0 ¼ ½0:6 expf1:2ðhjþ i 1:8Þg þ 1:2 1 qg þ qg f f qffiffiffiffiffiffiffiffiffiffiffiffiffi 1:2 0:2 qg =qf qffiffiffiffiffiffiffiffiffiffiffiffiffi 1:2 0:2 qg =qf qffiffiffiffiffiffiffiffiffiffiffiffiffi 1:2 0:2 qg =qf
Drift velocity Vþ gj
¼
Vþ gj;B
Applicable range
expð1:39hjþ g iÞ
þ
Vþ gj;P f1
expð1:39hjþ g iÞg
þ
þ
þ Bubbly flow 0 hjþ g i=hj i 0:9 þ
þ
þ þ Vþ gj ¼ V gj;B expð1:39hjg iÞ þ V gj;P f1 expð1:39hjg iÞg
Bubbly flow 0:9 hjg i=hj i 1
þ Vþ gj ¼ V gj;P
Cap bubbly flow < a >< 0:3; 0 hj i 1:8
Vþ gj
Cap bubbly flow < a >< 0:3; 1:8 hjþ i
¼
þ
Vþ gj;P
0:157 0:809 qg N 0:562 Vþ lf gj ¼ 0:0019 minðDH ; 30Þ qf 0:157 q g ¼ 0:92 Vþ gj qf pffiffiffi rg Dq 1=4 2 q2
Cap bubbly flow N lf < 2:25 103
0
Annular flow
Cap bubbly flow N lf > 2:25 103 Churn-turbulent flow
f
1þ
1hai pffiffiffiffiffiffiffiffiffiffi haiþ4 qg =qf
plotted with the predictions calculated by the model for the 0.152 m and 0.203 m test sections, respectively. The void fraction is plotted in this case because it is a directly measured parameter and therefore carries less uncertainty than other possible parameters. Additionally, this allows for direct evaluation of the prediction accuracy of the drift-flux models for void fraction. For the 0.152 m channel the lower liquid velocity conditions agree with the model prediction quite well, although at high liquid velocity the data does not show as much change in void fraction as expected. For the 0.203 m diameter channel, the predictions in bubbly flow are very good. At the lowest liquid velocity condition there is a significant amount of variation in the data, however this may be due to measurement uncertainty caused by the development of recirculating secondary flow patterns at low volumetric fluxes that make accurate measurements difficult. At higher void fractions the effect of the liquid velocity on the void fraction is smaller than expected but the data falls in the approximate range predicted by the model. Generally the model predicts the data quite well with an average error of 12.4%. 4.3. Axial flow development Fig. 11 shows the axial development of the area-averaged interfacial area concentration. The data in the figure shows the ratio of
Fig. 9. Drift-flux model evaluation, DH = 0.152 m.
the measured interfacial area concentration to the expected interfacial area concentration, or n ¼ hai;meas i=hai;pred i. The expected value is calculated by assuming that bubble expansion is the only mechanism for change in interfacial area concentration. Based on the IATE without bubble interaction models, this expected value is determined by the following equations for group 1 and group 2, respectively:
d ðhai1 ihhv g1 iiÞ ¼ dz
2 hai1 i ha1 ihhv g1 ii dP CDc1 3 ha1 i P dz
d 2 hai2 i ha2 ihhv g2 ii dP ðhai2 ihhv g2 iiÞ ¼ dz 3 ha2 i P dz ha i h a ihh v 1 g1 ii dP i1 þ CDc1 ha1 i P dz
ð6Þ
ð7Þ
Here P is the pressure. The constant C has been determined by previous modeling efforts [3,4]. Using the inlet conditions as the initial condition, these equations can be used to estimate the change in interfacial area concentration at each of the remaining two measurement locations. This procedure results in the data shown in Fig. 11, where values greater than unity indicate that interfacial area concentration sources are dominant, while values less than unity indicate that interfacial area sinks are dominant. For the 0.152 m test section, the data shows very similar patterns
Fig. 10. Drift-flux model evaluation, DH = 0.203 m.
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22
21
Fig. 11. Axial development of area-averaged interfacial area concentration.
for all of the flow conditions with some bubble breakup initially and bubble coalescence dominating later. The data in the 0.203 m test section shows much more varied trends. This may have several causes. Increased turbulence may play some role, as well as changes in the average bubble size during injection. It may be useful to attempt measurement of turbulence intensity using Laser-Doppler Anemometry or Hot-Film Anemometry to determine if this is the case. Larger liquid flow rates required to sustain a given superficial liquid velocity may result in smaller bubbles at the injection location, reducing the initial breakup effect but leading to more bubble breakup further along the test section. Overall, the data shows that the measured interfacial area concentration can vary significantly from the expected value considering only bubble expansion, which means that accurate models for the bubble interaction terms are essential for developing accurate predictions of interfacial area concentration for the prediction of the behavior of nuclear reactor systems.
pipes has been expanded through the addition of 132 area-averaged data points. The effect of pressure and diameter on the twophase flow structure has been investigated and the data used to evaluate the performance of the current state-of-the-art drift-flux models for large diameter pipes. The interfacial area concentration data collected shows the necessity of developing additional source and sink term models and can provide a solid basis for benchmarking and verifying those models for flows in the bubbly, cap/slug and churn-turbulent flow regimes.
Acknowledgement This work was performed at Purdue University, in the Institute of Thermal Hydraulics, under the auspices of the US Nuclear Regulatory Commission.
References 5. Conclusions A review of the literature has shown that the database for interfacial area concentration in large diameter pipes has severe limitations. To address these limitations, an experiment has been undertaken to measure the local flow parameters in pipes with diameters of 0.152 m and 0.203 m under a wide variety of flow conditions with void fractions from 0.20 to 0.75 and at system pressures of 180 kPa and 280 kPa. The profiles of void fraction, interfacial area concentration, gas velocity and Sauter mean diameter all show reasonable trends and the data measured by electrical conductivity probes agrees well with that determined using other metrics such as gas flow rate measured by a Venturi mass flow meter. The database for interfacial area transport in large
[1] S. Elgholbashi, T. Abou-Arab, Two-equation turbulence model for two-phase flows, Physics of Fluids 26 (1983) 931–938. [2] X.Y. Fu, Interfacial area measurement and transport modeling in air-water two-phase flow. Ph.D. Thesis, Purdue University, West Lafayette, IN, USA, 2001. [3] X.Y. Fu, M. Ishii, Two-group interfacial area transport in vertical air-water flow: I. Mechanistic model, Nuclear Engineering and Design 219 (2) (2003) 143–168. [4] X.Y. Fu, M. Ishii, Two-group interfacial area transport in vertical air-water flow: II. Model evaluation, Nuclear Engineering and Design 219 (2) (2003) 169–190. [5] T. Hibiki, M. Ishii, One-group interfacial area transport of bubbly flows in vertical round tubes, International Journal of Heat and Mass Transfer 43 (15) (2000) 2711–2726. [6] T. Hibiki, M. Ishii, Experimental study on interfacial area transport in bubbly two-phase flows, International Journal of Heat and Mass Transfer 42 (1999) 3019–3035. [7] T. Hibiki, M. Ishii, One-dimensional drift-flux model for two-phase flow in a large diameter pipe, International Journal of Heat and Mass Transfer 46 (2003) 1773–1790.
22
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22
[8] T. Hibiki, T.H. Lee, J.Y. Lee, M. Ishii, Interfacial area concentration of boiling bubbly flow systems, Chemical Engineering Science 61 (2006) 7979–7990. [9] M. Ishii, One-dimensional Drift-flux Model and Constitutive Equations for Relative Motion between Phases in Various Two-phase Flow Regimes, Argonne Report, vol. ANL-77-47, 1977. [10] M. Ishii, K. Mishima, Two-fluid model and hydrodynamic constitutive relations, Nuclear Engineering and Design 82 (1984) 107–126. [11] M. Ishii, T. Hibiki, Thermo-Fluid Dynamics of Two-Phase Flow, second ed., Springer, New York, 2010. [12] I. Katoaka, M. Ishii, A. Serizawa, Local formulation and measurements of interfacial area concentration in two-phase flow, International Journal of Multiphase Flow 12 (4) (1986) 505–529. [13] I. Kataoka, M. Ishii, Drift-flux model for large diameter pipe and new correlation for pool void fraction, International Journal of Heat and Mass Transfer 30 (1987) 1927–1939. [14] I. Kataoka and A. Serizawa, Modeling and prediction of turbulence in bubbly two-phase flow. Proc. 2nd Int. Conference on Multiphase Flow, 11–16. April 3– 7, 1995. [15] S. Kim, X.Y. Fu, X. Wang, M. Ishii, Development of the miniaturized four-sensor conductivity probe and the signal processing scheme, International Journal of Heat and Mass Transfer 43 (22) (2000) 4101–4118. [16] G. Kocamustafaogullari, M. Ishii, Foundations of the interfacial area transport equation and its closure relations, International Journal of Heat and Mass Transfer 38 (3) (1995) 481–493. [17] D. Lucas, M. Beyer, L. Szalinski, P. Schutz, A new database on the evolution of air-water flows along a large vertical pipe, International Journal of Thermal Sciences 49 (2010) 664–674. [18] A. Manera, B. Ozar, S. Paranjape, M. Ishii, H.M. Prasser, Comparison between wire-mesh sensors and conductive needle-probes for measurements of twophase flow parameters, Nuclear Engineering and Design 239 (2009) 1718– 1724. [19] K. Mishima, M. Ishii, Flow regime transition criteria for upward two phase flow in vertical tubes, International Journal of Heat and Mass Transfer 27 (5) (1984) 723–737. [20] A. Ohnuki and H. Akimoto. Prediction of phase distribution under bubbly flow in a large vertical pipe by multidimensional two-fluid model. Third Int. Conference on Multiphase Flow, ICMF ’98, Lyon, France, June 8–12, 1998.
[21] A. Ohnuki, H. Akimoto, Experimental study on transition of flow pattern and phase distribution in upward air-water two-phase flow along a vertical pipe, International Journal of Multiphase Flow 26 (3) (2000) 367–386. [22] A. Ohnuki, H. Akimoto, Model development for bubble turbulent diffusion and bubble diameter in large vertical pipes, Journal of Nuclear Science and Technology 38 (2001) 1074–1080. [23] H.M. Prasser, Evolution of interfacial area concentration in a vertical air-water flow measured by wire-mesh sensors, Nuclear Engineering and Design 237 (2007) 1608–1617. [24] J.P. Schlegel, P. Sawant, S. Paranjape, B. Ozar, T. Hibiki, M. Ishii, Void fraction and flow regime in adiabatic upward two-phase flow in large diameter pipes, Nuclear Engineering and Design 238 (2009) 2864–2874. [25] J.P. Schlegel, T. Hibiki, M. Ishii, Development of a comprehensive set of driftflux constitutive models for pipes of various hydraulic diameters, Progress in Nuclear Energy 52 (7) (2010) 666–677. [26] M.E. Shawkat, C.Y. Ching, M. Shoukri, Bubble and liquid turbulence characteristics of bubbly flow in a large diameter vertical pipe, International Journal of Multiphase Flow 34 (2008) 767–785. [27] X. Shen, Y. Saito, K. Mishima, H. Nakamura, A study on the characteristics of upward air-water two-phase flow in a large diameter pipe, Experimental Thermal and Fluid Science 31 (2006) 21–36. [28] M. Shoukri, I. Hassan, I. Gerges, Two-phase bubbly flow structure in largediameter vertical pipes, The Canadian Journal of Chemical Engineering 81 (2003) 205–211. [29] T.R. Smith, Two-group Interfacial Area Transport Equation in Large Diameter Pipes, Ph.D. Thesis, Purdue University, 2002. [30] X. Sun, T.R. Smith, S. Kim, M. Ishii, J. Uhle, Interfacial area of bubbly flow in a relatively large diameter pipe, Experimental Thermal and Fluid Science 27 (1) (2002) 97–109. [31] X. Sun, M. Ishii, J. Kelly, Modified two-fluid model for the two-group interfacial area transport equation, Annals of Nuclear Energy 30 (16) (2003) 1601–1622. [32] Q. Wu, S. Kim, M. Ishii, S.G. Beus, One-group interfacial area transport in vertical bubbly flow, International Journal of Heat and Mass Transfer 41 (1998) 1109–1112. [33] K. Yoneda, A. Yasuo, T. Okawa, Flow structure and bubble characteristics of steam-water two-phase flow in a large diameter pipe, Nuclear Engineering and Design 217 (3) (2002) 267–281.
Contents lists available at SciVerse ScienceDirect
Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs
Experimental study of two-phase flow structure in large diameter pipes J.P. Schlegel, S. Miwa, S. Chen, T. Hibiki, M. Ishii ⇑ School of Nuclear Engineering, Purdue University, 400 Central Dr., West Lafayette, IN 47907-2017, United States
a r t i c l e
i n f o
Article history: Received 15 June 2011 Received in revised form 30 November 2011 Accepted 29 January 2012 Available online 15 February 2012 Keywords: Large diameter Interfacial area Two-fluid model Void fraction
a b s t r a c t Current thermal–hydraulic analysis codes use static, flow-regime-dependent empirical models which introduce several sources of error and numerical instability. The interfacial area transport equation offers a more robust, reliable prediction of interfacial area and can allow for dynamic predictions of two-phase flows. In order to develop reliable mechanistic models for interfacial area concentration sources and sinks an extensive database is required, however the current database lacks significant data for pipes larger than 0.1 m diameter and for void fractions above 0.4. To improve and extend the database experiments have been performed in pipes with diameters of 0.152 m and 0.203 m with void fractions of up to 0.7, providing valuable data regarding the local profiles and axial development that can be used to evaluate current interfacial area transport models and assist in the development of new mechanistic models for interfacial area concentration sources and sinks. Ó 2012 Elsevier Inc. All rights reserved.
1. Introduction Two phase flows are essential to industrial applications in many fields. In the nuclear industry, fundamental understanding of twophase flows under various conditions is essential for predicting the steady-state behavior of Boiling Water Reactors (BWRs) of all types as well as accident scenarios in both BWRs and Pressurized Water Reactors (PWRs), and even in liquid–metal-cooled reactors. Prediction of behavior in new natural-circulation BWR designs is even more sensitive to the reliability of the models used, as these systems drive natural circulation through the inclusion of a long chimney section above the core to provide sufficient gravity head. This region is extremely sensitive to changes in the flow conditions, and fundamentally sound, accurate models are essential for accurate prediction of the natural circulation flow rate and Reactor Pressure Vessel (RPV) liquid inventory. This region behaves as a large diameter pipe, and indeed many of the flow channels in reactor systems are significantly larger than the transition size,
DH DH ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P 40 r=g Dq
ð1Þ
which is about 7 cm under typical BWR conditions, and can therefore be considered as having ‘large diameter.’ Large diameter pipes differ from those considered small diameter because two-phase flows in large pipes can no longer sustain slug bubbles which bridge the entire cross-section of the flow channel, due to Raleigh–Taylor instability. For flow channels larger than the transition value, this interaction of the two types of instability results in large bubbles ⇑ Corresponding author. Tel.: +1 765 494 4587. E-mail address: [email protected] (M. Ishii). 0894-1777/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.expthermflusci.2012.01.034
being broken into many smaller cap-shaped bubbles. This causes many changes to the hydrodynamics of the flow, producing additional turbulence due to bubble drag, enhancing turbulent diffusion, and producing strong secondary recirculations in the flow. These changes result in very different physical mechanisms behind the transport of gas and liquid, meaning that models typically applied to flows in small-diameter pipes can no longer be guaranteed to predict flows in large-diameter channels accurately [13]. The two-fluid model, sometimes called the six-equation model, is the most-used model in engineering applications today [11]. This model calculates the balance of mass, momentum, and energy for each phase separately. Time-averaging of the equations results in interfacial transfer terms to account for the transfer of these quantities from one phase to the other. While numerical methods such as LES and DNS can provide more accurate results, these types of calculations take much longer than two-fluid model calculations and the two-fluid model can be area-averaged to give a onedimensional form suitable for use in advanced computational codes. The disadvantage to the two-fluid model, and the major challenge facing its implementation, is accurate modeling of the interfacial transfer terms for mass, momentum and energy. The interfacial transfer terms can be expressed as the product of the driving potential for the transfer across the interface (i.e. the interfacial drag for momentum transfer) and a term representing the geometry of the interface, or ‘flow regime.’ This representation of the interfacial geometry is often given as the interfacial area concentration (IAC), ai, which is defined as the amount of surface area per unit volume of the two-phase mixture. The current method used by most advanced system analysis codes is a two-step method. An experimentally determined flow regime map is used to determine the approximate flow geometry
13
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22
Nomenclature Latin characters A area (m2) interfacial area concentration (m1) ai C constant () DH hydraulic diameter (m) g gravitational acceleration (m s2) j superficial velocity (m s1) n normal vector () P pressure (Pa) v velocity (m s1) z axial location (m) Greek characters a void fraction () u interfacial area concentration source or sink (m1 s1) Dq density difference (kg m3)
for a given flow condition, then empirical correlations for the driving force and IAC are used to predict the interfacial transfer. For large pipes, the recommended flow regime map is that given by Schlegel et al. [24], which is supported by other data available in the literature [21]. Using the example of momentum transfer, once the flow regime is determined a drift-flux model such as that developed by Hibiki and Ishii [7] is used to calculate the drag coefficient, then another empirical equation is used to compute the IAC [11]. This approach has two significant problems. The first is the uncertainties in the flow regime boundaries, as the transitions actually occur over a region on the flow regime map and in reality are not abrupt transitions. The second is the error in the empirical models used. These models are developed under steady-state, fully developed conditions and may not be applicable to highly transient conditions such as accident scenarios or reactor startup computations. To mitigate these effects in advanced computational codes, the interfacial area transport equation (IATE) is currently under development [11]. In this approach a transport equation is used to model the change in interfacial area concentration by accounting for the interaction of bubbles given reasonable boundary conditions. This eliminates the requirement for flow regime maps and reduces error and numerical oscillations or bifurcations. The transport equation is also dynamic, allowing the effect of transient conditions to be predicted. Constitutive models for the driving forces are still required, however the ability of the IATE to provide bubble size estimates can also improve the performance of those models. Developing the IATE accurately requires the creation of mechanistic models for IAC sources and sinks due to interactions between bubbles and due to phase change. In order to accomplish this, these models must be developed based on the hydrodynamics of the flow and verified using a database of interfacial area transport measurements. A review of the literature has revealed that while models for flows in small diameter channels are well-developed, the database for flows in large-diameter pipes has significant shortcomings. To remedy this shortcoming, the void fraction, interfacial area concentration, gas velocity and bubble size have been measured at three axial locations in test facilities with diameters of 0.152 m and 0.203 m and at absolute pressures of 180 kPa and 280 kPa. Flow conditions varied widely, with void fractions up to 0.7, much higher than those seen in previous experiments in such large flow channels. 2. Previous work Flows in large pipes and small pipes are very different. These differences are summarized in Table 1. The presence of cap-shaped
r
surface tension (N m) ratio of actual to predicted IAC () time elapsed (s)
n Dt
Sub/superscripts pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ⁄ non-dimensionalized value using r=g Dq 1 group 1 2 group 2 c1 critical value for group 1 f liquid phase g gas phase j measurement or bubble mechanism Operators hi area-averaged quantity void-weighted area-averaged quantity
bubbles also has a strong effect on turbulence in large pipe flows [14]. Along with the lift force and wall lubrication force, turbulence plays an important part in determining the void profiles, i.e. the wall-peaking or center-peaking phenomenon. Increased turbulent diffusion for flows in large diameter pipes can reduce wall-peaking, a phenomenon which has been observed previously by Ohnuki and Akimoto [20,22]. Stronger turbulence can also result in enhanced bubble breakup although these differences may become less significant for higher liquid velocities where the turbulent intensity is already very high [1]. The change in the hydrodynamics can also be noted in various efforts to develop flow regime maps for large pipes and in the differences in the criteria used in small pipe flows and large pipe flows to determine flow regime transitions [21,24]. The major developments related to the development of IATE source and sink terms, a brief review of the status of IATE models in pipes, is given in Table 2. Ishii and Mishima [10] developed the modern formulation of the two-fluid model and developed static IAC correlations for small round pipes. The IATE was first proposed by Kocamustafaogullari and Ishii [16]. It was later modified to account for the expansion and contraction of bubbles due to pressure change [32,5] and has been derived in a two-group form that allows accurate prediction of cap/slug and churn-turbulent flows where two groups of bubbles, small spherical and distorted bubbles and large cap-shaped Taylor bubbles, with very different behaviors exist [5]. These equations can then be area-averaged to develop a onedimensional form that is suitable for inclusion in advanced system analysis codes. This form of the two-group IATE is given as [11]
@hai1 i @ 2 hai1 i @ þ hai1 ihhv i1 ii ¼ CðDc1 Þ2 ha1 ihhv g1 ii @t @z 3 ha1 i @z P þ h/j1 i
ð2Þ
j
@hai2 i @ 2hai2 i @ hai1 i @ þ hai2 ihhv i2 ii ¼ ha2 ihhv g2 ii þ CðDc1 Þ2 @t @z 3ha2 i @z ha1 i @z P ha1 ihhv g1 ii þ h/j2 i j
ð3Þ The meanings of the symbols in these equations can be found in the nomenclature. The boundary between the two bubble groups is defined as the maximum distorted bubble size, which is
Db Db ¼ qffiffiffiffiffiffi ¼ 4: r
g Dq
ð4Þ
14
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22 Table 1 Summary of differences between flows in small and large pipes. Small pipes DH < 2Q
Large pipes DH > 40
Flow structure (Flow regime)
Bubbly, slug, churn-turbulent, annular Mishima and Ishii [19]
Bubbly, cap-turbufent, churn-turbulent, annular Schlegel et al. [24]
Diameter effect
Significant effects Ishii, [8]; Mishima and Ishii [19]
Effect of wall very reduced Kataoka and Ishii [13]; Schlegel et al. [25]
Entrance effect
Injection method insensitive Hibiki and Ishii [5]
Sensitive to injection method Hibiki and Ishii [7]
Recirculation Effects
Insignificant Hibiki and Ishii [5]
Very significant for some flow conditions Kataoka and Ishii [13]
Wall-peaking
Strong for some flow conditions Hibiki and Ishii, [6]
Reduced or eliminated for all flow conditions Ohnuki and Akimoto [20]
Drift-flux model
Available Ishii, [9]; Hibiki and Ishii, 2002
Available Hibiki and Ishii [7]
IAC correlations
Available Hibiki and Ishii, 2002;Hibiki et al. [8]
Available Hibiki et al. [8]
IATE
Available Hibiki and Ishii [5]; Fu and Ishii [3]
Not available
The solution of the IATE requires some changes to the typical two-fluid model. The most significant change is that the continuity equation for the gas phase must be rewritten as two equations, one for each bubble group, with a term added to account for mass transfer between the groups. This term can be computed based on the interfacial area transfer terms. The other major change is appropriate averaging of the momentum equation to account for the differences between the bubble groups. This change is detailed by Sun et al. [31]. Given this form of the IATE, the next necessary step is to develop the source, sink, and inter-group transfer terms which account for bubble interactions. While these interfacial transfer terms have not been well-developed for flows in large diameter pipes, much effort has been devoted to the development of interfacial area transport models for small diameter pipes. One of the most welldeveloped sets of interfacial area transport models was developed by Fu [3,4] for small-diameter pipes. Based on this work, it is possible to determine all of the models which need to be developed for flows in large diameter pipes. In order to develop accurate models for interfacial area transport, an experimental database is needed to aid in determining the relative strengths of each bubble interaction type and to verify the performance of the models which are developed. A review of the literature has found several efforts to measure quantities relevant to interfacial area transport in large pipes which are summarized in Table 3. Fig. 1 illustrates the flow ranges for each of the studies detailed here. As the figure shows, there is a distinct lack of data in the cap/slug and churn-turbulent flow regimes, where
Table 2 Summary of development of IATE for large diameter pipes. Researcher
Significant development
lshii and Mishima [19] Kocamustafaogullari and Ishii [16] Wu et al. [32], Hibiki and Ishii [5] Hibiki and Ishii [5] Sun et al. [31]
Two-fluid model, static IAC correlations Proposal and preliminary formulation of IATE
Fu [3]
Ishii and Hibiki [11]
One-group IATE for small round pipes Two-group IATE forsmall round pipes Modified two-fluid model for use with two p-group IATE Identification of all necessary source and sink models, Updated models for two-group IATE in small round pipes Review of development of IATE and significant models
the two-group form of the IATE is essential to accurately predict two-phase flows. Previously experiments by Smith [29] and Lucas et al. [17] have collected data in this region, however extensive data from Smith [29] has only been collected for pipes of 0.102 m diameter. The data collected by Lucas et al. [17] extends into the churn-turbulent regime and has a similar range of flow conditions to the present study, however it has some limitations. First, the gas is injected from the side of the pipe. This may not mimic the development of typical boiling flows in industrial systems well, as such systems typically have internal heaters. Also, interfacial area concentration measurements are not reported and the current data would be difficult to use for evaluation of interfacial area transport in two-phase systems. Further, the reported data is largely for low void fraction cases. The use of wire mesh sensors presents several possible difficulties. For instance the resolution of the wire mesh sensor is limited to 3 mm, and individual bubble velocities for small bubbles is not directly measured but inferred from cross-correlation of two mesh sensors. Finally, the mesh sensor may distort the bubble interface for large bubbles. Manera et al. [18] showed that for small diameter pipes in the bubbly and slug flow regimes measurements made using wire mesh sensors and local probe techniques agree reasonably well, however this study did not extend to the churn-turbulent flow regime or into pipes with diameters larger than 5.08 cm. Thus the measurements reported in the literature should be confirmed by another measurement method and further expanded for use in evaluation of interfacial area transport models. For that reason it is essential that additional data be collected for pipes of 0.152 m and larger diameter and at higher void fraction conditions in order to facilitate the development and validation of the two-group IATE for flows in large diameter pipes. 3. Experiment Fig. 2 shows a schematic of the facility used in this experiment. The liquid flow rate is measured using a magnetic flow meter with an experimental uncertainty of ±1%, and controlled using a centrifugal pump with a variable frequency drive. Compressed air is supplied by a compressor with a large storage tank and pressure regulator to prevent upstream pressure from having a significant effect on the gas flow rate. The gas flow rate is measured using a Venturi flow meter with uncertainty of ±2%. The air and water are mixed in an injector unit, also shown in Fig. 2, utilizing sintered metal elements surrounded by steel annuli. This configuration
15
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22 Table 3 Summary of experimental research on interfacial area concentration in large pipes. Researcher
Pipe diameter (m)
Void fraction range
Liquid velocity range (m s1)
Instrumentation
Sun et al. [30]
0.102
0.02–0.30
0.00–1.00
Yoneda et al. [33] Shoukri et al. [28] Shen et al. [27] Prasser [23] Shawkat et al. [26] Lucas et al. [17]
0.155 0.200 0.200 0.195 0.200 0.195
0.00–0.20 0.00–0.04 0.00–0.40 0.00–0.30 0.012–0.154 0.01–0.74
0.00–0.60 0.00–0.40 0.14–1.12 1.02 0.2–0.68 0.04–1.6
Four-sensor electrical conductivity probes Dual-sensor optical probes Dual-sensor optical probes Dual-sensor optical probes Wire-mesh sensors Dual-sensor optical probes Wire-mesh sensors
allows the liquid flow rate through the annuli to be controlled so that the initial bubble size can be maintained for a variety of flow conditions. This allows evaluation of the effect of initial bubble size on the properties of the flow, although this analysis is beyond the scope of the current study and in these experiments the liquid velocity in the annuli was held constant so that initial bubble size was approximately constant for all tests. Test sections of 0.152 m and 0.203 m diameter are constructed of clear acrylic to allow flow visualization. Measurements of system pressure and local flow parameters are made at three locations along each test section, at z/D = 11.7, 17.7 and 33.9 in the 0.152 m facility and z/D = 5.4. 9.8 and 26.0 in the 0.203 m facility. Pressure is measured using pressure transducers with measurement uncertainty of ±0.25% of the full range and local flow data is measured at 15 radial locations using four-sensor electrical conductivity probes. Each of these three locations have been staggered around the pipe, so that no measurements are made directly above a lower probe. The four-sensor electrical conductivity probe was developed by Kataoka et al. [12] and miniaturized by Kim et al. [15]. The
Fig. 1. Experimental ranges of previous studies.
Number of flow conditions 6 36 25 10 6 48 48
miniaturized probe can measure bubbles as small as 1 mm in diameter. It uses the conductive properties of air and water to determine when each of the four sensors is surrounded by air or water. By spacing the sensors very closely it is possible to determine the time taken for a bubble interface to move between two sensors, thereby allowing the computation of the interface velocity. The time-averaged interfacial area concentration can then be calculated as
ai ¼
1 P 1 Dt j ~ v j ~nj
ð5Þ
Further, by using the measured interface velocity and bubble residence time, the bubble chord length can be measured. Bubbles are classified as group 1 or group 2 based on whether the measured chord length exceeds the maximum distorted bubble limit given in Eq. (4) [2]. Probe measurements were spaced evenly at 15 radial locations with the first being in the exact center of the pipe and the last being about 2.5 mm from the pipe wall. The measurement uncertainty of conductivity probes can generally be divided into two categories. First is the probe structure, which includes the interface velocity, probe geometry, measurement frequency and response time. These give the uncertainty in the velocity of a single interface based on the uncertainty in the time at which the interface encounters a given sensor. The uncertainty due to this source is 10.3%. The second major source of uncertainty is due to the deformation of bubble surfaces on contact with the probe. This was investigated by Kim et al. [15] by comparing the probe measurement with the results of image processing techniques in a narrow rectangular channel. After accounting for the uncertainty due to probe structure, they noted an additional uncertainty due to deformation of bubble interfaces of approximately 6%. As the probes used in this experiment have similar structure, it can be assumed that deformation of the bubble interface is similar. Further, based on this study, the effect of lateral deflection of bubbles is expected to be negligible due to the very small size of the needle sensors. The use of the four-sensor probe allows measurement of interface velocity in three dimensions, negating the need for bubble shape assumptions that cause flowregime-based uncertainty when using dual-sensor local probes. Thus using error propagation techniques, the conductivity probe method has an experimental uncertainty of 11.9%. The uncertainty in void fraction is partially based on statistical considerations and total measurement time, 60 s. The rise and fall time of the electronic signal also contributes to uncertainty in void fraction due to a small degree of uncertainty in the residence time of each bubble at the probe location. Based on the work of Kim et al. [15], this leads to an uncertainty in the void fraction of 10%. It would also be possible for distortions in the flow field to cause additional uncertainty, however at the measurement location the flow obstruction caused by the probe is due only to the sensor needles and as a result is less than 0.1%. The probe body, located about 5 cm downstream of the measurement location, has a flow obstruction of 2.7% but has very little effect on the measurement. It is expected
16
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22
Fig. 2. Schematic of experimental facility.
that for such small flow obstruction, all effects of the intrusive probe will disappear within one to two pipe diameters downstream, however to ensure that downstream measurement locations are not affected by flow distortions the measurements are made in a staggered fashion so that no measurement is made directly above an upstream probe. Test conditions include liquid velocities of up to 1 m s1 and gas velocities of up to 3 m s1, with tests performed at system pressures of 180 kPa and 280 kPa and void fractions from 0.2 up to 0.7. Fig. 3 shows the test conditions with the flow regime transitions predicted by Schlegel et al. [24]. These tests provide valuable data for the transition from bubbly to cap/slug flow and from cap/ slug to churn-turbulent flow and extend the experimental database for pipes of 0.152 m diameter and larger into regions where data has not been collected previously. In total, this experiment results in 78 new area-averaged data points in the 0.152 m diameter facility and 54 new data points in the 0.203 m diameter facility. 4. Results
turbulent phenomena because of eddies created near bubble skirts. Kataoka and Serizawa [14] showed that transfer of turbulence to bubbles through the interface at small length scales decreases turbulence because of the energy required to move the interface, while the interfacial drag on large bubbles results in the production of turbulence. Experimental data [20] showed that wall-peaking in large pipes is over-predicted when using models developed for small pipes, which indicates that turbulent dispersion forces near the wall are significantly larger than the lift force for flows in large pipes. Additionally, the enhanced turbulence results in additional bubble breakup due to turbulent impact, meaning that average bubble sizes are smaller.
4.1.1. Void fraction The void fraction profiles measured during the experiment are given in Fig. 4. Fig. 4a shows all flow conditions with liquid velocity of 0.40 m s1 in the 0.152 m diameter test facility, collected at an axial location of z/DH = 33.9. Each of the data sets represents a
4.1. Profiles of local measured quantities The local profiles of various quantities can provide very valuable information regarding the flow structure and behavior. For this reason, the measured profiles for several test conditions are presented in Figs. 4–7. These local profiles are very different from those seen in flows in small pipes. Typically data from small pipes shows wall-peaking behavior at lower void fraction and centerpeaking behavior at higher void fractions, but flows in large pipes are typically developing flows while flows in small pipes are generally fully developed. For the current experiment, the L/D of the 0.152 m test section is 33.9, while for the 0.203 m test section it is only 26.0. Significant changes to the bubble size, void fraction, and gas velocity profiles can occur within the first several pipe diameters following the inlet. Thus for large diameter pipes with L/D less than 12–15, flow development may not be negligible when developing predictions for flow behavior. Turbulence in two-phase flows also plays a significant role in the shape of the local profiles. Larger diameter pipes have higher Reynolds number for a given flow condition and therefore show greater turbulence, however very small bubbles and high liquid fluxes may attenuate this effect due to suppression of eddies with similar size to the bubbles [1]. Large group 2 bubbles can enhance
Fig. 3. Flow conditions.
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22
17
different gas velocity, showing the effect of the gas flow rate on the local parameter profiles. It should be noted that group 2 bubbles are present for all of the test conditions shown. This results in nearly flat group 1 void fraction profiles with a peak near the middle range of r/R. This is reasonable given what is known of bubble behavior. The lift force acts to carry small bubbles towards areas of high velocity gradient, i.e. near the wall. Under the conditions in this study however the velocity profile, as indicated in Section 4.1.3, is very flat except near the wall. Additionally, as shown by Ohnuki and Akimoto [22], the turbulent intensity is much higher in large diameter channels than in small diameter channels. In this case, turbulent diffusion overwhelms the lift force, resulting in the much flatter void fraction profiles noted here. Further, the wake structure following large group 2 bubbles may result in limited motion for following group 2 bubbles, leading to the formation of large-scale eddies. The group 1 void fraction does not peak in the center though, because as the group 2 void profile shows the larger bubbles tend to gather in that region, forcing group 1 bubbles away from the center or absorbing them. The effect of varying pipe diameter is shown in Fig. 4b. Three test conditions were selected with varying liquid flow rate and similar gas flow rate. In the 0.152 m diameter test facility, this data was collected at z/D = 33.9. In the 0.203 m diameter test section the data was collected at z/D = 26.0. Thus the profiles should be fully developed for both cases. The colors represent tests at similar flow conditions and the differing symbols represent the two different diameters. As the figure shows, the data from the smaller test section shows lower group 1 void fraction and larger group 2 void fraction. As mentioned previously, turbulence is more significant in flows in larger pipes. This may lead to additional bubble breakup due to turbulence in larger pipe sizes, which results in fewer large bubbles and additional group 1 bubbles. Fig. 4c shows the effect of system pressure on the flow, as well as the effect of liquid velocity. Again, conditions at three liquid velocities and similar gas velocities are shown, with each color representing a flow condition and the different symbols representing pressures of 180 kPa and 280 kPa, respectively. In general, the only significant effect of the system pressure is to affect the density of the gas phase. In the current experiments, the gas volumetric flux rather than mass flow rate is used as the boundary condition, so changes in bubble properties will be small over the observed range of system pressures resulting in nearly immeasurable changes to bubble properties or bubble rise velocity, so only very small differences in the profiles are expected. As the figure shows, neither the liquid velocity over the range studied nor the system pressure over the range studied has any significant effect on the local profiles. The small differences between the profiles at different pressures can easily be accounted for as experimental error and small differences in the test conditions.
4.1.2. Gas velocity The gas velocity profiles are shown in Fig. 5. Fig. 5a shows flow conditions identical to that in 4a, and the data shows that the gas velocity increases as the gas flow rate increases. The gas velocity profiles also show that the velocity for group 1 bubbles is nearly constant across the pipe, with some decrease in the gas velocity near the pipe wall. This can be caused by enhanced turbulent diffusion resulting in significant mixing of the two-phase mixture, as was indicated in previous studies. For group 2 bubbles, the decrease in gas velocity near the pipe wall is somewhat smaller but begins slightly further from the pipe wall than for group 1 bubbles. This is simply because the bubbles are larger, meaning that while the effect of the wall is felt further away, the larger bubble is more resistant to changes in momentum due to the influence of the pipe wall.
Fig. 4. Void fraction profiles.
Fig. 5b, with flow conditions identical to Fig. 4b and measurements shown at z/D = 33.9 in the 0.152 m test section and z/ D = 26.0 in the 0.203 m test section, indicates that the group 1 gas velocity is slightly elevated in the 0.152 m test section when compared to the 0.203 m test section, but that the group 2 gas velocities are reasonably similar and perhaps slightly elevated in the 0.203 m test section. These differences are likely due to the effect of secondary recirculating flow patterns, which develop due to the effect of the large group 2 bubble moving through the mixture.
18
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22
Fig. 6. Comparison of gas flux measurements.
weighted sum. In Fig. 6, the comparison between the gas flux measured using a Venturi mass flow meter and the conductivity probe method is shown. The results show an average difference of 12.1%, while the expected uncertainty based on the velocity, void fraction, and Venturi meter measurement uncertainties is 12.9%. The maximum error for the tests in the 0.152 m diameter test facility is 12.3%, while the maximum error for the tests in the 0.203 m diameter test facility is 15.8%.
Fig. 5. Gas velocity profiles.
The data seems to indicate that the recirculation effects may be more significant in the smaller pipe sizes very close to the boundary between large and small pipes and become less important as the pipe size increases. Fig. 5c shows that the gas velocity has almost no variation due to pressure, which is expected for the flow conditions tested. Some variation in the group 2 velocity measured near the pipe wall is likely due to the small number of large bubbles encountered, which can have a negative effect on the measurement accuracy. To confirm the performance of the conductivity probe measurement technique, the gas flux has been calculated from the measured local gas velocity and void fraction measurements using a
4.1.3. Interfacial area concentration Fig. 7a shows the effect of varying the gas velocity on the interfacial area concentration profiles. The flow conditions shown are identical to those shown in Fig. 4a. Here, the interfacial area concentration profile follows much the same trend as the void fraction profile. These trends are expected as the group 1 bubble size is expected to remain relatively constant. Fig. 7b shows the effect of pipe diameter on the interfacial area concentration profile, again using the same test conditions as Fig. 4b and at the same axial locations. The profile indicates a slightly higher group 1 interfacial area concentration and slightly lower group 2 interfacial area concentration in the larger diameter test section. This is consistent with the previous observations regarding the void fraction and indicates that a larger portion of the void fraction is made up of smaller spherical and distorted bubbles in the 0.203 m test section when compared to the 0.152 m test section. Fig. 7c shows the effect of pressure using the same test conditions as in Fig. 4c, and as in Fig. 4c the pressure effect of pressure over the range measured in this study and the effect of superficial liquid velocity are negligible. 4.1.4. Average bubble size The bubble size in this case is estimated by the Sauter mean diameter, DSm ¼ 6a=ai which is based on the measured volume and surface area of the bubbles. The average bubble size profiles are given in Fig. 8. Fig. 8a shows that the average group 1 bubble size increases as the gas flow rate increases but reaches a maximum of just over 3 mm at roughly the same gas flow rate. Overall the profiles are very flat, but the group 1 bubble size tends to decrease near the pipe wall. This agrees with what is known about the lift force, namely that small bubbles are pulled toward the wall and large bubbles pushed away from the wall. The group 2 profile, however, shows an increase in the average bubble size near the
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22
19
Fig. 7. Interfacial area concentration profiles. Fig. 8. Average bubble diameter profiles.
wall. This may be because only very large group 2 bubbles are able to get near the wall while smaller ones are forced away. This would result in slightly larger measured bubble sizes. Fig. 8b shows that the bubble size is not significantly affected by changes in pressure. Fig. 8b shows that while the group 2 bubble size is not significantly affected by the change in pipe diameter, the group 1 bubble size is slightly increased in the larger channel. This is likely due to the increase in group 1 void fraction, which causes additional coalescence by to random collision of group 1 bubbles. Fig. 8c shows that the bubble size is not significantly affected by changes in pressure.
4.2. Comparison with drift-flux models for large pipes Most analysis codes for thermal–hydraulic systems use the onedimensional formulation of the two-fluid model. Therefore, the area-averaged data is of great interest in developing and validating models for application in such analysis codes. The area averaged data collected in this experiment has therefore been compared to the most up-to-date drift-flux model in large pipes. This model is that of Hibiki and Ishii [7], as determined by Schlegel et al. [25] and detailed in Table 4. Therefore in Figs. 9 and 10 the data is
20
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22
Table 4 Distribution parameter and drift velocity specified by Hibiki and Ishii [7]. Distribution parameter qffiffiffiffi þ 1:69 qffiffiffiffi hj i q q C 0 ¼ exp 0:475 hjgþ i 1 qg þ qg f f qffiffiffiffi n hjþ i o qffiffiffiffi q q C 0 ¼ 2:88 hjgþ i þ 4:08 1 qg þ qg f f qffiffiffiffi qffiffiffiffi q q C 0 ¼ 1:2 expð0:110hjþ i2:22 Þ 1 qg þ qg f f qffiffiffiffi qffiffiffiffi q q C 0 ¼ ½0:6 expf1:2ðhjþ i 1:8Þg þ 1:2 1 qg þ qg f f qffiffiffiffiffiffiffiffiffiffiffiffiffi 1:2 0:2 qg =qf qffiffiffiffiffiffiffiffiffiffiffiffiffi 1:2 0:2 qg =qf qffiffiffiffiffiffiffiffiffiffiffiffiffi 1:2 0:2 qg =qf
Drift velocity Vþ gj
¼
Vþ gj;B
Applicable range
expð1:39hjþ g iÞ
þ
Vþ gj;P f1
expð1:39hjþ g iÞg
þ
þ
þ Bubbly flow 0 hjþ g i=hj i 0:9 þ
þ
þ þ Vþ gj ¼ V gj;B expð1:39hjg iÞ þ V gj;P f1 expð1:39hjg iÞg
Bubbly flow 0:9 hjg i=hj i 1
þ Vþ gj ¼ V gj;P
Cap bubbly flow < a >< 0:3; 0 hj i 1:8
Vþ gj
Cap bubbly flow < a >< 0:3; 1:8 hjþ i
¼
þ
Vþ gj;P
0:157 0:809 qg N 0:562 Vþ lf gj ¼ 0:0019 minðDH ; 30Þ qf 0:157 q g ¼ 0:92 Vþ gj qf pffiffiffi rg Dq 1=4 2 q2
Cap bubbly flow N lf < 2:25 103
0
Annular flow
Cap bubbly flow N lf > 2:25 103 Churn-turbulent flow
f
1þ
1hai pffiffiffiffiffiffiffiffiffiffi haiþ4 qg =qf
plotted with the predictions calculated by the model for the 0.152 m and 0.203 m test sections, respectively. The void fraction is plotted in this case because it is a directly measured parameter and therefore carries less uncertainty than other possible parameters. Additionally, this allows for direct evaluation of the prediction accuracy of the drift-flux models for void fraction. For the 0.152 m channel the lower liquid velocity conditions agree with the model prediction quite well, although at high liquid velocity the data does not show as much change in void fraction as expected. For the 0.203 m diameter channel, the predictions in bubbly flow are very good. At the lowest liquid velocity condition there is a significant amount of variation in the data, however this may be due to measurement uncertainty caused by the development of recirculating secondary flow patterns at low volumetric fluxes that make accurate measurements difficult. At higher void fractions the effect of the liquid velocity on the void fraction is smaller than expected but the data falls in the approximate range predicted by the model. Generally the model predicts the data quite well with an average error of 12.4%. 4.3. Axial flow development Fig. 11 shows the axial development of the area-averaged interfacial area concentration. The data in the figure shows the ratio of
Fig. 9. Drift-flux model evaluation, DH = 0.152 m.
the measured interfacial area concentration to the expected interfacial area concentration, or n ¼ hai;meas i=hai;pred i. The expected value is calculated by assuming that bubble expansion is the only mechanism for change in interfacial area concentration. Based on the IATE without bubble interaction models, this expected value is determined by the following equations for group 1 and group 2, respectively:
d ðhai1 ihhv g1 iiÞ ¼ dz
2 hai1 i ha1 ihhv g1 ii dP CDc1 3 ha1 i P dz
d 2 hai2 i ha2 ihhv g2 ii dP ðhai2 ihhv g2 iiÞ ¼ dz 3 ha2 i P dz ha i h a ihh v 1 g1 ii dP i1 þ CDc1 ha1 i P dz
ð6Þ
ð7Þ
Here P is the pressure. The constant C has been determined by previous modeling efforts [3,4]. Using the inlet conditions as the initial condition, these equations can be used to estimate the change in interfacial area concentration at each of the remaining two measurement locations. This procedure results in the data shown in Fig. 11, where values greater than unity indicate that interfacial area concentration sources are dominant, while values less than unity indicate that interfacial area sinks are dominant. For the 0.152 m test section, the data shows very similar patterns
Fig. 10. Drift-flux model evaluation, DH = 0.203 m.
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22
21
Fig. 11. Axial development of area-averaged interfacial area concentration.
for all of the flow conditions with some bubble breakup initially and bubble coalescence dominating later. The data in the 0.203 m test section shows much more varied trends. This may have several causes. Increased turbulence may play some role, as well as changes in the average bubble size during injection. It may be useful to attempt measurement of turbulence intensity using Laser-Doppler Anemometry or Hot-Film Anemometry to determine if this is the case. Larger liquid flow rates required to sustain a given superficial liquid velocity may result in smaller bubbles at the injection location, reducing the initial breakup effect but leading to more bubble breakup further along the test section. Overall, the data shows that the measured interfacial area concentration can vary significantly from the expected value considering only bubble expansion, which means that accurate models for the bubble interaction terms are essential for developing accurate predictions of interfacial area concentration for the prediction of the behavior of nuclear reactor systems.
pipes has been expanded through the addition of 132 area-averaged data points. The effect of pressure and diameter on the twophase flow structure has been investigated and the data used to evaluate the performance of the current state-of-the-art drift-flux models for large diameter pipes. The interfacial area concentration data collected shows the necessity of developing additional source and sink term models and can provide a solid basis for benchmarking and verifying those models for flows in the bubbly, cap/slug and churn-turbulent flow regimes.
Acknowledgement This work was performed at Purdue University, in the Institute of Thermal Hydraulics, under the auspices of the US Nuclear Regulatory Commission.
References 5. Conclusions A review of the literature has shown that the database for interfacial area concentration in large diameter pipes has severe limitations. To address these limitations, an experiment has been undertaken to measure the local flow parameters in pipes with diameters of 0.152 m and 0.203 m under a wide variety of flow conditions with void fractions from 0.20 to 0.75 and at system pressures of 180 kPa and 280 kPa. The profiles of void fraction, interfacial area concentration, gas velocity and Sauter mean diameter all show reasonable trends and the data measured by electrical conductivity probes agrees well with that determined using other metrics such as gas flow rate measured by a Venturi mass flow meter. The database for interfacial area transport in large
[1] S. Elgholbashi, T. Abou-Arab, Two-equation turbulence model for two-phase flows, Physics of Fluids 26 (1983) 931–938. [2] X.Y. Fu, Interfacial area measurement and transport modeling in air-water two-phase flow. Ph.D. Thesis, Purdue University, West Lafayette, IN, USA, 2001. [3] X.Y. Fu, M. Ishii, Two-group interfacial area transport in vertical air-water flow: I. Mechanistic model, Nuclear Engineering and Design 219 (2) (2003) 143–168. [4] X.Y. Fu, M. Ishii, Two-group interfacial area transport in vertical air-water flow: II. Model evaluation, Nuclear Engineering and Design 219 (2) (2003) 169–190. [5] T. Hibiki, M. Ishii, One-group interfacial area transport of bubbly flows in vertical round tubes, International Journal of Heat and Mass Transfer 43 (15) (2000) 2711–2726. [6] T. Hibiki, M. Ishii, Experimental study on interfacial area transport in bubbly two-phase flows, International Journal of Heat and Mass Transfer 42 (1999) 3019–3035. [7] T. Hibiki, M. Ishii, One-dimensional drift-flux model for two-phase flow in a large diameter pipe, International Journal of Heat and Mass Transfer 46 (2003) 1773–1790.
22
J.P. Schlegel et al. / Experimental Thermal and Fluid Science 41 (2012) 12–22
[8] T. Hibiki, T.H. Lee, J.Y. Lee, M. Ishii, Interfacial area concentration of boiling bubbly flow systems, Chemical Engineering Science 61 (2006) 7979–7990. [9] M. Ishii, One-dimensional Drift-flux Model and Constitutive Equations for Relative Motion between Phases in Various Two-phase Flow Regimes, Argonne Report, vol. ANL-77-47, 1977. [10] M. Ishii, K. Mishima, Two-fluid model and hydrodynamic constitutive relations, Nuclear Engineering and Design 82 (1984) 107–126. [11] M. Ishii, T. Hibiki, Thermo-Fluid Dynamics of Two-Phase Flow, second ed., Springer, New York, 2010. [12] I. Katoaka, M. Ishii, A. Serizawa, Local formulation and measurements of interfacial area concentration in two-phase flow, International Journal of Multiphase Flow 12 (4) (1986) 505–529. [13] I. Kataoka, M. Ishii, Drift-flux model for large diameter pipe and new correlation for pool void fraction, International Journal of Heat and Mass Transfer 30 (1987) 1927–1939. [14] I. Kataoka and A. Serizawa, Modeling and prediction of turbulence in bubbly two-phase flow. Proc. 2nd Int. Conference on Multiphase Flow, 11–16. April 3– 7, 1995. [15] S. Kim, X.Y. Fu, X. Wang, M. Ishii, Development of the miniaturized four-sensor conductivity probe and the signal processing scheme, International Journal of Heat and Mass Transfer 43 (22) (2000) 4101–4118. [16] G. Kocamustafaogullari, M. Ishii, Foundations of the interfacial area transport equation and its closure relations, International Journal of Heat and Mass Transfer 38 (3) (1995) 481–493. [17] D. Lucas, M. Beyer, L. Szalinski, P. Schutz, A new database on the evolution of air-water flows along a large vertical pipe, International Journal of Thermal Sciences 49 (2010) 664–674. [18] A. Manera, B. Ozar, S. Paranjape, M. Ishii, H.M. Prasser, Comparison between wire-mesh sensors and conductive needle-probes for measurements of twophase flow parameters, Nuclear Engineering and Design 239 (2009) 1718– 1724. [19] K. Mishima, M. Ishii, Flow regime transition criteria for upward two phase flow in vertical tubes, International Journal of Heat and Mass Transfer 27 (5) (1984) 723–737. [20] A. Ohnuki and H. Akimoto. Prediction of phase distribution under bubbly flow in a large vertical pipe by multidimensional two-fluid model. Third Int. Conference on Multiphase Flow, ICMF ’98, Lyon, France, June 8–12, 1998.
[21] A. Ohnuki, H. Akimoto, Experimental study on transition of flow pattern and phase distribution in upward air-water two-phase flow along a vertical pipe, International Journal of Multiphase Flow 26 (3) (2000) 367–386. [22] A. Ohnuki, H. Akimoto, Model development for bubble turbulent diffusion and bubble diameter in large vertical pipes, Journal of Nuclear Science and Technology 38 (2001) 1074–1080. [23] H.M. Prasser, Evolution of interfacial area concentration in a vertical air-water flow measured by wire-mesh sensors, Nuclear Engineering and Design 237 (2007) 1608–1617. [24] J.P. Schlegel, P. Sawant, S. Paranjape, B. Ozar, T. Hibiki, M. Ishii, Void fraction and flow regime in adiabatic upward two-phase flow in large diameter pipes, Nuclear Engineering and Design 238 (2009) 2864–2874. [25] J.P. Schlegel, T. Hibiki, M. Ishii, Development of a comprehensive set of driftflux constitutive models for pipes of various hydraulic diameters, Progress in Nuclear Energy 52 (7) (2010) 666–677. [26] M.E. Shawkat, C.Y. Ching, M. Shoukri, Bubble and liquid turbulence characteristics of bubbly flow in a large diameter vertical pipe, International Journal of Multiphase Flow 34 (2008) 767–785. [27] X. Shen, Y. Saito, K. Mishima, H. Nakamura, A study on the characteristics of upward air-water two-phase flow in a large diameter pipe, Experimental Thermal and Fluid Science 31 (2006) 21–36. [28] M. Shoukri, I. Hassan, I. Gerges, Two-phase bubbly flow structure in largediameter vertical pipes, The Canadian Journal of Chemical Engineering 81 (2003) 205–211. [29] T.R. Smith, Two-group Interfacial Area Transport Equation in Large Diameter Pipes, Ph.D. Thesis, Purdue University, 2002. [30] X. Sun, T.R. Smith, S. Kim, M. Ishii, J. Uhle, Interfacial area of bubbly flow in a relatively large diameter pipe, Experimental Thermal and Fluid Science 27 (1) (2002) 97–109. [31] X. Sun, M. Ishii, J. Kelly, Modified two-fluid model for the two-group interfacial area transport equation, Annals of Nuclear Energy 30 (16) (2003) 1601–1622. [32] Q. Wu, S. Kim, M. Ishii, S.G. Beus, One-group interfacial area transport in vertical bubbly flow, International Journal of Heat and Mass Transfer 41 (1998) 1109–1112. [33] K. Yoneda, A. Yasuo, T. Okawa, Flow structure and bubble characteristics of steam-water two-phase flow in a large diameter pipe, Nuclear Engineering and Design 217 (3) (2002) 267–281.