- Email: [email protected]
Downward two phase flow experiment and general flow regime transition criteria for various pipe sizes
International Journal of Heat and Mass Transfer 125 (2018) 179–189
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Downward two phase flow experiment and general flow regime transition criteria for various pipe sizes Zijiang Yang a,b, Zhuoran Dang b, Xiaohong Yang b, Mamoru Ishii b,⇑, Jianqiang Shan a a b
School of Nuclear Science and Technology, Xian Jiaotong University, Xi’an, Shaanxi, China School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907, USA
a r t i c l e
i n f o
Article history: Received 28 October 2017 Received in revised form 20 March 2018 Accepted 22 March 2018
Keywords: Downward flow regime Probability density profile Neural network method Flow regime boundary criteria
a b s t r a c t Flow regime map is often used in choosing constitutive correlations for the two-phase flow model. The related research mainly concentrates on the vertical upward and horizontal flow, while it is not sufficient in the vertical downward flow. Downward flow is very important as it is frequently encountered in the industrial applications. To enrich the downward flow research, an experiment is performed on a piping system with an inner diameter of 0.1524 m. Four different flow patterns (bubbly flow, cap bubbly flow, churn turbulent flow, and annular flow) are classified with the artificial neural network method. The probability density function (PDF) profile of each flow pattern is discussed. The proposed flow regime map is compared with the other experiments and the effect of the pipe size is discussed. The existing downward flow regime boundary criteria are assessed with the experiment results. It is found that these criteria cannot fit the experiment results well. A set of general boundary criteria are still needed. In this paper, the criteria for the boundary of the bubbly flow, the boundary between the cap bubbly flow and the slug flow, and the boundary of the falling film regime are proposed. They are verified with the experiments on different size pipes. A significant inlet effect on the flow regime boundary is found. The falling film boundary criterion proposed cannot be applied when a sparger is used to inject gas into the downward test section. Published by Elsevier Ltd.
1. Introduction Recently, more and more system analysis codes, such as RELAP5 [1], TRACE [2], are developed based on the two-fluid model. The two-fluid model is complex and contains a lot of constitutive correlations. In different flow regimes, different constitutive correlations are utilized to ensure that a correct flow structure is considered. In the past several decades, most of the flow regime analyses are focused on the upward or horizontal directions [3–5]. The flow regime transition and modeling analyses on the downward flow are rare. The downward flow analysis is important in many industrial applications, including the advanced reactor designs where passive safety systems [6–8] are extensively used. For example, a passive containment cooling system is utilized in the AP1000. When this passive system is put into work, the gas-water mixture flows downwardly along the containment inner and outer wall. Moreover, in many gravity driven safety systems, two-phase downward flow is also a common phenomenon. A clear downward flow regime map is of great importance when the thermal hydrau⇑ Corresponding author. E-mail address: [email protected] (M. Ishii). https://doi.org/10.1016/j.ijheatmasstransfer.2018.03.072 0017-9310/Published by Elsevier Ltd.
lic behaviors of the advanced reactors are simulated and analyzed. However, for most sub-channel, system, and containment analysis codes, a downward flow regime map is lacked. These codes’ simulation capability is suspicious when they are applied to advanced reactors. Some studies have focused on the downward flow regime map. Usui [9,10] performed downward co-current experiments on 0.016 m and 0.024 m inner diameter pipes. In the experiment, two-phase flow was injected into the test section using an inverted U-tube. With the downward flow’s local void fraction measured by a conductance needle probe, a center peaked void fraction profile for the downward bubbly flow was proposed. Based on the experiment results, some boundary criteria were proposed. Both upward and downward experiments on 0.0254 m and 0.0508 m pipes were performed by Lee et al. [11], who also developed an instantaneous and objective flow regime identification method. It was found that in the vertical downward flow, flow regimes’ boundaries are highly dependent on the pipes’ diameter. The kinetic wave propagation was observed in the experiments. Downward co-current flow experiments on 0.0254 m and 0.0508 m pipes were also conducted by Goda et al. [12]. The artificial neural network method was applied to eliminate researcher’s subjective error in sorting the
180
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189
Nomenclature Symbol PDF CPDF Vnon-D Vmeasured Vair Vwater hjfi hjgi
a g D C0 C1 Cw Frl Frg Eo
probability density function cumulative probability density function non-dimensional voltage measured voltage measured voltage when the loop is filled with air measured voltage when the loop is filled with water liquid superficial velocity gas superficial velocity void fraction gravity force pipe diameter distribution parameter drift velocity coefficient wall friction factor liquid froude number gas froude number Eotvos number
flow regimes. Four flow regimes (bubbly, slug, churn-turbulent, and annular flow) were observed. The flow regime maps classified by the neural network were compared with the results got through conventional flow visualization method. And the neural network classification method was validated. A 0.0254 m diameter pipe downward flow experiment was performed by Pan et al. [13]. A new fuzzy C-means clustering algorithm and relief attribute weighting algorithm method was adopted in classifying flow regimes. Entrance effect on the flow regime transition was discussed. Pan’s result was similar to that of Lee’s. In the 1980 s, Barnea et al. [14] performed researches on 0.0254 m and 0.0508 m pipes. However, the proposed flow regime map differs from other researchers. Downward and upward flow experiments on a 0.038 m pipe and a 0.04 m pipe were conducted by Kendoush and Al-Khatab [15] and Yamaguchi and Yamazaki [16], respectively. Yamaguchi also performed experiments on a 0.08 m pipe. In Yamaguchi’s experiments, the flow reimge maps showed significant difference of flow pattern transition boundaries within upward flow, countercurrent flow and downward flow’s comparison. Julia et al. [17] performed vertical co-current downward experiments on a 0.0508 m pipe. Local void fraction was measured by a three double-sensor conductivity probe. With the void fraction signal, local flow regime maps were classified by the neural network method. It was found that only the local flow regimes in the pipe center agree with the global flow regimes. Qiao et al. [18] conducted a downward experiment on a 0.0508 m pipe and studied the inlet effect on two-phase flow parameters. Three types of inlet conditions (elbow, sparger, and sparger with a straightener) were considered. Flow regime maps for each inlet were developed and compared to identify the inlet effects. It was found that in the downward co-current bubbly flow, the void fraction profile is center-peaked. Lokanathan and Hibiki [19] reviewed downward flow experiments, existing boundary criteria, and downward drift flux models in his paper. As mentioned above, it can be found that the existing experiments are mostly conducted on small pipes. The need for large pipe’s downward flow experiments is urgent. As for the flow regime transition analysis, a set of downward flow regime criteria were provided by Usui and Barnea, respectively. Lee proposed a criterion for the boundary between the slug flow and the churn turbulent flow. Crawford et al. [20] provided a set of empirical criteria. When compared with the experiment’s
r ql qg Kug Vgj Dd,max Ref dmean v Hwave RIM AIM B CB CT AN FF
surface tension liquid density gas density gas kutateladze number drift velocity maximum distorted bubble limit fluid Reynolds number mean film thickness kinematic viscosity wave amplitude ring type impedance meter arc type impedance meter bubbly flow cap bubbly flow churn turbulent flow annular flow falling film flow
data in this paper, most of the existing criteria can only satisfy their own experimental data. The general flow regime boundary criteria are still lacked. In conclusion, the research on the downward flow regime is still not enough. Besides, experiments for relative large inner diameter pipes are lacked. A set of general flow regime boundary criteria have not been provided yet. Thus, the purpose of this paper is to analyze the experimental data obtained on a 0.1524 m diameter piping loop and propose a set of general flow regime boundary criteria for the downward pipe flow.
2. Experiment setup The experimental loop utilized in this investigation is an adiabatic, vertical and air-water system. The schematic diagram of the experimental loop is shown in Fig. 1. The test section has three parts: a top horizontal section, a vertical downward section, and a bottom horizontal section. They are all 0.1524 m inner diameter transparent acrylic pipes. It should be noted that the top horizontal section also serves as an inlet to the vertical downward flow. The length of the top horizontal section is 8.47 m, which allows the
Fig. 1. Schematic of the Experiment Facility.
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189
two-phase horizontal flow to be fully developed. The length of the vertical downward pipe and the bottom horizontal pipe is 6.42 m and 3.25 m, respectively. Two 90° PVC elbows are used to connect these test sections. Water is supplied by a centrifugal pump and controlled by a combination of a frequency driver and a bypass. The water flow rate is measured by an electro-magnetic flow meter whose accuracy is within ±5%. Air is supplied via external compressors with a pressure maintained by a pressure regulator at 0.551 MPa and is controlled by a globe valve. The gas flow rate is measured by rotameters and Venturi flow meters with an error less than ±4%. The range of hjgi is from 0.05 m/s to 9.8 m/s. At the inlet of the top horizontal section, air is injected through a pipe with an inner diameter of 0.0508 m. Water flows into the horizontal section through a vertical upward feed water line. The range of hjfi is from 0.1 m/s to 2.7 m/s. Water and air mix with each other in the top section. After the two-phase flow is fully developed, it goes into a 90° downward elbow and changes the flow direction. The focus of this paper is the fully developed vertical downward flow. The air-water mixture finally flows through the test section and goes into two large water tanks. These tanks are connected with the atmosphere to maintain pressure and are used to separate water from gas. Water can be pumped into the test loop again. In this experiment, the most important purpose is to get the downward fully developed flow regime map. Thus, the pressure in the downward data-gotten position (z/D = 102.17) is maintained around 0.1 MPa. The range of the pressure is from 0.095 MPa to 0.105 MPa. The pressure effect on the downward flow regime map is not discussed in this paper. An impedance void meter is a non-intrusive conductance type probe that relies upon the difference of the electrical conductivity between air and water. It is utilized to measure average void fraction. Six impedance meters are applied on the test section. Three of them are ring type impedance meters (RIM) and the others are arc type impedance meters (AIM). In this paper, only the data of the impedance meters (RIM2, AIM3 as illustrated on Fig. 1) at z/D = 51.67, z/D = 102.17 are analyzed, for the flow is fully developed at these two points. The position of AIM3 lies at z/D = 46.6 below the elbow. For an arc type impedance meter, the nondimensional voltage is taken as the void fraction value. The correlation is as follow:
V non-D ðNon-Dimensional VoltageÞ ¼
V meassured V air V water V air
ð1Þ
3. Artificial neural network In this paper, flow regimes are categorized by the Kohonen artificial neural network. The neural network’s structure is shown in
Fig. 2. Structure of the Kohonen Neural Network.
181
Fig. 2. The neural network’s classification theory is based on the preservation of topology. The Kohonen neural network is a selforganized classification tool and has a two-layer network which can categorize input data into different groups. Inputs are fed to the neural network as vectors. The weighting factors of the neural network form vectors which have the same dimensionality as that of the input vectors. The Kohonen network then aligns the weight vectors with intrinsic clusters in the data. Thus, the characteristic weight vectors are used to classify input vectors. The advantage of the neural network method is that this method moderates subjective influences in distinguishing the flow regimes. Kohonen neural network’s procedure is illustrated in Fig. 3. In this paper, flow regimes are classified into four groups: the bubbly flow (B), the cap bubbly flow (CB), the churn turbulent flow (CT), and the annular flow (AN). The input signal is the void fraction CPDF which is the abbreviation of the cumulative probability density function. Signals are automatically put into two groups, the training group and the identification group. The program is trained with the signals in the training group to find the characteristics of each classification group. Based on the characteristics, the input signals in the identification group can be classified. 4. Experiment results 4.1. Flow regimes This chapter describes the flow regime maps of the test section. Firstly, the flow regime map of the horizontal test section is discussed. In the experiment, the wavy stratified flow, the pseudo slug flow, the plug flow, and the slug flow are observed. The wavy stratified flow is a separated flow in which gas is in the upper part and liquid is in the lower part. In the pseudo slug flow, the interface is wavy. However, most waves cannot reach the upper wall due to the relatively low liquid level. Only waves with large amplitude can reach the upper wall occasionally. In the plug flow, the wave creates the liquid bridge with no vortex. The gas part observed in the plug flow has a long slender tail. In the slug flow, a vortex which carries bubbles is observed in the liquid slug. The appearance of vortexes is a main difference between the slug flow and the plug flow, for bubbles in vortexes increase the interfacial area. The horizontal flow regime map from this experiment is presented in Fig. 4. The flow regime map agrees well with Mandhane’s flow regime map [21]. However, a higher hjfi is observed at the boundaries between the stratified flow and the plug flow and between the plug flow and the slug flow. It can be explained as the effect of the pipe size. As can be seen in Fig. 4, the hjfi on the stratified flow boundary increases from Kong’s experiment [22]
Fig. 3. Flow regime identification procedure.
182
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189
Fig. 6. Cap bubbly flow. Fig. 4. Horizontal Flow regime.
Fig. 7. Churn turbulent flow. Fig. 5. Bubbly flow.
whose pipe’s inner diameter is 0.038 m to a higher value in Jepson’s experiment [23] whose inner diameter is 0.3 m. In this experiment, the stratified flow’s boundary matches that of Jepson’s, which means pipe size effect is not significant in large pipes. As for the boundary between the plug flow and the slug flow, the transition boundary in Kong’s flow regime map differs from that in Mandhane’s flow regime map. Our result is similar with Kong’s map. In the vertical downward part, the bubbly flow, the cap bubbly flow, the annular flow, and the churn turbulent flow are observed. The pictures took during the experiment are presented here to show each flow pattern. The bubbly flow (as in Fig. 5) has the form of the bubbly flow in the vertical upward flow. However, due to the coring phenomenon, small bubbles migrate to the center part of the pipe. Because of the pipe size effect, the cap bubbly flow (as in Fig. 6) is observed instead of the slug flow. In the cap bubbly flow, the flow is quite chaotic, with irregular large bubbles observed near the wall. With a relative low hjfi, the annular flow (as in Fig. 8) is the most common flow pattern. In the low hjgi, the annular flow observed in the experiments are the so-called ‘‘falling film flow [14]”. With a high hjgi and a high hjfi, the flow
pattern changes to the churn turbulent flow (as in Fig. 7). The churn turbulent flow is very chaotic and is a transition flow pattern between the cap bubbly flow and the annular mist flow. The downward flow regime map is presented in Fig. 9. The flow regime map produced by the neural network is compared with that of Qiao et al’s 0.0508 m pipe experiment, Lee’s 0.0254 mm pipe experiment, and Usui’s 0.024 m experiment. As in the figure, when pipe size increases, the falling film boundary goes to a higher hjfi. Slug bubbles are not observed in this experiment, which means the slug flow does not exist in large downward pipes. It is of interest that the bubbly flow boundary does not change too much in different pipes. It is mainly because that, for all size pipes, small bubbles mitigate to the pipe center area where cap bubbles can be generated easily. 4.2. Probability density function analysis Characteristic probability density function (PDF) profiles of the horizontal flow regimes are presented in Fig. 10. As illustrated in the figure, the PDF profile of the stratified flow is a single high peak which means that the void fraction variation in stratified flow is very small. The location of the PDF peak is determined by the liquid
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189
Fig. 8. Annular flow.
Fig. 9. Downward Flow regime.
Fig. 10. PDF of horizontal flow regimes.
183
Fig. 11. Slug flow PDF profiles with different hjfi (hjgi = 1.75 m/s).
level. In the plug flow, liquid bridges (with few bubbles) appear, which results in a high PDF peak at the point where void fraction equals zero. Another PDF peak in the plug flow exists at a large void fraction point, which indicates the wave valleys. As for the slug flow, the PDF profile is similar with that of the plug flow. However, as the slug flow has bubbles in its liquid bridge, its first PDF peak is more scattered than that in the plug flow. The pseudo slug flow is a very chaotic regime whose liquid surface is very wavy. Thus, its PDF profile is much more scattered than the other flow regimes’ PDF profiles. As the pseudo slug flow happens at a high hjgi, its average void fraction is larger than the others. The slug flow PDF profiles with different hjfi and hjgi are shown in Figs. 11 and 12, respectively. As the hjfior hjgi goes larger, the second peak of the PDF profile becomes more scattered. It is mainly due to that the wave amplitude increases with an increase in the hjfi or hjgi. Increased wave amplitude means longer liquid bridges which need more water. It leads to lower wave valleys. The decrease in the height of wave valleys results in an increase in the maximum void fraction. In the plug flow, the variation trend is same. The characteristic probability density function (PDF) profiles of the downward flow regimes are presented in Fig. 13. It is found that the PDF profiles of all the flow patterns are characterized by one single peak. For the bubbly flow, the peak exists at very low void fraction due to the small bubbles. In the cap bubbly flow, the existence of large bubbles makes the peak at a relatively higher void fraction and more scattered than the bubbly flow. The peak of the cap bubbly flow pattern’s PDF profile locates at a void fraction which is smaller than 0.5. The structure of the churn turbulent flow is so chaotic that its PDF profile is scattered and has a large averaged void fraction value (larger than 0.5). The annular flow is characterized by a continuous gas core which leads to a large void fraction peak. The cap bubbly flow’s and the churn turbulent flow’s PDF profiles with different hjfi are shown in Figs. 14 and 15, respectively. As illustrated in Fig. 14, with an increase in the hjfi, the average void fraction of the cap bubbly flow decreases. Moreover, as the hjfi increases, the flow becomes more chaotic. Large bubbles break up into small bubbles, which accounts for the high peak at a low void fraction value. In terms of the churn turbulent flow, an increase in the hjfi also decreases the average void fraction. In this flow pattern, a larger hjfi leads to a much more scattered PDF profile. It should be noted that, in the downward flow, no significant difference lies between the cap bubbly flow and the churn turbulent
184
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189
Fig. 12. Slug flow PDF profiles with different hjgi (hjfi = 1.0 m/s).
Fig. 15. Churn turbulent flow PDF profiles with different hjfi (hjgi = 3.3 m/s).
flow. They are both very chaotic and contain an amount of large and small bubbles. 5. Downward flow regime criteria 5.1. Existing criteria Since almost all the existing experiments are conducted on small pipes, the existing flow regime boundary criteria can only be applied on small pipes. Specifically, Usui, Barnea, and Crawford proposed criteria for the boundary between the bubbly flow and the slug flow. Usui’s (Eq. (2)) and Barnea’s criteria (Eq. (3)) are both determined by a critical void fraction. rawford’s criteria (Eq. (4)) is an empirical correlation.
Fig. 13. PDF of downward flow regimes.
a ¼ 0:175
ð2Þ
a ¼ 0:25
ð3Þ
jg jg þ jf pffiffiffiffiffiffi ¼ 0:117 pffiffiffiffiffiffi gD gD
!1:6 ð4Þ
For the boundary between the slug flow and the churn turbulent flow, Lee proposed a critical void fraction criterion (Eq. (5)).
a ¼ 0:5
ð5Þ
For the boundary between the churn turbulent flow and the annular mist flow, correlations were given by Usui (Eq. (6)) and Crawford (Eq. (12)).
" # jg C1 1 þ 1 ¼1 2 7=23 C 0 Fr l jf gC 0 f1 ð2C w Fr l Þ
ð6Þ
The constants C0 and C1 in Eq. (6), represent the distribution parameter and the drift velocity coefficient respectively.
Fig. 14. Cap bubbly flow PDF profiles with different hjfi (hjgi = 0.25 m/s).
C 0 ¼ 1:2 1=ð2:95 þ 350E1:3 Þ 0
ð7Þ
C 1 ¼ 0:345½1 expfð3:37 E0 Þ=10g
ð8Þ
E0 ¼ ðql qg ÞgD2 =r
ð9Þ
C w ¼ 0:046
ð10Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Frl ¼ jf = gDðql qg Þ=ql
ð11Þ
185
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189
Crawford’s correlation is as follow:
1:9
jg jf
!1=8 0:18 ¼ Ku0:2 g Fr g
ð12Þ
where
Kug ¼ jg ðqg Þ0:5 =½gðql qg Þr1=4 2
Fr g ¼ jg =gD
ð13Þ ð14Þ
As for the boundary of the falling film regime, Criteria were proposed by Barnea (Eq. (15)) and Usui (Eq. (16)).
a ¼ 0:65
ð15Þ
Fr g ¼ ðK1 K2 =E0 Þ
23=18
ð16Þ
towards the pipe center. Thus, bubbles migrate to the center area, which is the so called ‘‘coring phenomenon”. Cap bubbles tend to be generated in the center area. It should be noted that for pipes of different diameters, their velocity profiles are similar, which results in similar void fraction profiles. It is supposed that the maximum void fraction in the bubbly flow may not vary with the pipe diameter. Through the experiment data analysis, it is found that the maximum void fraction of the bubbly flow is roughly 0.055. Utilizing Goda’s drift flux model [24] (Eq. (20)), the critical void fraction criterion is compared with the experiment data in Fig. 17. The prediction fits the experiment data well. Goda’s drift flux model is as follow,
hjg i ¼ hhv g ii ¼ C 0 hji þ V gj hai
ð20Þ
where
where
K 1 ¼ 0:92
ð17Þ
K 2 ¼ 7:0
ð18Þ
E0 ¼ ðql qg ÞgD2 =r
ð19Þ
After the presentation of these criteria, they are compared with the experiment data of this paper in Fig. 16. It is shown in Fig. 16 that Lee’s criterion which predicts the boundary between the slug flow and the churn turbulent flow matches the experiment result well. Other criteria cannot fit the experiment data. It should be noted that Usui’s, Barnea’s, and Crawford’s bubbly flow boundary criteria are determined for the boundary between the cap bubbly flow and the slug flow. However, the slug flow doesn’t exist in a large diameter pipe. As for the falling film boundary, it can be found in Fig. 16 that both Usui’s model and Barnea’s model show a larger hjfi boundary prediction. For the boundary between the churn turbulent flow and the annular mist flow, Usui’s model gives a smaller hjgiboundary prediction, and Crawford’s criterion generally matches the data. 5.2. Bubbly flow boundary In a single phase downward turbulent pipe flow, the velocity profile is of a power shape. The maximum velocity exists in the center of a pipe. In the bubbly flow, if the number of bubbles is small, the velocity profile maintains the power shape. The power profile of the velocity exerts a lift force on bubbles with a direction
Fig. 16. Assessment of existing criteria.
pffiffiffi V gj ¼ 2
!14
r g Dq q2f
ð21Þ sffiffiffiffiffiffi!
C 0 ¼ð0:0214hj iþ0:772Þþ 0:0214hj iþ0:228
qg ;206hj i<0 qf ð22Þ
C 0 ¼ð0:2expð0:00848ðhj iþ20ÞÞþ1:0Þ0:2expð0:00848ðhj iþ20ÞÞ sffiffiffiffiffiffi
qg ;hj i<20 qf
ð23Þ
where
hj i ¼
hji V gj
ð24Þ
For most of the small pipe experiments, the cap bubbly flow is not characterized as a flow pattern. The boundary between the bubbly flow and the cap bubbly flow is not clear in most flow regime maps. However, in Lee’s 0.0254 m and 0.0508 m experiments, the cap bubbly flow is distinguished as a different flow pattern. Thus, Lee’s experiments are used to verify the boundary criterion proposed in this paper. Fig. 18 shows the comparison
Fig. 17. Comparison between the bubbly flow boundary criterion with the experiment data.
186
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189
between the criterion with Lee’s 0.0254 m experiment. Fig. 19 shows the comparison between the criterion with Lee’s 0.0508 m experiment. The criterion fits well with these experiments, which means it is reliable and can be applied in pipes of different sizes. 5.3. Boundary between the cap bubbly flow and the slug flow In the cap bubbly flow, cap bubbles migrate to off-center area. When the local void fraction of this area exceeds 0.3, these large cap bubbles hit each other to generate larger bubbles (Taylor bubbles). Then, the downward flow pattern becomes the slug flow. Cap bubbles’ appearance changes the velocity profile and the void fraction profile greatly. It is unfortunately that few research is conducted on these profiles. It is the major difficulty in developing theoretical models for the boundary. However, it is fortunately that the transition from the cap bubble flow to the slug flow is still determined by the void fraction. By utilizing Goda’s drift flux model, the critical void fraction of available flow regime maps is determined. The result is shown in Table 1. It is illustrated in the table that the critical void fraction decreases with an increase in the pipe diameter, which means the critical void fraction is a function of the pipe diameter. An empirical correlation (Eq. (25)) is then proposed to fit these experiment data. Fig. 20 shows the comparison between the prediction and the experiments data. It should be noted that a void fraction of 0.055 is assumed for a 0.1524 m pipe in the fitting procedure. The slug flow doesn’t exist in large pipes. This point is used to keep the line smooth and ensure the minimum predicted void fraction is larger than 0.055. Moreover, large bubbles are also generated in large pipes. Yet, they cannot occupy the whole pipe inner area. It is illustrated in Fig. 20 that as the pipe diameter increases, the large bubbles generation void fraction decreases. Thus, in a 0.1524 m diameter pipe, the large bubbles generation void fraction is around 0.055 according to the boundary critical void fraction variation tendency.
ac ¼
9:25 105 Dd;max ðD Þ
2
þ 0:051
Fig. 19. Comparison between the bubbly flow boundary criterion with Lee’s 0.0508 m downward flow regime map.
Table 1 Slug flow/cap bubbly flow boundary critical void fraction of available flow regime maps. Researcher
Pipe diameter (m)
Void fraction
Usui Goda Lee Bouyahiaoui Kendoush Goda Qiao Julia
0.024 0.0254 0.0254 0.034 0.038 0.0508 0.0508 0.0508
0.175 0.2 0.22 0.11 0.12 0.07 0.09 0.1
ð25Þ
where Dd,max is the maximum distorted bubble limit, D⁄ is the nondimensional pipe diameter.
rffiffiffiffiffiffiffiffiffiffi
Dd;max ¼ 4
r
g Dq
ð26Þ
Fig. 20. Comparison between the correlation and the experiment data.
D ¼
Fig. 18. Comparison between the bubbly flow boundary criterion with Lee’s 0.0254 m downward flow regime map.
D 0:024 m 6 D < 0:1016m Dd;max
ð27Þ
It should be noted that this correlation can only be applied to pipes whose diameter is larger than 0.024 m and smaller than 0.1016 m. When the pipe’s diameter is 0.0254 m, the prediction critical void fraction is 0.198. With Goda’s drift flux model, this prediction value is compared with Pan’s 0.0254 m downward flow regime map in Fig. 21. The correlation predicts the boundary well.
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189
Fig. 21. Comparison between the correlation prediction with Pan’s downward flow regime map.
Fig. 22. Wave regime map [25].
Two difficulties are encountered when trying to build a theoretical model: (1) Velocity profile and void fraction profile interact with each other; (2) Both profiles change with the pipe diameter.
5.4. Falling film boundary In the falling film regime, liquid flows along the pipe wall. If a liquid bridge is generated in the gas core, the flow pattern turns into the cap bubbly flow or the churn turbulent flow. Two requirements are needed to form a liquid bridge. First, the film surface should become wavy. It is large waves’ growth and combination which cause the formation of a liquid bridge. The other requirement is an enough liquid amount (film thickness). The generation of a liquid bridge needs enough liquid. Webb and Hewitt [25] studied downward free falling film’s characteristics. In his paper, waves are categorized into several types. The wave regime map is presented in Fig. 22. It can be concluded from the map that, at the falling film boundary, the film surface has already covered with regular waves which are caused by
187
Fig. 23. Falling film wave amplitude and mean film thickness variation with Ref. [26].
Fig. 24. Comparison between Usui annular void fraction correlation and the experiment data.
the kelvin-helmholtz instability. The instability neural line lies below the falling film boundary. Thus, it is the film thickness which determines whether a liquid bridge can be formed or not. Two assumptions are made: (1) A maximum mean film thickness exists. When the film thickness is larger than this value, the wave amplitude is high enough to form a liquid bridge. (2) The wave amplitude (Hwave) is a linear function of the mean film thickness (dmean ); The second assumption is based on Karapantisios’ research. He found that if the liquid Reynolds number is large enough, both the wave amplitude and the mean film thickness grow linearly. The variation of the wave amplitude and the mean film thickness are presented in Fig. 23. Then, attempts are made to find a critical value of dmean . First, a D good film thickness model or a void fraction prediction model is needed. In the 0.1524 m experiment of this paper, Usui’s annular void fraction prediction correlation (Eq. (16)) matches with the
188
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189
Table 2 Performance evaluation of the Usui annular void fraction correlation. Total points
Percentage of points predicted within
Maximum error
26
±1% 4 (15.4%)
8.76%
±5% 21 (80.8%)
±10% 26 (100%)
Table 3 Verification of the falling film regime’s boundary criterion with different experiments. Researcher
Pipe diameter (m)
Experiment – hjfi (m/s)
Prediction – hjfi (m/s)
Error (%)
USUI BOUYAHIAOUI YAMAGUCHI Julia Qiao I (elbow inlet)
0.024 0.034 0.04 0.0508 0.0508
0.35 0.5 0.55 0.62 0.6
0.357 0.46 0.528 0.648 0.648
+2.0 8.0 5.8 +4.5 +8.0
experiment data well. It is illustrated in Fig. 24 that most points (80.8%) are predicted within 5% error. The maximum error is 8.76%, as shown in Table 2. However, Usui’s annular void fraction correlation doesn’t predict well when applied to small pipes. Bhagwat [27] compared Usui’s correlation with his 0.0127 m downward flow experiment. The error is roughly 30%. Through the literature review, it is found that Karapantisios’ film thickness correlation (Eq. (28)) is relatively good, and has been verified through 0.0254 mm and 0.0508 mm experiments [26]. Thus, Karapantisios’ correlation is recommended to be applied on small pipes’ conditions.
dmean
v 1=3 Ref 0:538 ¼ 0:451 g 4 2
ð28Þ
where
Ref ¼
hjf i D
v
ð29Þ
In the falling film regime, the entrainment is not heavy. The void fraction can be used to present the film thickness. In this experiment, the falling film regime’s boundary void fraction is roughly 0.8, which means the dmean is roughly 0.0528. The predicted D hjfi by Usui’s correlation is 0.868 m/s. The boundary hjfi in the experiment can be found in Fig. 9. It is larger than 0.75 m/s and less than 1.0 m/s. The Usui’s correlation prediction matches well with the experiment data. This criterion is then compared with the other experiments. The results are shown on Table 3. The error is within 10%, which means that the criterion can be applied on pipes with different diameters. However, as studied by Qiao, the inlet condition has a great influence on the downward flow regime boundary. If a sparger is utilized to inject gas into the test section, the boundary of the falling film regime is not a constant hjfi. The criterion proposed here cannot be applied. 6. Conclusion To further study downward flow regime map, an experiment is conducted on a pipe whose diameter is 0.1524 m. In the top horizontal section, four flow patterns (the stratified flow, the plug flow, the slug flow, and the pseudo slug flow) are observed. In the downward vertical section, four flow patterns (the bubbly flow, the cap bubbly flow, the churn turbulent flow, and the annular flow) are observed. The PDF’s profile of each flow pattern is discussed. As for the downward flow regime boundary criteria, existing criteria are reviewed and compared with the experiment. It can be concluded that most existing criteria cannot be applied on large
pipes. However, Lee’s criterion predicts the boundary between the cap bubbly flow and the churn turbulent flow well. In this paper, several criteria are proposed. 1. A critical void fraction (0.055) is proposed for the boundary between the bubbly flow and the cap bubbly flow. 2. A general empirical critical void fraction correlation has been proposed for the boundary between the cap bubbly flow and the slug flow. This correlation can only be applied on pipes whose diameter is larger than 0.024 m, and less than 0.1016 m. 3. The boundary of the falling film regime is determined by the film thickness. When the mean film thickness exceeds 0.0528D, the wave amplitude is large enough to form a liquid bridge. However, inlet effect affects this boundary greatly. If a sparger is used to inject gas into the test section, the criterion cannot be applied. 4. As for the boundary between the cap bubbly flow and the churn turbulent flow, Lee’s criterion is recommended. 5. The annular mist regime’s boundary is not discussed in this paper. It is because that the boundaries found in different experiments cannot agree with each other. No boundary criterion is found. Crawford’s empirical correlation is recommended. Conflict of interest None. Acknowledgments This work was performed at Purdue University under the auspices of the U.S. Nuclear Regulatory Commission (NRC), Office of Nuclear Regulatory Research, through the Institute of ThermalHydraulics. The authors would like to express their gratitude to technical staff of the United States Nuclear Regulatory Commission for their support on this project. This paper was prepared as an account of work sponsored by an agency of the U.S. Government. Neither the U.S. Government nor any agency thereof, nor any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for any third party’s use, or the results of such use, of any information, apparatus, product, or process disclosed in this report, or represents that its use by such third party would not infringe privately owned rights. The views expressed in this paper are not necessarily those of the United States Nuclear Regulatory Commission. References [1] C. Fletcher, R. Schultz, RELAP5/MOD3 code Manual Volume V: User’s Guidelines, Idaho National Engineering Laboratory, Lockheed Idaho Technologies Company, Idaho Falls, Idaho, 1995 (83415). [2] S. Bajorek, TRACE V5. 0 Theory manual, field equations, solution methods and physical models, United States Nuclear Regulatory Commission (2008). [3] M. Kaichiro, M. Ishii, Flow regime transition criteria for upward two-phase flow in vertical tubes, Int. J. Heat Mass Transf. 27 (5) (1984) 723–737. [4] T. Smith, J.P. Schlegel, T. Hibiki, M. Ishii, Two-phase flow structure in large diameter pipes, Int. J. Heat Fluid Flow 33 (1) (2012) 156–167. [5] Y. Taitel, A. Dukler, A model for predicting flow regime transitions in horizontal and near horizontal gas-liquid flow, AIChE J. 22 (1) (1976) 47–55. [6] D. Hinds, C. Maslak, Next-generation nuclear energy: the ESBWR, Nuclear News 49 (1) (2006) 35–40. [7] T.L. Schulz, Westinghouse AP1000 advanced passive plant, Nucl. Eng. Des. 236 (14) (2006) 1547–1557. [8] Z. Yang, J. Shan, J. Gou, Preliminary assessment of a combined passive safety system for typical 3-loop PWR CPR1000, Nucl. Eng. Des. 313 (2017) 148–161. [9] K. Usui, Vertically downward two-phase flow,(II) Flow regime transition criteria, J. Nucl. Sci. Technol. 26 (11) (1989) 1013–1022. [10] K. Usui, K. Sato, Vertically downward two-phase flow, (I) Void distribution and average void fraction, J. Nucl. Sci. Technol. 26 (7) (1989) 670–680. [11] J.Y. Lee, M. Ishii, N.S. Kim, Instantaneous and objective flow regime identification method for the vertical upward and downward co-current two-phase flow, Int. J. Heat Mass Transf. 51 (13) (2008) 3442–3459.
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189 [12] H. Goda, S. Kim, Y. Mi, J.P. Finch, M. Ishii, J. Uhle, Flow regime identification of co-current downward two-phase flow with neural network approach, in: Proceedings of 10th International Conference of Nuclear Engineering (ICONE10), Arlington, VA, 2002. [13] L.M. Pan, M. Zhang, P. Ju, H. He, M. Ishii, Vertical co-current two-phase flow regime identification using fuzzy C-means clustering algorithm and ReliefF attribute weighting technique, Int. J. Heat Mass Transf. 95 (2016) 393–404. [14] D. Barnea, O. Shoham, Y. Taitel, Flow pattern transition for vertical downward two phase flow, Chem. Eng. Sci. 37 (5) (1982) 741–744. [15] A.A. Kendoush, S.A. Al-Khatab, Experiments on flow characterization in vertical downward two-phase flow, Exp. Therm. Fluid Sci. 9 (1) (1994) 34–38. [16] K. Yamaguchi, Y. Yamazaki, Combinated flow pattern map for cocurrent and countercurrent air-water flows in vertical tube, J. Nucl. Sci. Technol. 21 (5) (1984) 321–327. [17] J.E. Julia, Y. Liu, T. Hibiki, M. Ishii, Local flow regime analysis in vertical co-current downward two-phase flow, Exp. Therm Fluid Sci. 44 (1) (2013) 345–355. [18] S. Qiao, D. Mena, S. Kim, Inlet effects on vertical-downward air–water two-phase flow, Nucl. Eng. Des. 312 (2017) 375–388.
189
[19] M. Lokanathan, T. Hibiki, Flow regime, void fraction and interfacial area transport and characteristics of co-current downward two-phase flow, Nucl. Eng. Des. 307 (2016) 39–63. [20] T. Crawford, C. Weinberger, J. Weisman, Two-phase flow patterns and void fractions in downward flow Part I: Steady-state flow patterns, Int. J. Multiphase Flow 11 (6) (1985) 761–782. [21] J. Mandhane, G. Gregory, K. Aziz, A flow pattern map for gas—liquid flow in horizontal pipes, Int. J. Multiph. Flow 1 (4) (1974) 537–553. [22] R. Kong, S. Kim, Characterization of horizontal air–water two-phase flow, Nucl. Eng. Des. 312 (2017) 266–276. [23] W. Jepson, R. Taylor, Slug flow and its transitions in large-diameter horizontal pipes, Int. J. Multiphase Flow 19 (3) (1993) 411–420. [24] H. Goda, T. Hibiki, S. Kim, M. Ishii, J. Uhle, Drift-flux model for downward twophase flow, Int. J. Heat Mass Transfer 46 (25) (2003) 4835–4844. [25] D. Webb, G. Hewitt, Downwards co-current annular flow, Int. J. Multiph. Flow 2 (1) (1975) 35–49. [26] T. Karapantsios, S.t. Paras, A. Karabelas, Statistical characteristics of free falling films at high Reynolds numbers, Int. J. Multiph. Flow 15 (1) (1989) 1–21. [27] S.M. Bhagwat, Study of flow patterns and void fraction in vertical downward two phase flow, Oklahoma State University, 2011.
Contents lists available at ScienceDirect
International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt
Downward two phase flow experiment and general flow regime transition criteria for various pipe sizes Zijiang Yang a,b, Zhuoran Dang b, Xiaohong Yang b, Mamoru Ishii b,⇑, Jianqiang Shan a a b
School of Nuclear Science and Technology, Xian Jiaotong University, Xi’an, Shaanxi, China School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907, USA
a r t i c l e
i n f o
Article history: Received 28 October 2017 Received in revised form 20 March 2018 Accepted 22 March 2018
Keywords: Downward flow regime Probability density profile Neural network method Flow regime boundary criteria
a b s t r a c t Flow regime map is often used in choosing constitutive correlations for the two-phase flow model. The related research mainly concentrates on the vertical upward and horizontal flow, while it is not sufficient in the vertical downward flow. Downward flow is very important as it is frequently encountered in the industrial applications. To enrich the downward flow research, an experiment is performed on a piping system with an inner diameter of 0.1524 m. Four different flow patterns (bubbly flow, cap bubbly flow, churn turbulent flow, and annular flow) are classified with the artificial neural network method. The probability density function (PDF) profile of each flow pattern is discussed. The proposed flow regime map is compared with the other experiments and the effect of the pipe size is discussed. The existing downward flow regime boundary criteria are assessed with the experiment results. It is found that these criteria cannot fit the experiment results well. A set of general boundary criteria are still needed. In this paper, the criteria for the boundary of the bubbly flow, the boundary between the cap bubbly flow and the slug flow, and the boundary of the falling film regime are proposed. They are verified with the experiments on different size pipes. A significant inlet effect on the flow regime boundary is found. The falling film boundary criterion proposed cannot be applied when a sparger is used to inject gas into the downward test section. Published by Elsevier Ltd.
1. Introduction Recently, more and more system analysis codes, such as RELAP5 [1], TRACE [2], are developed based on the two-fluid model. The two-fluid model is complex and contains a lot of constitutive correlations. In different flow regimes, different constitutive correlations are utilized to ensure that a correct flow structure is considered. In the past several decades, most of the flow regime analyses are focused on the upward or horizontal directions [3–5]. The flow regime transition and modeling analyses on the downward flow are rare. The downward flow analysis is important in many industrial applications, including the advanced reactor designs where passive safety systems [6–8] are extensively used. For example, a passive containment cooling system is utilized in the AP1000. When this passive system is put into work, the gas-water mixture flows downwardly along the containment inner and outer wall. Moreover, in many gravity driven safety systems, two-phase downward flow is also a common phenomenon. A clear downward flow regime map is of great importance when the thermal hydrau⇑ Corresponding author. E-mail address: [email protected] (M. Ishii). https://doi.org/10.1016/j.ijheatmasstransfer.2018.03.072 0017-9310/Published by Elsevier Ltd.
lic behaviors of the advanced reactors are simulated and analyzed. However, for most sub-channel, system, and containment analysis codes, a downward flow regime map is lacked. These codes’ simulation capability is suspicious when they are applied to advanced reactors. Some studies have focused on the downward flow regime map. Usui [9,10] performed downward co-current experiments on 0.016 m and 0.024 m inner diameter pipes. In the experiment, two-phase flow was injected into the test section using an inverted U-tube. With the downward flow’s local void fraction measured by a conductance needle probe, a center peaked void fraction profile for the downward bubbly flow was proposed. Based on the experiment results, some boundary criteria were proposed. Both upward and downward experiments on 0.0254 m and 0.0508 m pipes were performed by Lee et al. [11], who also developed an instantaneous and objective flow regime identification method. It was found that in the vertical downward flow, flow regimes’ boundaries are highly dependent on the pipes’ diameter. The kinetic wave propagation was observed in the experiments. Downward co-current flow experiments on 0.0254 m and 0.0508 m pipes were also conducted by Goda et al. [12]. The artificial neural network method was applied to eliminate researcher’s subjective error in sorting the
180
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189
Nomenclature Symbol PDF CPDF Vnon-D Vmeasured Vair Vwater hjfi hjgi
a g D C0 C1 Cw Frl Frg Eo
probability density function cumulative probability density function non-dimensional voltage measured voltage measured voltage when the loop is filled with air measured voltage when the loop is filled with water liquid superficial velocity gas superficial velocity void fraction gravity force pipe diameter distribution parameter drift velocity coefficient wall friction factor liquid froude number gas froude number Eotvos number
flow regimes. Four flow regimes (bubbly, slug, churn-turbulent, and annular flow) were observed. The flow regime maps classified by the neural network were compared with the results got through conventional flow visualization method. And the neural network classification method was validated. A 0.0254 m diameter pipe downward flow experiment was performed by Pan et al. [13]. A new fuzzy C-means clustering algorithm and relief attribute weighting algorithm method was adopted in classifying flow regimes. Entrance effect on the flow regime transition was discussed. Pan’s result was similar to that of Lee’s. In the 1980 s, Barnea et al. [14] performed researches on 0.0254 m and 0.0508 m pipes. However, the proposed flow regime map differs from other researchers. Downward and upward flow experiments on a 0.038 m pipe and a 0.04 m pipe were conducted by Kendoush and Al-Khatab [15] and Yamaguchi and Yamazaki [16], respectively. Yamaguchi also performed experiments on a 0.08 m pipe. In Yamaguchi’s experiments, the flow reimge maps showed significant difference of flow pattern transition boundaries within upward flow, countercurrent flow and downward flow’s comparison. Julia et al. [17] performed vertical co-current downward experiments on a 0.0508 m pipe. Local void fraction was measured by a three double-sensor conductivity probe. With the void fraction signal, local flow regime maps were classified by the neural network method. It was found that only the local flow regimes in the pipe center agree with the global flow regimes. Qiao et al. [18] conducted a downward experiment on a 0.0508 m pipe and studied the inlet effect on two-phase flow parameters. Three types of inlet conditions (elbow, sparger, and sparger with a straightener) were considered. Flow regime maps for each inlet were developed and compared to identify the inlet effects. It was found that in the downward co-current bubbly flow, the void fraction profile is center-peaked. Lokanathan and Hibiki [19] reviewed downward flow experiments, existing boundary criteria, and downward drift flux models in his paper. As mentioned above, it can be found that the existing experiments are mostly conducted on small pipes. The need for large pipe’s downward flow experiments is urgent. As for the flow regime transition analysis, a set of downward flow regime criteria were provided by Usui and Barnea, respectively. Lee proposed a criterion for the boundary between the slug flow and the churn turbulent flow. Crawford et al. [20] provided a set of empirical criteria. When compared with the experiment’s
r ql qg Kug Vgj Dd,max Ref dmean v Hwave RIM AIM B CB CT AN FF
surface tension liquid density gas density gas kutateladze number drift velocity maximum distorted bubble limit fluid Reynolds number mean film thickness kinematic viscosity wave amplitude ring type impedance meter arc type impedance meter bubbly flow cap bubbly flow churn turbulent flow annular flow falling film flow
data in this paper, most of the existing criteria can only satisfy their own experimental data. The general flow regime boundary criteria are still lacked. In conclusion, the research on the downward flow regime is still not enough. Besides, experiments for relative large inner diameter pipes are lacked. A set of general flow regime boundary criteria have not been provided yet. Thus, the purpose of this paper is to analyze the experimental data obtained on a 0.1524 m diameter piping loop and propose a set of general flow regime boundary criteria for the downward pipe flow.
2. Experiment setup The experimental loop utilized in this investigation is an adiabatic, vertical and air-water system. The schematic diagram of the experimental loop is shown in Fig. 1. The test section has three parts: a top horizontal section, a vertical downward section, and a bottom horizontal section. They are all 0.1524 m inner diameter transparent acrylic pipes. It should be noted that the top horizontal section also serves as an inlet to the vertical downward flow. The length of the top horizontal section is 8.47 m, which allows the
Fig. 1. Schematic of the Experiment Facility.
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189
two-phase horizontal flow to be fully developed. The length of the vertical downward pipe and the bottom horizontal pipe is 6.42 m and 3.25 m, respectively. Two 90° PVC elbows are used to connect these test sections. Water is supplied by a centrifugal pump and controlled by a combination of a frequency driver and a bypass. The water flow rate is measured by an electro-magnetic flow meter whose accuracy is within ±5%. Air is supplied via external compressors with a pressure maintained by a pressure regulator at 0.551 MPa and is controlled by a globe valve. The gas flow rate is measured by rotameters and Venturi flow meters with an error less than ±4%. The range of hjgi is from 0.05 m/s to 9.8 m/s. At the inlet of the top horizontal section, air is injected through a pipe with an inner diameter of 0.0508 m. Water flows into the horizontal section through a vertical upward feed water line. The range of hjfi is from 0.1 m/s to 2.7 m/s. Water and air mix with each other in the top section. After the two-phase flow is fully developed, it goes into a 90° downward elbow and changes the flow direction. The focus of this paper is the fully developed vertical downward flow. The air-water mixture finally flows through the test section and goes into two large water tanks. These tanks are connected with the atmosphere to maintain pressure and are used to separate water from gas. Water can be pumped into the test loop again. In this experiment, the most important purpose is to get the downward fully developed flow regime map. Thus, the pressure in the downward data-gotten position (z/D = 102.17) is maintained around 0.1 MPa. The range of the pressure is from 0.095 MPa to 0.105 MPa. The pressure effect on the downward flow regime map is not discussed in this paper. An impedance void meter is a non-intrusive conductance type probe that relies upon the difference of the electrical conductivity between air and water. It is utilized to measure average void fraction. Six impedance meters are applied on the test section. Three of them are ring type impedance meters (RIM) and the others are arc type impedance meters (AIM). In this paper, only the data of the impedance meters (RIM2, AIM3 as illustrated on Fig. 1) at z/D = 51.67, z/D = 102.17 are analyzed, for the flow is fully developed at these two points. The position of AIM3 lies at z/D = 46.6 below the elbow. For an arc type impedance meter, the nondimensional voltage is taken as the void fraction value. The correlation is as follow:
V non-D ðNon-Dimensional VoltageÞ ¼
V meassured V air V water V air
ð1Þ
3. Artificial neural network In this paper, flow regimes are categorized by the Kohonen artificial neural network. The neural network’s structure is shown in
Fig. 2. Structure of the Kohonen Neural Network.
181
Fig. 2. The neural network’s classification theory is based on the preservation of topology. The Kohonen neural network is a selforganized classification tool and has a two-layer network which can categorize input data into different groups. Inputs are fed to the neural network as vectors. The weighting factors of the neural network form vectors which have the same dimensionality as that of the input vectors. The Kohonen network then aligns the weight vectors with intrinsic clusters in the data. Thus, the characteristic weight vectors are used to classify input vectors. The advantage of the neural network method is that this method moderates subjective influences in distinguishing the flow regimes. Kohonen neural network’s procedure is illustrated in Fig. 3. In this paper, flow regimes are classified into four groups: the bubbly flow (B), the cap bubbly flow (CB), the churn turbulent flow (CT), and the annular flow (AN). The input signal is the void fraction CPDF which is the abbreviation of the cumulative probability density function. Signals are automatically put into two groups, the training group and the identification group. The program is trained with the signals in the training group to find the characteristics of each classification group. Based on the characteristics, the input signals in the identification group can be classified. 4. Experiment results 4.1. Flow regimes This chapter describes the flow regime maps of the test section. Firstly, the flow regime map of the horizontal test section is discussed. In the experiment, the wavy stratified flow, the pseudo slug flow, the plug flow, and the slug flow are observed. The wavy stratified flow is a separated flow in which gas is in the upper part and liquid is in the lower part. In the pseudo slug flow, the interface is wavy. However, most waves cannot reach the upper wall due to the relatively low liquid level. Only waves with large amplitude can reach the upper wall occasionally. In the plug flow, the wave creates the liquid bridge with no vortex. The gas part observed in the plug flow has a long slender tail. In the slug flow, a vortex which carries bubbles is observed in the liquid slug. The appearance of vortexes is a main difference between the slug flow and the plug flow, for bubbles in vortexes increase the interfacial area. The horizontal flow regime map from this experiment is presented in Fig. 4. The flow regime map agrees well with Mandhane’s flow regime map [21]. However, a higher hjfi is observed at the boundaries between the stratified flow and the plug flow and between the plug flow and the slug flow. It can be explained as the effect of the pipe size. As can be seen in Fig. 4, the hjfi on the stratified flow boundary increases from Kong’s experiment [22]
Fig. 3. Flow regime identification procedure.
182
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189
Fig. 6. Cap bubbly flow. Fig. 4. Horizontal Flow regime.
Fig. 7. Churn turbulent flow. Fig. 5. Bubbly flow.
whose pipe’s inner diameter is 0.038 m to a higher value in Jepson’s experiment [23] whose inner diameter is 0.3 m. In this experiment, the stratified flow’s boundary matches that of Jepson’s, which means pipe size effect is not significant in large pipes. As for the boundary between the plug flow and the slug flow, the transition boundary in Kong’s flow regime map differs from that in Mandhane’s flow regime map. Our result is similar with Kong’s map. In the vertical downward part, the bubbly flow, the cap bubbly flow, the annular flow, and the churn turbulent flow are observed. The pictures took during the experiment are presented here to show each flow pattern. The bubbly flow (as in Fig. 5) has the form of the bubbly flow in the vertical upward flow. However, due to the coring phenomenon, small bubbles migrate to the center part of the pipe. Because of the pipe size effect, the cap bubbly flow (as in Fig. 6) is observed instead of the slug flow. In the cap bubbly flow, the flow is quite chaotic, with irregular large bubbles observed near the wall. With a relative low hjfi, the annular flow (as in Fig. 8) is the most common flow pattern. In the low hjgi, the annular flow observed in the experiments are the so-called ‘‘falling film flow [14]”. With a high hjgi and a high hjfi, the flow
pattern changes to the churn turbulent flow (as in Fig. 7). The churn turbulent flow is very chaotic and is a transition flow pattern between the cap bubbly flow and the annular mist flow. The downward flow regime map is presented in Fig. 9. The flow regime map produced by the neural network is compared with that of Qiao et al’s 0.0508 m pipe experiment, Lee’s 0.0254 mm pipe experiment, and Usui’s 0.024 m experiment. As in the figure, when pipe size increases, the falling film boundary goes to a higher hjfi. Slug bubbles are not observed in this experiment, which means the slug flow does not exist in large downward pipes. It is of interest that the bubbly flow boundary does not change too much in different pipes. It is mainly because that, for all size pipes, small bubbles mitigate to the pipe center area where cap bubbles can be generated easily. 4.2. Probability density function analysis Characteristic probability density function (PDF) profiles of the horizontal flow regimes are presented in Fig. 10. As illustrated in the figure, the PDF profile of the stratified flow is a single high peak which means that the void fraction variation in stratified flow is very small. The location of the PDF peak is determined by the liquid
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189
Fig. 8. Annular flow.
Fig. 9. Downward Flow regime.
Fig. 10. PDF of horizontal flow regimes.
183
Fig. 11. Slug flow PDF profiles with different hjfi (hjgi = 1.75 m/s).
level. In the plug flow, liquid bridges (with few bubbles) appear, which results in a high PDF peak at the point where void fraction equals zero. Another PDF peak in the plug flow exists at a large void fraction point, which indicates the wave valleys. As for the slug flow, the PDF profile is similar with that of the plug flow. However, as the slug flow has bubbles in its liquid bridge, its first PDF peak is more scattered than that in the plug flow. The pseudo slug flow is a very chaotic regime whose liquid surface is very wavy. Thus, its PDF profile is much more scattered than the other flow regimes’ PDF profiles. As the pseudo slug flow happens at a high hjgi, its average void fraction is larger than the others. The slug flow PDF profiles with different hjfi and hjgi are shown in Figs. 11 and 12, respectively. As the hjfior hjgi goes larger, the second peak of the PDF profile becomes more scattered. It is mainly due to that the wave amplitude increases with an increase in the hjfi or hjgi. Increased wave amplitude means longer liquid bridges which need more water. It leads to lower wave valleys. The decrease in the height of wave valleys results in an increase in the maximum void fraction. In the plug flow, the variation trend is same. The characteristic probability density function (PDF) profiles of the downward flow regimes are presented in Fig. 13. It is found that the PDF profiles of all the flow patterns are characterized by one single peak. For the bubbly flow, the peak exists at very low void fraction due to the small bubbles. In the cap bubbly flow, the existence of large bubbles makes the peak at a relatively higher void fraction and more scattered than the bubbly flow. The peak of the cap bubbly flow pattern’s PDF profile locates at a void fraction which is smaller than 0.5. The structure of the churn turbulent flow is so chaotic that its PDF profile is scattered and has a large averaged void fraction value (larger than 0.5). The annular flow is characterized by a continuous gas core which leads to a large void fraction peak. The cap bubbly flow’s and the churn turbulent flow’s PDF profiles with different hjfi are shown in Figs. 14 and 15, respectively. As illustrated in Fig. 14, with an increase in the hjfi, the average void fraction of the cap bubbly flow decreases. Moreover, as the hjfi increases, the flow becomes more chaotic. Large bubbles break up into small bubbles, which accounts for the high peak at a low void fraction value. In terms of the churn turbulent flow, an increase in the hjfi also decreases the average void fraction. In this flow pattern, a larger hjfi leads to a much more scattered PDF profile. It should be noted that, in the downward flow, no significant difference lies between the cap bubbly flow and the churn turbulent
184
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189
Fig. 12. Slug flow PDF profiles with different hjgi (hjfi = 1.0 m/s).
Fig. 15. Churn turbulent flow PDF profiles with different hjfi (hjgi = 3.3 m/s).
flow. They are both very chaotic and contain an amount of large and small bubbles. 5. Downward flow regime criteria 5.1. Existing criteria Since almost all the existing experiments are conducted on small pipes, the existing flow regime boundary criteria can only be applied on small pipes. Specifically, Usui, Barnea, and Crawford proposed criteria for the boundary between the bubbly flow and the slug flow. Usui’s (Eq. (2)) and Barnea’s criteria (Eq. (3)) are both determined by a critical void fraction. rawford’s criteria (Eq. (4)) is an empirical correlation.
Fig. 13. PDF of downward flow regimes.
a ¼ 0:175
ð2Þ
a ¼ 0:25
ð3Þ
jg jg þ jf pffiffiffiffiffiffi ¼ 0:117 pffiffiffiffiffiffi gD gD
!1:6 ð4Þ
For the boundary between the slug flow and the churn turbulent flow, Lee proposed a critical void fraction criterion (Eq. (5)).
a ¼ 0:5
ð5Þ
For the boundary between the churn turbulent flow and the annular mist flow, correlations were given by Usui (Eq. (6)) and Crawford (Eq. (12)).
" # jg C1 1 þ 1 ¼1 2 7=23 C 0 Fr l jf gC 0 f1 ð2C w Fr l Þ
ð6Þ
The constants C0 and C1 in Eq. (6), represent the distribution parameter and the drift velocity coefficient respectively.
Fig. 14. Cap bubbly flow PDF profiles with different hjfi (hjgi = 0.25 m/s).
C 0 ¼ 1:2 1=ð2:95 þ 350E1:3 Þ 0
ð7Þ
C 1 ¼ 0:345½1 expfð3:37 E0 Þ=10g
ð8Þ
E0 ¼ ðql qg ÞgD2 =r
ð9Þ
C w ¼ 0:046
ð10Þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Frl ¼ jf = gDðql qg Þ=ql
ð11Þ
185
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189
Crawford’s correlation is as follow:
1:9
jg jf
!1=8 0:18 ¼ Ku0:2 g Fr g
ð12Þ
where
Kug ¼ jg ðqg Þ0:5 =½gðql qg Þr1=4 2
Fr g ¼ jg =gD
ð13Þ ð14Þ
As for the boundary of the falling film regime, Criteria were proposed by Barnea (Eq. (15)) and Usui (Eq. (16)).
a ¼ 0:65
ð15Þ
Fr g ¼ ðK1 K2 =E0 Þ
23=18
ð16Þ
towards the pipe center. Thus, bubbles migrate to the center area, which is the so called ‘‘coring phenomenon”. Cap bubbles tend to be generated in the center area. It should be noted that for pipes of different diameters, their velocity profiles are similar, which results in similar void fraction profiles. It is supposed that the maximum void fraction in the bubbly flow may not vary with the pipe diameter. Through the experiment data analysis, it is found that the maximum void fraction of the bubbly flow is roughly 0.055. Utilizing Goda’s drift flux model [24] (Eq. (20)), the critical void fraction criterion is compared with the experiment data in Fig. 17. The prediction fits the experiment data well. Goda’s drift flux model is as follow,
hjg i ¼ hhv g ii ¼ C 0 hji þ V gj hai
ð20Þ
where
where
K 1 ¼ 0:92
ð17Þ
K 2 ¼ 7:0
ð18Þ
E0 ¼ ðql qg ÞgD2 =r
ð19Þ
After the presentation of these criteria, they are compared with the experiment data of this paper in Fig. 16. It is shown in Fig. 16 that Lee’s criterion which predicts the boundary between the slug flow and the churn turbulent flow matches the experiment result well. Other criteria cannot fit the experiment data. It should be noted that Usui’s, Barnea’s, and Crawford’s bubbly flow boundary criteria are determined for the boundary between the cap bubbly flow and the slug flow. However, the slug flow doesn’t exist in a large diameter pipe. As for the falling film boundary, it can be found in Fig. 16 that both Usui’s model and Barnea’s model show a larger hjfi boundary prediction. For the boundary between the churn turbulent flow and the annular mist flow, Usui’s model gives a smaller hjgiboundary prediction, and Crawford’s criterion generally matches the data. 5.2. Bubbly flow boundary In a single phase downward turbulent pipe flow, the velocity profile is of a power shape. The maximum velocity exists in the center of a pipe. In the bubbly flow, if the number of bubbles is small, the velocity profile maintains the power shape. The power profile of the velocity exerts a lift force on bubbles with a direction
Fig. 16. Assessment of existing criteria.
pffiffiffi V gj ¼ 2
!14
r g Dq q2f
ð21Þ sffiffiffiffiffiffi!
C 0 ¼ð0:0214hj iþ0:772Þþ 0:0214hj iþ0:228
qg ;206hj i<0 qf ð22Þ
C 0 ¼ð0:2expð0:00848ðhj iþ20ÞÞþ1:0Þ0:2expð0:00848ðhj iþ20ÞÞ sffiffiffiffiffiffi
qg ;hj i<20 qf
ð23Þ
where
hj i ¼
hji V gj
ð24Þ
For most of the small pipe experiments, the cap bubbly flow is not characterized as a flow pattern. The boundary between the bubbly flow and the cap bubbly flow is not clear in most flow regime maps. However, in Lee’s 0.0254 m and 0.0508 m experiments, the cap bubbly flow is distinguished as a different flow pattern. Thus, Lee’s experiments are used to verify the boundary criterion proposed in this paper. Fig. 18 shows the comparison
Fig. 17. Comparison between the bubbly flow boundary criterion with the experiment data.
186
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189
between the criterion with Lee’s 0.0254 m experiment. Fig. 19 shows the comparison between the criterion with Lee’s 0.0508 m experiment. The criterion fits well with these experiments, which means it is reliable and can be applied in pipes of different sizes. 5.3. Boundary between the cap bubbly flow and the slug flow In the cap bubbly flow, cap bubbles migrate to off-center area. When the local void fraction of this area exceeds 0.3, these large cap bubbles hit each other to generate larger bubbles (Taylor bubbles). Then, the downward flow pattern becomes the slug flow. Cap bubbles’ appearance changes the velocity profile and the void fraction profile greatly. It is unfortunately that few research is conducted on these profiles. It is the major difficulty in developing theoretical models for the boundary. However, it is fortunately that the transition from the cap bubble flow to the slug flow is still determined by the void fraction. By utilizing Goda’s drift flux model, the critical void fraction of available flow regime maps is determined. The result is shown in Table 1. It is illustrated in the table that the critical void fraction decreases with an increase in the pipe diameter, which means the critical void fraction is a function of the pipe diameter. An empirical correlation (Eq. (25)) is then proposed to fit these experiment data. Fig. 20 shows the comparison between the prediction and the experiments data. It should be noted that a void fraction of 0.055 is assumed for a 0.1524 m pipe in the fitting procedure. The slug flow doesn’t exist in large pipes. This point is used to keep the line smooth and ensure the minimum predicted void fraction is larger than 0.055. Moreover, large bubbles are also generated in large pipes. Yet, they cannot occupy the whole pipe inner area. It is illustrated in Fig. 20 that as the pipe diameter increases, the large bubbles generation void fraction decreases. Thus, in a 0.1524 m diameter pipe, the large bubbles generation void fraction is around 0.055 according to the boundary critical void fraction variation tendency.
ac ¼
9:25 105 Dd;max ðD Þ
2
þ 0:051
Fig. 19. Comparison between the bubbly flow boundary criterion with Lee’s 0.0508 m downward flow regime map.
Table 1 Slug flow/cap bubbly flow boundary critical void fraction of available flow regime maps. Researcher
Pipe diameter (m)
Void fraction
Usui Goda Lee Bouyahiaoui Kendoush Goda Qiao Julia
0.024 0.0254 0.0254 0.034 0.038 0.0508 0.0508 0.0508
0.175 0.2 0.22 0.11 0.12 0.07 0.09 0.1
ð25Þ
where Dd,max is the maximum distorted bubble limit, D⁄ is the nondimensional pipe diameter.
rffiffiffiffiffiffiffiffiffiffi
Dd;max ¼ 4
r
g Dq
ð26Þ
Fig. 20. Comparison between the correlation and the experiment data.
D ¼
Fig. 18. Comparison between the bubbly flow boundary criterion with Lee’s 0.0254 m downward flow regime map.
D 0:024 m 6 D < 0:1016m Dd;max
ð27Þ
It should be noted that this correlation can only be applied to pipes whose diameter is larger than 0.024 m and smaller than 0.1016 m. When the pipe’s diameter is 0.0254 m, the prediction critical void fraction is 0.198. With Goda’s drift flux model, this prediction value is compared with Pan’s 0.0254 m downward flow regime map in Fig. 21. The correlation predicts the boundary well.
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189
Fig. 21. Comparison between the correlation prediction with Pan’s downward flow regime map.
Fig. 22. Wave regime map [25].
Two difficulties are encountered when trying to build a theoretical model: (1) Velocity profile and void fraction profile interact with each other; (2) Both profiles change with the pipe diameter.
5.4. Falling film boundary In the falling film regime, liquid flows along the pipe wall. If a liquid bridge is generated in the gas core, the flow pattern turns into the cap bubbly flow or the churn turbulent flow. Two requirements are needed to form a liquid bridge. First, the film surface should become wavy. It is large waves’ growth and combination which cause the formation of a liquid bridge. The other requirement is an enough liquid amount (film thickness). The generation of a liquid bridge needs enough liquid. Webb and Hewitt [25] studied downward free falling film’s characteristics. In his paper, waves are categorized into several types. The wave regime map is presented in Fig. 22. It can be concluded from the map that, at the falling film boundary, the film surface has already covered with regular waves which are caused by
187
Fig. 23. Falling film wave amplitude and mean film thickness variation with Ref. [26].
Fig. 24. Comparison between Usui annular void fraction correlation and the experiment data.
the kelvin-helmholtz instability. The instability neural line lies below the falling film boundary. Thus, it is the film thickness which determines whether a liquid bridge can be formed or not. Two assumptions are made: (1) A maximum mean film thickness exists. When the film thickness is larger than this value, the wave amplitude is high enough to form a liquid bridge. (2) The wave amplitude (Hwave) is a linear function of the mean film thickness (dmean ); The second assumption is based on Karapantisios’ research. He found that if the liquid Reynolds number is large enough, both the wave amplitude and the mean film thickness grow linearly. The variation of the wave amplitude and the mean film thickness are presented in Fig. 23. Then, attempts are made to find a critical value of dmean . First, a D good film thickness model or a void fraction prediction model is needed. In the 0.1524 m experiment of this paper, Usui’s annular void fraction prediction correlation (Eq. (16)) matches with the
188
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189
Table 2 Performance evaluation of the Usui annular void fraction correlation. Total points
Percentage of points predicted within
Maximum error
26
±1% 4 (15.4%)
8.76%
±5% 21 (80.8%)
±10% 26 (100%)
Table 3 Verification of the falling film regime’s boundary criterion with different experiments. Researcher
Pipe diameter (m)
Experiment – hjfi (m/s)
Prediction – hjfi (m/s)
Error (%)
USUI BOUYAHIAOUI YAMAGUCHI Julia Qiao I (elbow inlet)
0.024 0.034 0.04 0.0508 0.0508
0.35 0.5 0.55 0.62 0.6
0.357 0.46 0.528 0.648 0.648
+2.0 8.0 5.8 +4.5 +8.0
experiment data well. It is illustrated in Fig. 24 that most points (80.8%) are predicted within 5% error. The maximum error is 8.76%, as shown in Table 2. However, Usui’s annular void fraction correlation doesn’t predict well when applied to small pipes. Bhagwat [27] compared Usui’s correlation with his 0.0127 m downward flow experiment. The error is roughly 30%. Through the literature review, it is found that Karapantisios’ film thickness correlation (Eq. (28)) is relatively good, and has been verified through 0.0254 mm and 0.0508 mm experiments [26]. Thus, Karapantisios’ correlation is recommended to be applied on small pipes’ conditions.
dmean
v 1=3 Ref 0:538 ¼ 0:451 g 4 2
ð28Þ
where
Ref ¼
hjf i D
v
ð29Þ
In the falling film regime, the entrainment is not heavy. The void fraction can be used to present the film thickness. In this experiment, the falling film regime’s boundary void fraction is roughly 0.8, which means the dmean is roughly 0.0528. The predicted D hjfi by Usui’s correlation is 0.868 m/s. The boundary hjfi in the experiment can be found in Fig. 9. It is larger than 0.75 m/s and less than 1.0 m/s. The Usui’s correlation prediction matches well with the experiment data. This criterion is then compared with the other experiments. The results are shown on Table 3. The error is within 10%, which means that the criterion can be applied on pipes with different diameters. However, as studied by Qiao, the inlet condition has a great influence on the downward flow regime boundary. If a sparger is utilized to inject gas into the test section, the boundary of the falling film regime is not a constant hjfi. The criterion proposed here cannot be applied. 6. Conclusion To further study downward flow regime map, an experiment is conducted on a pipe whose diameter is 0.1524 m. In the top horizontal section, four flow patterns (the stratified flow, the plug flow, the slug flow, and the pseudo slug flow) are observed. In the downward vertical section, four flow patterns (the bubbly flow, the cap bubbly flow, the churn turbulent flow, and the annular flow) are observed. The PDF’s profile of each flow pattern is discussed. As for the downward flow regime boundary criteria, existing criteria are reviewed and compared with the experiment. It can be concluded that most existing criteria cannot be applied on large
pipes. However, Lee’s criterion predicts the boundary between the cap bubbly flow and the churn turbulent flow well. In this paper, several criteria are proposed. 1. A critical void fraction (0.055) is proposed for the boundary between the bubbly flow and the cap bubbly flow. 2. A general empirical critical void fraction correlation has been proposed for the boundary between the cap bubbly flow and the slug flow. This correlation can only be applied on pipes whose diameter is larger than 0.024 m, and less than 0.1016 m. 3. The boundary of the falling film regime is determined by the film thickness. When the mean film thickness exceeds 0.0528D, the wave amplitude is large enough to form a liquid bridge. However, inlet effect affects this boundary greatly. If a sparger is used to inject gas into the test section, the criterion cannot be applied. 4. As for the boundary between the cap bubbly flow and the churn turbulent flow, Lee’s criterion is recommended. 5. The annular mist regime’s boundary is not discussed in this paper. It is because that the boundaries found in different experiments cannot agree with each other. No boundary criterion is found. Crawford’s empirical correlation is recommended. Conflict of interest None. Acknowledgments This work was performed at Purdue University under the auspices of the U.S. Nuclear Regulatory Commission (NRC), Office of Nuclear Regulatory Research, through the Institute of ThermalHydraulics. The authors would like to express their gratitude to technical staff of the United States Nuclear Regulatory Commission for their support on this project. This paper was prepared as an account of work sponsored by an agency of the U.S. Government. Neither the U.S. Government nor any agency thereof, nor any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for any third party’s use, or the results of such use, of any information, apparatus, product, or process disclosed in this report, or represents that its use by such third party would not infringe privately owned rights. The views expressed in this paper are not necessarily those of the United States Nuclear Regulatory Commission. References [1] C. Fletcher, R. Schultz, RELAP5/MOD3 code Manual Volume V: User’s Guidelines, Idaho National Engineering Laboratory, Lockheed Idaho Technologies Company, Idaho Falls, Idaho, 1995 (83415). [2] S. Bajorek, TRACE V5. 0 Theory manual, field equations, solution methods and physical models, United States Nuclear Regulatory Commission (2008). [3] M. Kaichiro, M. Ishii, Flow regime transition criteria for upward two-phase flow in vertical tubes, Int. J. Heat Mass Transf. 27 (5) (1984) 723–737. [4] T. Smith, J.P. Schlegel, T. Hibiki, M. Ishii, Two-phase flow structure in large diameter pipes, Int. J. Heat Fluid Flow 33 (1) (2012) 156–167. [5] Y. Taitel, A. Dukler, A model for predicting flow regime transitions in horizontal and near horizontal gas-liquid flow, AIChE J. 22 (1) (1976) 47–55. [6] D. Hinds, C. Maslak, Next-generation nuclear energy: the ESBWR, Nuclear News 49 (1) (2006) 35–40. [7] T.L. Schulz, Westinghouse AP1000 advanced passive plant, Nucl. Eng. Des. 236 (14) (2006) 1547–1557. [8] Z. Yang, J. Shan, J. Gou, Preliminary assessment of a combined passive safety system for typical 3-loop PWR CPR1000, Nucl. Eng. Des. 313 (2017) 148–161. [9] K. Usui, Vertically downward two-phase flow,(II) Flow regime transition criteria, J. Nucl. Sci. Technol. 26 (11) (1989) 1013–1022. [10] K. Usui, K. Sato, Vertically downward two-phase flow, (I) Void distribution and average void fraction, J. Nucl. Sci. Technol. 26 (7) (1989) 670–680. [11] J.Y. Lee, M. Ishii, N.S. Kim, Instantaneous and objective flow regime identification method for the vertical upward and downward co-current two-phase flow, Int. J. Heat Mass Transf. 51 (13) (2008) 3442–3459.
Z. Yang et al. / International Journal of Heat and Mass Transfer 125 (2018) 179–189 [12] H. Goda, S. Kim, Y. Mi, J.P. Finch, M. Ishii, J. Uhle, Flow regime identification of co-current downward two-phase flow with neural network approach, in: Proceedings of 10th International Conference of Nuclear Engineering (ICONE10), Arlington, VA, 2002. [13] L.M. Pan, M. Zhang, P. Ju, H. He, M. Ishii, Vertical co-current two-phase flow regime identification using fuzzy C-means clustering algorithm and ReliefF attribute weighting technique, Int. J. Heat Mass Transf. 95 (2016) 393–404. [14] D. Barnea, O. Shoham, Y. Taitel, Flow pattern transition for vertical downward two phase flow, Chem. Eng. Sci. 37 (5) (1982) 741–744. [15] A.A. Kendoush, S.A. Al-Khatab, Experiments on flow characterization in vertical downward two-phase flow, Exp. Therm. Fluid Sci. 9 (1) (1994) 34–38. [16] K. Yamaguchi, Y. Yamazaki, Combinated flow pattern map for cocurrent and countercurrent air-water flows in vertical tube, J. Nucl. Sci. Technol. 21 (5) (1984) 321–327. [17] J.E. Julia, Y. Liu, T. Hibiki, M. Ishii, Local flow regime analysis in vertical co-current downward two-phase flow, Exp. Therm Fluid Sci. 44 (1) (2013) 345–355. [18] S. Qiao, D. Mena, S. Kim, Inlet effects on vertical-downward air–water two-phase flow, Nucl. Eng. Des. 312 (2017) 375–388.
189
[19] M. Lokanathan, T. Hibiki, Flow regime, void fraction and interfacial area transport and characteristics of co-current downward two-phase flow, Nucl. Eng. Des. 307 (2016) 39–63. [20] T. Crawford, C. Weinberger, J. Weisman, Two-phase flow patterns and void fractions in downward flow Part I: Steady-state flow patterns, Int. J. Multiphase Flow 11 (6) (1985) 761–782. [21] J. Mandhane, G. Gregory, K. Aziz, A flow pattern map for gas—liquid flow in horizontal pipes, Int. J. Multiph. Flow 1 (4) (1974) 537–553. [22] R. Kong, S. Kim, Characterization of horizontal air–water two-phase flow, Nucl. Eng. Des. 312 (2017) 266–276. [23] W. Jepson, R. Taylor, Slug flow and its transitions in large-diameter horizontal pipes, Int. J. Multiphase Flow 19 (3) (1993) 411–420. [24] H. Goda, T. Hibiki, S. Kim, M. Ishii, J. Uhle, Drift-flux model for downward twophase flow, Int. J. Heat Mass Transfer 46 (25) (2003) 4835–4844. [25] D. Webb, G. Hewitt, Downwards co-current annular flow, Int. J. Multiph. Flow 2 (1) (1975) 35–49. [26] T. Karapantsios, S.t. Paras, A. Karabelas, Statistical characteristics of free falling films at high Reynolds numbers, Int. J. Multiph. Flow 15 (1) (1989) 1–21. [27] S.M. Bhagwat, Study of flow patterns and void fraction in vertical downward two phase flow, Oklahoma State University, 2011.