Numerical study of adiabatic two-phase flow patterns

Applied Thermal Engineering 110 (2017) 1101–1110

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Research Paper

Numerical study of adiabatic two-phase flow patterns in vertical rectangular narrow channels Lie Wei, Liang-Ming Pan ⇑, Yan-Ming Zhao, Quan-Yao Ren, Wen-Zhi Zhang Key Laboratory of Low-grade Energy Utilization Technologies and Systems (Chongqing University), Ministry of Education, Chongqing 400044, China

h i g h l i g h t s Adiabatic two-phase flow pattern map in upward rectangular channel was simulated. The range of annular flow in small channel is larger, while the one of slug and bubbly flow are smaller. With the reducing gap size, the flow pattern transition shifts to left. Simple inlet condition is testified applicably to simulate flow patterns. CFD method is a feasible way to draw the two-phase flow patterns map.

a r t i c l e

i n f o

Article history: Received 27 July 2015 Revised 31 August 2016 Accepted 3 September 2016 Available online 4 September 2016 Keywords: Narrow rectangular channel Void fraction distribution Flow pattern VOF model

a b s t r a c t The current paper investigates an upward two-phase flow of air-water mixture in vertical narrow rectangular channels with two different cross-sectional dimensions of 25 5 mm and 25 2 mm respectively by using VOF (Volume of Fluid) model. To facilitate the simulations of different flow patterns, a simple and practical inlet condition, which is validated by experimental results, is employed. In the VOF model, the inlet condition will make the gas phase to be air layers, and due to the entrainment effect, the layers would coalescent and break up to small bubbles. The simulation results reveal that the main flow patterns of the two-phase flow in narrow channels are bubbly flow, slug flow, churn-turbulent flow and annular flow, and the void fraction distributions of those flow patterns are quite different. The void fraction of bubbly flow is below 0.3, which is consistent with published literatures. As the Taylor bubbles are located at the center of the flow channel and the slug flow is intermittent, the void fraction of slug flow is more evenly distributed in the center. The flow pattern map has been drafted under various air–water superficial velocities. The central region of the annular flow is gas core entrained liquid droplets, thus the void fraction is almost constant in the central region. The two-phase flow pattern map of a vertical rectangular channel shows that the range of annular flow in the channel is larger, while the scopes of slug flow and bubbly flow in the channel are smaller in comparison with the flow pattern map of tube. In addition, the transitional boundaries between flow patterns occur at smaller gas velocity than those in the tube. While compared the 2 mm gap rectangular channel with the 5 mm ones, it is found that with the gap size reducing, the flow pattern transition boundary shifts to the left. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Gas-liquid two-phase flow is widely used in nuclear engineering, petrochemical and other industrial equipment such as evaporator, condenser, reactor and heat exchanger [1]. Comparing with conventional channels, the narrow channel is in possession of larger specific surface area, thus the narrow channel has much higher efficiency of heat transfer and can be easier to fabricate a ⇑ Corresponding author. E-mail address: [email protected] (L.-M. Pan). http://dx.doi.org/10.1016/j.applthermaleng.2016.09.007 1359-4311/Ó 2016 Elsevier Ltd. All rights reserved.

compact heat exchanger. Therefore, the non-circular crosssection channel is increasingly used in compact heat exchanger and micro chemical machinery applications [2,3]. The flow pattern is always an important aspect of the twophase flow, which is closely related to the resistance and the heat transfer characteristics of the two-phase flow system. Therefore, many references have devoted the researches to this matter in the narrow channels by mean of experimental investigations so far. Sadatomi et al. [4] performed an experimental study in a rectangular tube with the equivalent diameter >10 mm, and observed that bubbly flow, slug flow and annular flow were

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L. Wei et al. / Applied Thermal Engineering 110 (2017) 1101–1110

Nomenclature C-T Fr g p t u n

vb

De s w ug

churn-turbulent flow momentum source due to surface tension (N/m3) gravity acceleration, 9.807 m/s2 pressure (Pa) time (s) velocity vector (m/s) normal surface vector relative bubble velocity (m/s) equi-periphery diameter (m) channel gap (m) channel width (m) bubble velocity (m/s)

occurred consequently in the channel. Lowry and Kawaji [5] investigated the two-phase flow patterns of air-water mixture in the rectangular channels with the gaps of 0.5 mm, 1 mm and 2 mm, and proposed the transition criterion of annular flow. Xu et al. [6] experimentally studied the air-water upward flow in channels with the gaps of 0.3 mm, 0.6 mm and 1 mm. They found that the flow structures in the channels with the gap of 0.3 mm were different from that in channels with the gaps of 1.0 and 0.6 mm. There are also some other researches [7,8] about how the channel geometry and the pressure effect on the flow pattern. In theoretical research, Hibiki and Mishima [9] presented the flow regime transition criteria for upward two-phase flow in vertical narrow rectangular channels, and showed satisfactory agreements with those data. In addition to flow pattern, there are also some interesting and important characteristics of two-phase flow, e.g., pressure drop, void fraction and so on. Yoneda et al. [10] experimentally studied the flow structure and bubble characteristics of steam-water two-phase upward flow in a vertical pipe. The radial distribution of flow structure was obtained by horizontally traversing optical dual void probes through the pipe. Zhao and Bi [11] presented experimental data for the gas velocity, the void fraction, and the pressure drop of upward co-current air-water two-phase flow through vertical miniature triangular channels. They found that the pressure drop of two-phase flow in the miniature triangular channels can be well predicted by the Lockhart-Martinelli correlation. Pan et al. [12] experimentally studied air-water two-phase flow in a tube with 2.54 cm diameter, and proposed an objective methodology, which were based on the ReliefF-FCM clustering algorithm and the CPDF of void fraction, to distinguish flow regimes. Liu et al. [13] experimentally studied the non-uniform inlet conditions effects of vertical air-water two-phase flow in a narrow rectangular duct. They found the lateral development across the wider dimension of the duct was significant with a non-uniform inlet profile when compared to an uniform inlet profile. With the development of numerical methods and computational capability, some interface capturing methods [14,15] are employed to simulate the two-phase flow. Chen et al. [16] simulated the breakup of micro-droplets in micro-channel T-junction by using VOF model, and the continuum surface force (CSF) model [17] was implemented to calculation surface tension. They found four flow patterns of micro-droplets, and drawn the flow pattern map. Kashid et al. [18] used VOF model to study the liquid-liquid flow pattern in horizontal micro-capillaries, and the numerical results were consistent to the experiment results. Kawahara et al. [19] performed a numerical simulation to study the characteristics of gas-liquid two-phase flows through a sudden contraction in

Greek letters volume fraction, advancing angle (°) density (kg/m3) surface tension coefficient (N/m) curvature (1/m) dynamic viscosity (Pa s)

a q r j l

subscript q qth phase l liquid v vapor

rectangular micro-channels by exploiting VOF model, and the comparison of numerical results with experimental data elucidated that the VOF model could precisely obtain the characteristics of gas-liquid two-phase flows. Pouryoussefi and Zhang [20] utilized fuzzy logic and genetic algorithm to predict the flow patterns based upon the numerical simulation of two-phase flow in a vertical tube. Gregorc and Zˇun [21] experimentally studied the effect of inlet conditions on flow pattern in mini-channels. Additionally, they also used the VOF model to predict the flow patterns, and found that the inlet mixer had strong impact on bubble size and bubble distribution along the axial direction of mini-tube. However, for the case of numerical simulation, most of the studies about two-phase flow patterns are focus on microchannels. With respect to the numerical simulation of narrow rectangular channels, little emphasis, if any, is placed on the two-phase flow patterns, such as Refs. [22,23]. Therefore, in this paper, adiabatic two-phase flow patterns in vertical narrow rectangular channels are numerically investigated based upon the VOF model. It is notable that a simple and practical inlet condition is used to simulate different flow patterns. The results are testified through comparing with the experimental visualized results [24] and the theoretical calculation. It suggests that this inlet condition is applicable to narrow rectangular channels. After verifying the method, simulations of rectangular channel with the geometric dimension of 25 2 300 mm and 25 5 300 mm were performed. The void fraction and pressure drop characteristics are analyzed under different flow patterns. The flow patterns map of vertical rectangular channels has been drawn under different operating conditions. It reveals the distribution of various flow patterns and the transition boundary between flow patterns. The influences on flow pattern and its transition of the channel cross-sectional shape and size have been discussed as well.

2. Computation model 2.1. Physical models and boundary conditions Three-dimensional numerical simulation of the rectangular channels with two different cross-sectional dimensions of 25 5 300 mm and 25 2 300 mm are carried out. Fig. 1 is the schematic diagram of the computational domain. The superficial gas velocity ranges from 0.1 to 82 m/s, and the envelope of superficial liquid velocity is ranging from 0.1 to 2 m/s. The mixture air-water two-phase flow in the channel is assumed to be incompressible, isothermal and in the possession of constant physical property. Pressure-based being the solver and transient calculation are applied to this problem. Two-phase

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Fig. 2. Separation of phases at the channel inlet.

Fig. 1. Schematic diagram of the computational domain.

mass-flow rates and pressure outlet are chosen as the inlet condition and outlet condition respectively. The wall surface is set as the non-slipping wall condition. With reference to the VOF model, the gas phase will be deemed to be air layers under such inlet condition, and the air layers will coalesce and form the thicker air layers due to the entrainment effect. Subsequently, those air layers will break up and be in the form of bubbles affected by surface tension as shown in Fig. 2. 2.2. Governing equations and discretization scheme In VOF method, the volume fraction is used to distinguish each phase in the computational cell volume, which can be expressed as:

8 > < 1 ðfilled with qth phaseÞ aq ¼ 0 ðno filled with qth phaseÞ > : 0—1 ðinterfaceÞ

ð1Þ

Volume fraction equation being used in VOF method is to calculate the volume fraction of phase q, which is a deformation formula of continuity equation for the qth phase:

"

n X * 1 @ _ pq m _ qp Þ ðaq qq Þ þ r ðaq qq v q Þ ¼ Saq þ ðm qq @t p¼1

#

ð2Þ

_ pq and m _ qp are the mass transfer rates from phase p to where m phase q and from the phase q to phase p respectively. Saq is the mass source term for phase q. A single momentum equation, which is dependent on the volume fractions of all phases through the properties q and l as shown below, is solved throughout the domain, and the resulting velocity field is shared among the phases. * * * * * * * @ ðq v Þ þ r ðq v v Þ ¼ rp þ r ½lðr v þrv T Þ þ q g þ F @t

ð3Þ

where q is the mixture density; p is the pressure; l is the dynamic *

*

viscosity; g is the acceleration of gravity and F is the volume force. The continuum surface force (CSF) model proposed by Brackbill and Kothe [17] is used in the surface tension model. The surface tension can be expressed as a volume force according to the divergence theorem. For the gas-liquid system, the body force caused by surface tension is defined as follows,

Fr ¼ r

al ql jg rag þ ag qg jl ral ðql þ qg Þ=2

ð4Þ

where r is the surface tension; al is the liquid fraction; ag is the void fraction; ql and qg are the liquid density and gas density respectively. j is the curvature computed from the divergence of the unit surface normal vector n;

j¼rn¼r

n jnj

ð5Þ

The surface normal vector n is defined as the gradient of aq , where aq is the volume fraction of the qth phase.

n ¼ raq

ð6Þ

The geometric reconstruction scheme is used to track the gasliquid interface in the simulation. Fig. 3 shows a physical interface (a) and an actual interface shape (b) along the interface construction during computation based upon the geometric reconstruction scheme. The geometric reconstruction scheme is specifically tailored to the interface between fluids using a piecewise-linear approach, and is generalized for unstructured meshes from the work of Youngs [14]. It is assumed that the interface between two fluids has a linear slope within each cell, and the linear shape is applied to the calculation of the advection of fluid through the cell faces. The standard k-e turbulence model, which is robust, economic, and in possession of reasonable accuracy for a wide range of turbulence flows, is selected to close the governing equation.

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Fig. 3. Schematic diagram of the geometric reconstruction scheme: (a) a physical interface and (b) an actual interface shape.

The volume fraction equation is solved implicitly, and the standard finite difference interpolation method is applied to calculate the volume integral value in the current time step. In addition, under the convergent condition, the second-order upwind scheme is used for the momentum equation, turbulent kinetic energy equation and turbulent diffusivity equation in order to improve calculation accuracy. The PRESTO method is used for the discrete pressure, and the flow field is solved by mean of the SIMPLC method which is pressure-velocity coupled. The time step is set to 1 105 s, which can ensure the convergence of calculation to be relatively stable and sufficiently assure the reliability of the simulation. 3. Results and analysis

z 3.1. Grid independent test To find an appropriate grid number for the simulation, three different sets of grid are developed, i.e., 300,000 (G1), 570,000 (G2) and 1,100,000 (G3), respectively. The simulation results of cap bubble flow by mean of the aforementioned three different sets of grid are shown in Fig. 4. The visual difference between those results is not clear. Therefore, the cross-sectional void fraction distributions, which will be discussed in Section 3.4 in detailed, under the condition of three different sets of grid are obtained. As can be seen from Fig. 5, the void fraction distribution of G1 is quite different from the others. In aforementioned test, the effect of grid number on bubble shape and velocity is not clear. Therefore, a simulation of single-bubble rising in rectangular channel is performed to test grid independent, the initial position of the bubble was shown in Fig. 6(a), and the results under condition of different gird numbers are shown in Fig. 6(b)–(d), respectively. As can be seen from Fig. 6, the three bubbles all rise in a straight line. Fig. 7(a) shows evolutions of the bubbles’ centroids, and it is revealed that the bubble paths in G2 and G3 are almost the same. However, the bubble path of G1 is a little different from the other two cases. In addition, the shape of the bubble in the case of G1 is quite different from that of G2 and G3 as shown in Fig. 7(b), while the bubble shapes of G2 and G3 are similar. Therefore, in consideration of the quantity of simulation and the computational expenditure, the mesh with 570 thousand grids is finally utilized.

G1

G2

G3

y

Fig. 4. Simulation results with different grid number.

Fig. 5. Cross-sectional void fraction distribution under different grid number.

3.2. Model validation To verify the accuracy of numerical method, a threedimensional numerical simulation of the flow patterns under the

experimental conditions of Xu [24] is carried out firstly. The geometric dimension of the duct is 12 1 260 mm, and the working fluid is the mixture of air and water. The inlet condition

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L. Wei et al. / Applied Thermal Engineering 110 (2017) 1101–1110 Table 1 Flow parameters of numerical simulation cases for model validation. Case

Liquid superficial velocity (m s1)

Gas superficial velocity (m s1)

Flow pattern

1 2 3 4 5 6 7 8 9 10 11 12

0.3 1.5 2.0 0.6 2.0 1.0 0.4 0.25 0.4 0.3 0.1 0.2

0.06 0.3 0.9 2.0 1.5 1.0 1.0 1.0 2.0 4.0 4.5 5.0

Bubbly Bubbly Bubbly Slug Slug Slug Slug C-T C-T C-T Annular Annular

Fig. 6. (a) Initial bubble and (b)–(d) evolution of bubble with different set of grid.

is a uniform distribution mass flow rate, while the outlet condition is the pressure outlet, and the walls are non-slip wall conditions. The flow parameters of simulation verification cases are listed in Table 1. Most of selected conditions are close to the flow patterns transition boundaries. The corresponding positions of the cases marked on the flow pattern map of Xu [24] are shown in Fig. 8. Fig. 9 illustrates both of the visualization results by numerical simulation and the experimental results of Xu. From the perspective of qualitative visualization, the simulation results can coincide with the experimental results of Xu [24], because both the simulation and the experiment are in possession of the same flow pattern under the same work condition. In addition, from the quantitative analysis of points view, the bubble rising velocity is compared with theoretical value. It should be noted that, for the case of a medium size rectangular channel, Sadatomi et al. [4] have ever suggested that the bubble rising velocity v b , which was relative to the liquid velocity, could be well correlated by,

vb

pffiffiffiffiffiffiffiffi ¼ 0:35 gDe

ð7Þ

where g is the gravity, and De is the equi-periphery diameter being given as,

Fig. 8. Work conditions of numerical simulation cases for model validation on the flow pattern map of Xu [24].

De ¼ 2ðs þ wÞ=p

ð8Þ

in which, s and w are the channel gap and width, respectively. Finally, the bubble rising velocity can be expressed as,

pffiffiffiffiffiffiffiffi ug ¼ J þ 0:35 gDe where J is the superficial velocity.

Fig. 7. (a) Evolution of the height of bubbles and (b) the shape of bubbles.

ð9Þ

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Fig. 9. The flow patterns of numerical simulation for model validation: (a) bubbly flow; (b) cap-bubbly flow; (c) slug flow; (d) slug-churn flow; (e) churn-turbulent flow; and (f) annular flow.

Fig. 10 shows the bubbles in bubbly flow, cap-bubbly flow and slug flow, and the instantaneous positions of marked bubbles are measured to calculate the bubble velocity. Fig. 11 denotes the comparison of bubble velocities obtained by mean of simulation and theoretical calculation respectively. As can be seen in Fig. 13, the simulation results are almost in alignment with the theoretical prediction results. Therefore, both quantitative and qualitative analyses reveal that the VOF model and the present inlet condition can accurately predict the characteristics of two-phase flow patterns. 3.3. Characteristics of two-phase flow The air-water two-phase flows in the rectangular channels with 2 mm gap are simulated. Different flow patterns can be obtained by altering the inlet mass flow rates. As shown in Fig. 13, four typical flow patterns, namely, bubbly flow, slug flow, churn-turbulent flow and annular flow are observed. The corresponding flow parameters with respect to the aforementioned are listed in Table 2. (a) Bubbly flow: The gas phase, as shown in Fig. 12(a), is dispersed in the continuous flow of liquid in the form of small bubbles with different sizes. When the gas superficial velocity is low enough, bubbles keep spherical. At the direction of channel gap, bubbles will easily coalesce due to the limit of

Fig. 11. Comparison of bubble velocity obtained by numerical simulation and theoretical calculation.

channel gap. The diameters of the bubbles are close to the size of channel gap as shown in Fig. 13, and the corresponding flow pattern is case 1. The distribution of bubbles at the direction of channel width is flat. For the case of large gas flow rate, bubbles show pancake shapes and crushed cap

Fig. 10. The bubbles in bubbly flow, cap-bubbly flow and slug flow.

L. Wei et al. / Applied Thermal Engineering 110 (2017) 1101–1110 Table 2 Flow parameters corresponding to Fig. 12. Case

Liquid superficial velocity (m s1)

Gas superficial velocity (m s1)

Flow pattern

1 2 3 4 5 6 7

1.0 1.0 0.2 0.2 0.24 0.5 0.5

0.08 0.228 0.163 0.408 1.306 5.0 10.0

Bubbly Bubbly Slug Slug C-T Annular Annular

shapes due to the restricted space and agglomerate at the center of the channel. (b) Slug flow: With the increase of gas flow rate, the size of the bubbles expands to the width of channel as shown in Fig. 12 (b). The wall is surrounded by a quite thin liquid film which is consistent to the experiment results [24]. A big hemispherical headed slug is formed at the front end of the bubbles which has a smooth cylinder body in the middle. The

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spacing between the bubbles are roughly equal, and the shape of the bubbles’ tail is flat. Two slug bubbles, which is known as the Taylor bubble, are separated by liquid slugs (or liquid bridges). Additionally, there exist many small bubbles in the nose of the liquid slug due to the entrainment effect of the Taylor bubble. As the superficial gas velocity increases, the length of Taylor bubble becomes longer, and the bubble tail presents more irregular shapes. (c) Churn-turbulent flow: As shown in Fig. 12(c), with the further increase of gas flow rate, the Taylor bubbles are lined up right next to each other, and the liquid slugs become unstable. The gas mainly gathers at the central area, and the gas-liquid interface is very irregular. Thus, the entire flow under this work condition is in the possession of a confused state. Generally, slug flow and churn-turbulent flow belong to intermittent flow. (d) Annular flow: For the case of annular flow, as shown in Fig. 12(d), the channel is nearly filled with the gas phase in the form of the hollow core, and the surrounding liquid film flows along the wall. A fluctuation interface exists between

Fig. 12. Air-water flow patterns in vertical rectangular channel: (a) bubbly flow, (b) slug flow, (c) churn flow, and (d) annular flow.

Fig. 13. Distribution of bubbles under a small gas velocity in the narrow channel with 2 mm gap.

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the liquid film and the gas core. The gas core acts strong entrainment effect on the liquid film so that the small liquid droplets are entrained in the gas core, which resembles the small bubbles dispersing in the liquid film. Keeping the liquid superficial velocity constant, lower gas superficial velocity will result smoother gas-liquid interface, due to the combination effect of less gas flow resistance and less interaction between gas and liquid, which is consistent to the experimental results [25]. Besides, the annular flow is more stable than other flow patterns. With respect to the narrow channel, bubbles are easy to deform and aggregate due to the limit of narrow space. Thus, the air-water two-phase flow patterns are different from that of the round tube. For the case of bubbly flow, the bubble distribution can be categorized into two situations, i.e., bubbles keep spherical and their distribution is even when the gas velocity is low enough as shown in Fig. 11, and bubbles show pancake crushed cap shapes and their distribution is uneven when the gas velocity is large. With reference to the slug flow, the Taylor bubble tails are flat, and there exist small bubbles in the wake of the Taylor bubble due to the entrainment effect. It should be noted that there are no large differences in the churn-turbulent flow pattern and annular flow pattern.

3.4. Void fraction distribution in the channel In the process of the numerical simulation, the two phases flow is assumed to be steady state when the axial length z > 200 mm, which means the distribution of void fraction will not develop along the flow direction on the assumption that both of the two phases are incompressible in the simulation. Therefore, the local volume-average void fraction is assumed equal to the timeaverage local cross section void fraction. When post-processing the void fraction, the channel width is divided into 13 small parts, and each part of the volume-average void fraction is calculated. Finally, the void fraction distributions along the width direction are gained in vertical narrow rectangular channels, as shown in Fig. 14. Fig. 14 shows the distribution of void fraction related to four typical flow patterns. The cross-sectional void fraction values of bubbly flow are nearly constant and 0.9, which is consistent with the experimental result of Serizawa et al. [28]. It can be attributed to the fact that gas phase is always non-continuous phase for both bubbly flow and slug flow, which results in the similar manner between the average void fraction and the volume fraction. While the two phases in annular flow are continuous, thus the variation is different from the bubbly flow and slug flow. 3.6. Effects of flow pattern on pressure drop Fig. 16 depicts the pressure drop fluctuations under different flow patterns in rectangular channel. As can be seen from Fig. 16, the fluctuation characteristics of pressure drop under different flow patterns are in different manners. 1.0 simulation-1

0.8

simulation-2 exp [28] α=β

0.6

Ali

˞ 0.4

0.2

0

0

0.2

0.4

0.6

0.8

1.0

˟ Fig. 14. Distribution of void fraction along the width direction for different flow patterns in vertical narrow rectangular channel.

Fig. 15. Relationship between the average void fraction and the volume fraction.

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pressure drop/kPa

3 2.8 2.6 2.4 2.2 2

bubbly:J l =1.002 m/s,J g =0.184 m/s 0

10

20

30

5 4 3 2 1 0

50

60

time/ms 70

slug:J l =1.002 m/s,J g =1.838 m/s 0

2.5 2 1.5 1 0.5 0

40

10

20

30

40

50

60

time/ms

70

annular:J l =1.002 m/s,J g =11.025 m/s 0

10

20

30

40

50

60

time/ms 70

Fig. 16. Fluctuation of pressure drops under different flow patterns.

As the amount of gas is relatively small in the bubbly flow, numerous small bubbles disperse in the liquid. The frequency and amplitude of pressure drop fluctuations are small. The fluctuation amplitudes of the pressure drop basically stay in the range of 2.2–2.8 kPa. When the amount of gas increases, the slug flow is formed by the aggregation of small bubbles, leading to the increase of both the frequency and amplitude of pressure drop, and the fluctuation amplitudes of the pressure drop are in the range of 1–5 kPa. As to the annular flow, the pressure drop has a small fluctuation and ranges from 1 kPa to 2.5 kPa due to the uniform distribution of void fraction along the flow direction.

3.7. Flow pattern map The flow pattern maps of two-phase flow in the vertical rectangular channels with the gaps of 5 mm and 2 mm are drafted as shown in Figs. 17 and 18, respectively. In vertical rectangular channel, the flow pattern maps can be roughly divided into several regions which include bubbly flow, slug flow, churn-turbulent flow and annular flow. As can be seen from Figs. 17 and 18, there exist some similarities in the transition curves of the flow patterns for the two different channels. Bubbly flow appears in the low gas superficial velocity and high liquid superficial velocity, and the transition to the slug flow occurs at the decrease of liquid superficial velocity. However, transition from bubbly flow to slug flow or churn-turbulent flow will directly happens when the gas superficial velocity increases. In the flow pattern map, the churnturbulent flow is a transitional flow pattern, and occupies a small range. In contrast, the range of annular flow is large, and the annular flow appears at a smaller gas velocity compared to that in tube. Comparing with the flow pattern map in a conventional size rectangular, it can be found that as the surface tension of noncircular cross-section is more significant; the capacity of gathering the liquid is more conducive to the aggregation of bubbles. The drastic change of the phase distribution and velocity distribution make the boundaries of the transformations earlier, which means churn-turbulent flow and annular flow would appear in a smaller gas velocity. The result agrees well with the experimental results of Yang et al. [29]. Comparing the flow pattern map in two rectangular channels with different gap, it is found that with the size reduction of the gap, the bubbles are easier to deform and aggregate. The flow pattern transition boundary shifts to the left, which means the transition among the various flow patterns occurs at

Fig. 17. Flow pattern map in vertical small rectangular channel with 5 mm gap.

Fig. 18. Flow pattern map in vertical narrow rectangular channel with 2 mm gap.

smaller gas velocity. The flow pattern in tube [12] is also compared with present flow pattern in rectangular channel. It is quite disparate that bubble flow and slug flow take up a smaller part of the flow pattern of rectangular channel, while annular flow takes

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up a greater part. The minimum gas velocity of annular flow in flow map of narrow rectangular channel is approximately one-tenth of that in flow map of tube. 4. Conclusions The numerical simulations of upward two-phase flow in rectangular channels with different gap have been investigated, and the following conclusions can be achieved: (1) A simple and practical inlet condition is used to simulate different flow patterns and testified by simulation results. (2) There are four basic flow patterns of air-water two-phase flow, including bubbly flow, slug flow, churn-turbulent flow and annular flow, in upward rectangular flow channels. In general, when the liquid superficial velocity is constant and the gas superficial velocity increases, the flow patterns are followed in sequence by the bubbly flow, slug flow (or without this flow pattern), churn-turbulent flow, annular flow, respectively. (3) The void fraction of the bubbly flow is generally below 0.3. While the void fraction increases, the bubbles are apt to deform due to the bubbles motion restricted by the wall in narrow rectangular channel. Meanwhile, the bubbly flow become unstable and begins to transform to the slug flow or churn-turbulent flow directly. The values of void fraction of the simulation conditions are in good agreement with published experimental results and the model of Ali. (4) The frequency and amplitude of pressure drop fluctuations change with the flow pattern, and the qualitative discrimination of gas-liquid two-phase flow pattern can be done. (5) The two-phase flow pattern map of rectangular channel shows that, compared with the tube, the range of annular flow in the channel is larger, while the ranges of slug flow and bubbly flow in the channel are smaller. The transitional boundaries between flow patterns occur at smaller gas velocity than those in the tube. While compared rectangular channel with 2 mm gap to that with 5 mm gap, it can be found that with the reducing gap size, the flow pattern transition boundary shifts to the left. The study also shows that CFD method is a feasible way to draw the two-phase flow patterns map.

Acknowledgements The authors are grateful for the support of the Natural Science Foundation of China (Grant Nos.: 51376201, 51676020) and Natural Science Foundation Project of CQ CSTC (Grant No. cstc2015jcyjB0588). References [1] L.S. Tong, Y.S. Tang, Boiling Heat Transfer and Two-Phase Flow, second ed., CRC Press, 1997. [2] D.P. Huang, G.L. Ding, H. Quack, Theoretical analysis of deposition and melting process during throttling high pressure CO2 into atmosphere, Appl. Therm. Eng. 27 (2007) 1295–1302.

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