Simulation of two-phase refrigerant separation in horizontal T-junction

Applied Thermal Engineering 134 (2018) 333–340

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Research Paper

Simulation of two-phase refrigerant separation in horizontal T-junction a

a,⁎

a

a

b

Pei Lu , Li Zhao , Shuai Deng , Jing Zhang , Jue Wen , Qing Zhao a b

T

a

Key Laboratory of Efficient Utilization of Low and Medium Grade Energy (Tianjin University), MOE, Tianjin 300350, China China Datang Group Science and Technology, Research Institute Co., Ltd. Northwest Branch, Xi'an, Shanxi Province 710000, China

H I G H L I G H T S 3D numerical simulation is developed for the phase separation of refrigerants. • AEffects of inlet parameters on the phase separation at a T-junction are studied. • Two small recirculation regions are found in the branch pipe of a T-junction under different mass fluxes. •

A R T I C L E I N F O

A B S T R A C T

Keywords: Two-phase separation T-junction Refrigerants Numerical simulation

This paper describes a 3D numerical simulation to model the two-phase separation of refrigerants in a horizontal run-type T-junction. The computations are based on the Eulerian method with the k-ε turbulence model. Compared with data from existing experiments and phenomenological models, the average deviation of the established model is less than 5% when the liquid mass flow rate ratio is in the range 0.2–0.6. The effect of multiple parameters on phase separation is investigated using the validated model. The results show that the inlet qualities (0.3–0.7), saturation temperatures (279.15–284.15 K), and working fluids of R22 and R134a have little influence on the phase separation at the T-junction, whereas the gas mass flow rate ratio increases with the increase in inlet mass flux (100–500 kg m−2 s−1). Furthermore, it is found that two symmetric recirculation regions occur directly after the junction at the entrance to the branch.

1. Introduction T-junctions are widely applied in the engineering field and can be used as phase and component separators in thermodynamic cycles because of the uneven phase and component distribution within them. In 2002, Azzopardi et al. [1] reported the successful application of a Tjunction as a partial separator within the chemical industry. In 2012, Tuo and Hrnjak [2] showed that the coefficient of performance of a refrigerant system could be improved by introducing a T-junction bypass. These studies demonstrate the potential of T-junctions in enhancing the performance of thermodynamic cycles. To date, the main research methods consist of experimental, phenomenological models, and computational fluid dynamics. Original experimental research [3] has shown that there are many factors affecting the dividing characteristics. Subsequently, Azzopardi’s team conducted a substantial number of experiments on air–water phase separation. Azzopardi et al. [4,5] researched the effect of the upstream flow pattern and branch arm diameter on the dividing characteristics. The authors of [6,7] found that an increase in the liquid inlet velocity could lead to more liquid flow into the branch pipe. Several researchers [8–10] then studied phase ⁎

separation under different flow patterns. Recently, Meng et al. [11] and Monrós-Andreu et al. [12] focused on the flow details of the entrainment phenomenon, liquid film thickness, and void fraction of air–water or oil–air mixtures. However, only a few experiments [13–15] have been conducted with refrigerants. These experiments concerning refrigerants are based on vertical impact T-junctions (both outlets are perpendicular to the inlet), rather than the run-type T-junctions (the two outlets are perpendicular to one another) considered in this study. To date, only one experiment [16] has been performed with refrigerants in run-type Tjunctions, and the corresponding data [16] are used to validate the model described in this paper. Two categories of phenomenological models have been proposed. The first is proposed by Hwang et al. [17] and the second is based on the work of Azzopardi [4]. Tae and Cho [16] validated Hwang’s model experimentally and obtained reasonable results, whereas Chakrabarti [18] modified the model to calculate the liquid film thickness. However, until now, only a few results have been obtained with refrigerants. The methods described above can only be employed to calculate twophase streamline positions, and no detailed flow parameters can be acquired.

Corresponding author. E-mail address: [email protected] (L. Zhao).

https://doi.org/10.1016/j.applthermaleng.2018.01.087 Received 2 August 2017; Received in revised form 21 January 2018; Accepted 24 January 2018 1359-4311/ © 2018 Elsevier Ltd. All rights reserved.

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Nomenclature v p g f F D k Gk I m dp A S Re CD

Greek symbols

velocity, m s−1 pressure, Pa gravitational acceleration, m s−2 drag force, N m−3 mass flow rate ratio pipe diameter, m turbulent kinetic energy, m2 s−2 generation of turbulent kinetic energy unit tensor mass flux, kg m−2 s−1 droplet diameter, m cross-sectional area, m2 sum of forces relative Reynolds number drag force coefficient

density, kg m−3 dynamic viscosity, kg m−2 s−1 turbulent viscosity, kg m−2 s−1 kinematic viscosity, m2 s−1 turbulent dissipation, m2 s−3 surface tension coefficient, N m−1 volume fraction stress strain tensor

ρ μ μt ν ε σ α τ Subscript i m G L 1,2,3

Numerical approaches have the advantages of obtaining flow details while saving time and money. Issa and Oliveira [19] solved the full 3D two-fluid model equations for the dispersed two-phase bubble flow of air–water, and found that the effects of different turbulence models on the predictions were negligible. Hatziavramidis and Gidaspow [20] modeled 2D transient vapor–liquid and steam–water phase separation in horizontal run-type and impacting-type T-junctions, and found that the gas-momentum flux increased and the phase separation decreased as the inlet pressure increased. Stenmarl [21] attempted to identify models and settings that can accurately predict the phase separation of air–water and the effect of various parameters. They found that an Eulerian modeling approach was best for predicting the phase redistribution in the T-junction and that the drag force model of [22] was the most stable. Pao [23] investigated the influence of the side diameter to main arm diameter ratio, initial inlet gas saturation, and gas density variation on passive separation performance with an Eulerian model, and reported reasonable results. Sam [24] researched the effect of outlet pressure, gas–oil ratio, and arm length on the gas fraction using a 1D model. The results show that the outlet pressure ratio is the most influential parameter in ensuring efficient separation. Thus, it can be concluded that Eulerian models are a relatively effective method for simulating phase separation at a T-junction. However, relatively few simulations using refrigerants have been reported, and most simulation studies are based on 1D or 2D modeling in conventional-scale T-junction research field. In addition, few studies have investigated the flow characteristics inside the fluid. Hence, there is a long path to fully understanding the complicated mechanism, and a detailed analysis based on 3D modeling is required. In this paper, a 3D numerical simulation of the two-phase separation of refrigerants in a horizontal T-junction is investigated. The effects of various parameters on the mass flow rate ratio and relatively detailed results are described and discussed. It is considered that these will help

G or L two-phase mixture vapor phase liquid phase inlet, outlet, branch

to promote further understanding of two-phase separation mechanisms in conventional-scale run-type T-junctions. 2. Methodology 2.1. Physical model and meshing The 3D T-junction geometry is shown in Fig. 1 and the parameters and ranges are listed in Table 1. The inlet mass flux varies from 100–500 kg m−2 s−1 and the inlet quality (x1 = m1G/m1) varies from 0.3 to 0.7. To evaluate the uneven phase distribution, FG, FL, and F (mass flow rate ratio) are defined as:

Fi = m i3/ m i1

(1)

F = m3/ m1

(2)

The boundary conditions are presented in Table 2. The inlet real velocities are calculated as

uG = m1x1/ρG

(3)

uL = m1 (1−x1)/ρL

(4) −2

Gravitational acceleration (9.81 m s ) acts in the x direction. The operational pressure is 0 Pa and the reference pressure position is located at the point O shown in Fig. 1. The mesh shown in Fig. 2 is generated by the O-grid method, which Table 1 Parameters and ranges. Parameter

Unit

Range

Base case

Refrigerants Inlet mass flux (m1) Inlet quality (x1 = m1G/m1) Saturation temperature (Tsat)

– kg m−2 s−1 – K

R22, R134a 100, 300, 500 0.3, 0.5, 0.7 279.15, 281.65, 284.15

R22 300 0.3 281.65

Table 2 Boundary conditions. In

Fig. 1. T-junction geometry.

334

Liquid

Vapor

uL

uG

Exit of outlet pipe

Exit of branch pipe

F (mass flow rate ratio)

Wall

du/dz = 0 & dp/ dz = constant

du/dy = 0 & dp/ dy = constant

0.2/0.4/ 0.6/0.8

Smooth & adiabatic

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stratified wave. When fluid in the inlet pipe flows into the intersection region of the T-junction, one flow pattern may transfer to another [17]. Furthermore, the intersection region plays an unpredictable role in phase separation. However, few two-phase models have the capacity to simultaneously capture the liquid–vapor interface under various flow patterns in the T-junction. An Eulerian–Eulerian modeling approach is described in this paper. Our reasons for using this framework can be explained as follows. Firstly, the phase separation ratios are the most important parameters for studying the flow patterns in the inlet pipe, and it is not necessary to determine the interfaces between phases. Secondly, the bubble-mist flow transition in the intersection region may influence the phase separation, and bubble-mist flow is usually simulated by Eulerian–Eulerian models. The continuity equations are:

Fig. 2. Part of the grid of T-junction.

∇ ·(αi ρi vi) = 0 Table 3 Effect of cell numbers (F = 0.8). Grids

Mesh 1

Mesh 2

Mesh 3

Mesh 4

Numbers Vapor/liquid mass flow rate ratio

730 428 0.8/0.717

958 900 0.8/0.707

1 046 196 0.8/0.699

2 529 562 0.8/0.717

(5)

It is assumed that there is no mass transition between the two phases. The vapor phase is considered as the first phase. The sum of the liquid and vapor phase volume fractions is equal to 1, i.e.,

∑ αi = 1

(6)

The momentum conservation equations are expressed as

Table 4 Inlet flow patterns for R22 and R134a. Mass fluxes (kg m−2 s−1)

Vapor qualities

Flow patterns

100 300, 500 300, 500

0.3, 0.5, 0.7 0.3 0.5, 0.7

Stratified wave Intermittent Annular

∇ ·(αi ρi vi vi) = −αi ∇p + ∇ ·τi + αi ρi g + f + S

(7)

2 τi = αi (μi + μt ,m )(∇vi + ∇v Ti ) + αi ⎛λi− (μi + μt ,m ) ⎞ ∇ ·vi I 3 ⎝ ⎠

(8)

where S is the sum of other forces (which consist of the virtual mass force and surface tension). The coefficient of the virtual mass force is 0.5 and the coefficient of surface tension is 0.01. The interfacial area is calculated by ia-symmetric model. Here, the lift force, wall lubrication force, and turbulent dispersion force are small and can be neglected. The drag force coefficient model proposed by [22] is expressed as follows:

allows for a good presentation of the boundary layer. All cells are hexahedral. A mesh sensitivity analysis was carried out, and the results are presented in Table 3. It can be observed that the vapor/liquid mass flow rate ratio does not change significantly. Hence, Mesh 1 is chosen as the calculation mesh.

f = CDRe/24

(9)

24(1 + 0.15Re 0.678 )/ Re Re⩽1000 CD = ⎧ ⎨ R ⩾ 1000 ⎩ 0.44

2.2. Mathematical method

(10)

Re = ρG |v L−vG |dp/μ G

(11) −5

According to flow pattern research [25], there are three different flow patterns in the inlet pipe (see Table 4): annular, intermittent, and

The diameter dp of the liquid droplets is set to 10 m. The standard k-ε turbulence model is introduced to close the above equations.

Vortex 2

Vortex1

(b)

(a)

Fig. 3. (a) Contours of the mixture density (x = 0) and (b) vectors and parts of streamlines of liquid phase (FG = 0.6, T = 281.65 K, x1 = 0.3, m = 300 kg m−2 s−1).

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1.0 0.9 0.8

where σk, σε, C1, C2 are 1.0, 1.3, 1.44, 1.92, respectively. The mixture → density ρm, mixture viscosity μt,m, and mixture velocity vm are calculated as

R22,D=0.00812m -1 m1=300kg·m-2·s ,x1=0.3

N

0.7

ρm =

FG

0.6

∑

αi ρi

(14)

i=1

0.5 N

0.4

μm =

simulation Hwang experiment

0.3 0.2 0.1

N

vm =

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

N

αi ρi vi

(12)

μt ,m ⎞ ∇ε ⎟⎞ + ε (C1Gk,m−C2 ρ ε )−R ε ∇ ·(ρm vm ε ) = ∇ ·⎜⎛ ⎛μm + m σk ⎠ ⎠ k ⎝⎝

(13)

0.7

0.9

D=0.00812m,T=281.65K

0.8

m1=300kg·m-2·s-1,x1=0.3

0.7 0.6

0.5

0.5

FG

0.6

0.4 0.3

R22,D=0.00812m m1=300kg·m-2·s-1,x1=0.3

0.4

0.2

R22 R134a

0.1

284.15K 281.65K 279.15K

0.1

0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

FL

FL

(a)

(b)

0.9

0.8

R22,D=0.00812m T=281.65K,x1=0.3

0.7

R22,D=0.00812m m1=300kg·m-2·s-1,T=281.65K

0.6

0.6

0.5 FG

0.5 0.4

0.4 0.3

0.3 -

0.2

-1

100kg·m 2·s -1 300kg·m 2·s -1 500kg·m 2·s

0.2 0.1 0.0 0.0

(18)

0.3

0.2

0.7

(17)

In addition, a non-equilibrium wall function is applied to simulate near-wall flow. The conservation equations are discretized on the basis of the Finite Volume Method. The conservation equations are solved using the Semi-Implicit Method for Pressure-Linked Equations algorithm and a pressure-based steady solver. The convergence criterion of the residual is 10−5.

⎟

0.8

(16)

Gk,m = μt ,m [∇vm + ∇v Tm]/∇vm

0.9 0.8

αi ρi

i=1

where Cμ is an empirical constant, namely 0.0845.

⎟

⎜

∑

μt,m = ρm Cμ k 2/ ε

μt ,m ⎞ ∇k ⎞⎟ + Gk,m−ρ ε ∇ ·(ρm vm k ) = ∇ ·⎛⎜ ⎛μm + m σk ⎠ ⎠ ⎝ ⎝ ⎜

(15)

0.9

Fig. 4. Comparisons of the phase separation parameters among the simulation result, experimental data [17], and the predicted value based on the dividing streamline method [16].

FG

∑ i=1

FL

FG

αi μ i

i=1

0.0

0.0

∑

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.7 0.5 0.3

0.1 0.9

0.0 0.0

0.1

0.2

0.3

0.4

FL

FL

(c)

(d)

0.5

0.6

0.7

0.8

0.9

Fig. 5. Vapor and liquid mass flow rate ratios: (a) influence of working fluids, (b) influence of saturated temperature, (c) influence of inlet mass flux, (d) influence of inlet quality.

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3.5

velocity_y_phase2 velocity_z_phase2 velocity_y_phase1 velocity_z_phase1

Inlet

Velocity (m·s-1)

3.0 3.0

2.5

Four pairs of FG and FL are compared with experimental data for refrigerants [16]. Fig. 4 shows that when FL changes from 0.2 to 0.6, the simulation results are in reasonable agreement with the experimental data. The maximum deviation is 10% and the average deviation is less than 5%. However, when FL exceeds 0.6, the simulated FG is smaller than the experimental value, and the difference is up to 23.6%; this may be caused by the improper dp. Influenced by inertia, the droplet diameter may prefer to flow to the outlet when dp is greater than 10−5 m. Consequently, more liquid flows into the outlet. Remarkably, the results based on the experimental data of refrigerants [17] and the streamline method [16] are closer to the experimental results than the simulated results in Fig. 4. Nevertheless, the streamline method proposed by Hwang [17] cannot obtain detailed parameters. Additionally, it is not rigorous to consider the mass flow rate of each phase as being determined by the simplified position of streamlines (see Fig. 11).

Intersection 2.5

2.0

branch

2.0

1.5 1.0

1.5

0.5

1.0

0.0

0.5

outlet

-0.01

-0.4

0.00

-0.3

0.01

-0.2

0.02

-0.1

0.0

0.1

0.2

0.3

0.4

Position deviating from origin of coordinate (m) Fig. 6. Velocity of two phases along z-axis and y-axis of base case.

3. Results and discussion

2.3. Model validation

3.1. Parameters effects on mass flow rate ratios

Density contours and velocity vectors of the base case are presented in Fig. 3. As shown in Fig. 3(a), the mixture density in the branch arm is smaller than that in the outlet pipe, which is similar to previous observations [9]. As depicted in Fig. 3(b), there is a small vortex in the outlet pipe far from branch pipe, denoted by Vortex 1. Fluid is drawn into the branch pipe, and a recirculation zone is formed directly after the junction in the lower part of the branch, represented by Vortex 2. A similar observation is reported in [20].

Fig. 5 illustrates the effects of different refrigerants, inlet saturation temperatures, inlet mass fluxes, and inlet qualities on phase separation. It can be seen that FG is greater than FL for a fixed F in all cases, which means that a higher proportion of vapor generally tends to flow into the branch arm. Thus, the T-junction can be considered as a phase separator. Fig. 5(a) shows that the difference of FG on R22 and R134a is substantially uniform, so the effects of R22 and R134a on the mass flow

400

400

200

200

outlet

0

Pressure (Pa)

Pressure (Pa)

outlet inlet

-200

-400

-0.4

-0.3

-0.2

-0.1

inlet -200

-400

pressure_Y_R134a pressure_Z_R134a pressure_Y_R22 pressure_Z_R22

-600

0

-600

branch 0.0

0.1

0.2

0.3

-0.4

0.4

pressure_Y_284.15K pressure_Z_284.15K pressure_Y_281.65K pressure_Z_281.65K pressure_Y_279.15K pressure_Z_279.15K -0.3

-0.2

-0.1

branch

0.0

0.1

0.2

0.3

0.4

Position deviating from origin of coordinate (m) (b)

Position deviating from origin of coordinate (m) (a) 400

1000

outlet

outlet

200

500

Pressure (Pa)

Pressure (Pa)

0 0

inlet -500

pressure_Y_100kg·m-2·s-1 pressure_Z_100kg·m-2·s-1 pressure_Y_300kg·m-2·s-1 pressure_Z_300kg·m-2·s-1 pressure_Y_500kg·m-2·s-1 pressure_Z_500kg·m-2·s-1

-1000

-1500

-0.4

-0.3

-0.2

-0.1

inlet -200 -400 -600

branch

0.0

0.1

0.2

0.3

-800

0.4

-1000 -0.4

pressure_Y_x=0.7 pressure_Z_x=0.7 pressure_Y_x=0.5 pressure_Z_x=0.5 pressure_Y_x=0.3 pressure_Z_x=0.3 -0.3

-0.2

-0.1

branch

0.0

0.1

0.2

0.3

Position deviating from origin of coordinate (m)

Position deviating from origin of coordinate (m)

(c)

(d) Fig. 7. Static pressure along z-axis and y-axis under different conditions.

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6

velocity_y_100kg·m-2·s-1 velocity_z_100kg·m-2·s-1 velocity_y_300kg·m-2·s-1 velocity_z_300kg·m-2·s-1 velocity_y_500kg·m-2·s-1 velocity_z_500kg·m-2·s-1

Velocity (m·s-1)

5

4

3

2

1

0 -0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

Position deviating from origin of coordinate (m) Fig. 8. Phase 1 velocity along z-axis and y-axis under different mass fluxes (R22, x1 = 0.3).

rate ratio are negligible. These results are consistent with the experimental trend reported in [16]. The reason may be that the properties of R22 and R134a are similar. Fig. 5(b) depicts the effect of the saturation temperatures of R22 on the mass flow rate ratio. The measured vapor mass flow rate ratio at fixed FL decreases slightly as the saturated temperature increases, which demonstrates that the mass flow rate ratio is not sensitive to variations in the inlet saturation temperature. Fig. 5(c) plots the influence of the inlet mass flux on the mass flow rate ratio for R22. As the inlet mass flux increases, FL decreases for a fixed FG, which is similar to the results of [6]. Fig. 5(d) shows the effect of the inlet quality on the mass flow rate ratio for R22. As the inlet quality increases, FL decreases for a fixed FG. To gain a deep understanding of the uneven distribution phenomenon of phase separation in the T-junction, the velocity and pressure along the z-axis and y-axis are plotted in Fig. 6. This figure shows the velocity in the center of the pipe. It is known that the density of the vapor phase is lower than that of the liquid phase; therefore, the acceleration of the vapor phase is higher than that of the liquid phase at the same pressure difference, as shown in Fig. 6. Consequently, it is easier for vapor to change flow direction into the branch, which is one of the reasons why FG > FL. It is worth mentioning that the velocity in the direction of the y-axis first increases in the intersection region, then begin to decrease at the entrance to pressure (Pa)

the branch tube, and finally increases. The phenomenon of decreasing velocity can be explained by the presence of two symmetrical recirculation regions at the entrance to the branch tube. Fig. 7 plots the static pressure along the center of the z-axis and y-axis under different conditions. It can be seen that the pressure difference between the entrance of the outlet pipe and the branch increases with an increase in inlet mass flux, as shown in Fig. 7(c), and the biggest pressure difference reaches 2 kPa when the inlet mass flux is 500 kg m−2 s−1. The variation of pressure difference with the change of refrigerant, inlet saturation temperature, and inlet quality is smaller than that observed for changes in inlet mass flux. It can be concluded that pressure difference is one of the major factors affecting fluid velocity magnitude and direction in the intersection region. A comparison of Figs. 5 and 7 shows that the pressure difference clearly affects phase separation. Fig. 8 shows the gas phase velocity along the z-axis and y-axis under different mass fluxes at an inlet quality of 0.3. By comparing Fig. 7(c), Fig. 5(c), and Fig. 8, it can be concluded that an increase in the pressure

400

500 400 300 200 100 0 -100 -200 -300 -400 -500 -600 -700 -800 -900 -1000 -1100 -1200

Inlet

Fig. 10. Contour of pressure and parts of streamlines passing through the line x = 0, y = 0.014.

pressure_Z pressure_Y

200

Axis 2

pressure (Pa)

outlet 0

inlet

-200

-400 Zone 1

Axis 1

intersection region

-600

O

-0.4 - 0.02

- 0.01

branch

Zone 2

0

-0.01

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

-0.02

Position deviating from origin of coordinate(m)

Z(m)

(b)

(a)

Fig. 9. (a) Pressure contour in T-junction, (b) pressure drop in the direction of the branch.

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Fig. 11. Pressure contours and parts of streamlines passing through (a) y = 0.001, z = 0, (b) y = 0.002, z = 0, (c) y = −0.001, z = 0, (d) y = −0.002, z = 0.

fluid flows in Zone 1. Thus, the pressure in Zone 1 is lower than in surrounding areas, as illustrated in Fig. 9(b). It can be observed from Fig. 3(b) and Fig. 11(a) that there is a vortex (called Vortex 1) in the outlet pipe. This phenomenon can be explained by the fluid velocity in the direction of Axis 2 at the entrance of the outlet pipe being nonzero, which is caused by a rise in pressure at the entrance to the outlet pipe. Furthermore, the pressure at the entrance to the outlet pipe is greater than that at the entrance to the branch pipe, so some of the fluid that flows into the outlet pipe flows back into the branch pipe, as shown in Fig. 11(a). Fig. 10 depicts the fluid passing through the line x = 0, y = 0.014 and flowing into the branch pipe. Two symmetric recirculation regions form directly after the junction in the lower part of the branch pipe. A similar phenomenon was reported by Liu [26]. This phenomenon may be explained by the circumferential velocity going in the opposite direction in the branch pipe (such as the direction of streamlines in the branch in Fig. 11), which occurs because the pressure in Zone 1 is lower than in the surrounding regions, as illustrated in Fig. 9(a). As shown in Fig. 11 for the base case, fluid that passes through the lines y = 0.001, z = 0 and y = 0.002, z = 0 flows into the branch pipe; indeed, fluid flows into the branch pipe as long as it passes through the lines z = 0, y > 0.001. Fluid that passes through the lines y = −0.001, z = 0, and y = −0.002, z = 0 flows into the branch pipe and the outlet

difference between the exit of the inlet pipe and the entrance to the branch and outlet pipe results in an increased velocity gradient in the intersection region and an increase in FG/FL.

3.2. Flow characteristics Fig. 9 shows the pressure contour about the x = 0 plane and the pressure drop in the direction of the branch. The results in Fig. 9(a) demonstrate that the static pressure of the outlet pipe is higher than that of the inlet pipe and that the pressure of the branch pipe is lower than that of the inlet pipe. The pressure along Axis 1 and Axis 2 is presented in Fig. 9(b). The reasons for the static pressure variations may be explained as follows: for the pressure along Axis 1, when the fluid flows into the intersection region, part of the fluid flows into the branch pipe. Thus, the mass flux in the outlet pipe is less than that in the inlet pipe. Moreover, there is a kinetic energy loss owing to a portion of fluid mixing more chaotically and hitting the wall of the intersection region. Hence, the velocity decreases suddenly when fluid flows into the entrance of the outlet pipe, which leads to an increase in pressure. Once the pressure along the outlet pipe reaches a maximum, it decreases gradually under wall friction, drag force, and dissipation; for the pressure along Axis 2, the influence of inertia means that most of the fluid flows near the wall region, far from the incoming flow, and little 339

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100–500 kg m−2 s−1. The effects of R22 and R134a on the mass flow rate ratio are negligible; this may be because the refrigerants in this study have similar properties. Thus, other refrigerants should be included in future studies to provide more comprehensive conclusions. A mechanical flow analysis indicates that the separation mechanism is influenced by pressure differences. Two small symmetric recirculation regions occur directly after the junction in the lower part of the branch.

pipe. It can be predicted that more fluid will flow into the outlet pipe when y < −0.002. Moreover, Fig. 11(c) and (d) indicate that some of the fluid flows into the outlet pipe, and then flows back into the branch pipe. Thereby, a small vortex (called Vortex 1 in this paper) appears. 4. Conclusion When FL is in the range 0.2–0.6, the results for the base case are broadly in agreement with the experimental data. The inlet qualities and saturation temperatures have little influence on phase separation. However, the inlet mass flux has a significant effect on phase separation. FG increases with the increase in inlet mass flux over the range

Acknowledgements This work is supported by National Natural Science Foundation of China (51476110).

Appendix A A comparison of the results is obtained by Enhanced Wall Treatment (EWT), Standard Wall Function (SWF) and Non-equilibrium Wall Function (NEWF) under different turbulence models (standard k-ε turbulence model, realizable k-ε turbulence model, RNG k-ε turbulence model and k–ω SST turbulence model). The results of FG/FL are shown in Table A1 for F = 0.8 and Table A2 for F = 0.6.

Table A1 Results of FG/FL for F = 0.8. FG/FL

Standard k-ε turbulence model

Realizable k-ε turbulence model

RNG k-ε turbulence model

k–ω SST turbulence model

SWF NEWF EWT

0.8045/0.719 0.8045/0.718 0.8032/0.745

0.8045/0.719 0.8045/0.718 0.8030/0.746

0.8050/0.705 0.8046/0.716 Oscillation

/ / Oscillation

FG/FL

Standard k-ε turbulence model

Realizable k-ε turbulence model

RNG k-ε turbulence model

k–ω SST turbulence model

SWF NEWF EWT

0.606/0.488 0.606/0.486 0.603/0.546

0.606/0.486 0.606/0.484 0.603/0.548

0.606/0.495 0.606/0.495 0.603/0.551

/ / 0.603/0.547

Table A2 Results of FG/FL for F = 0.6.

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