International Journal of Multiphase Flow 98 (2018) 24–35
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A new flow pattern map for flow boiling of R1234ze(E) in a horizontal tube Zhi-Qiang Yang a,b, Gao-Fei Chen a, Xiao-Ru Zhuang a,b, Qing-Lu Song a,b, Zeng Deng a,b, Jun Shen a, Mao-Qiong Gong a,∗ a b
Chinese Academy of Sciences, Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Beijing, 100190, China University of Chinese Academy of Sciences, Beijing, 100049, China
a r t i c l e
i n f o
Article history: Received 14 June 2017 Revised 21 August 2017 Accepted 25 August 2017 Available online 1 September 2017 Keywords: R1234ze(E) Flow pattern Transition Force
a b s t r a c t Considerable attention has recently been given to the new environment-friendly refrigerant of R1234ze(E) for applications such as heat pump and air-conditioning systems. In this study, an experiment was carried out to investigate two-phase flow patterns and flow transitions for R1234ze(E) in a smooth horizontal tube with an inner diameter of 6 mm. The experiments were performed at conditions covering saturation pressures from 0.215 to 0.415 MPa, mass fluxes from 130 to 258 kg/m2 s and heat fluxes from 10.6 to 74.8 kW/m2 . The influences of saturation pressure, mass flux and heat flux on flow pattern transition were analyzed. Six well-known flow maps have been compared with the observed flow patterns of R1234ze(E). The results indicated that none of them can predict all the flow pattern transitions well. Thus, three dimensionless numbers K1 , K2 and K3 which represent the ratio of the evaporation momentum force to the inertia force, the evaporation momentum force to the surface tension force, and the shear force to the gravity force respectively were introduced. Based on dimensionless numbers K1 , K2 , K3 and Xtt , a new flow pattern map for R1234ze(E) was proposed which could accurately predict the experimental data. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction As refrigerants, hydrofluorocarbons (HFCs) are widely used in refrigeration and heat pump system. HFCs have zero ozone depletion potential (ODP) value, but they do have large global warming potential (GWP) value, which can lead to global warming. In 1997, the Kyoto Protocol issued rules to restrict the use of greenhouse gases including R134a and R32. Besides, United Nations (UN) Fgas regulation also established the limitations to the refrigerants with GWP value larger than 150 in new vehicle from 1 January 2011 and for all vehicles from 1 January 2017 (Union, 2006). Therefore, the use of environment-friendly refrigerant which has lowGWP and low-ODP value would be urgent demands in the refrigeration industry. In the recent years, halogenated olefins (HFOs) as one of the most promising alternatives have been investigated as possible solutions (Liu et al., 2016). In particular, R1234ze(E) (trans-CHF=CHCF3 ) has low flammability, non-toxicity, zero ODP and quite low GWP (Mota-Babiloni et al., 2016; Stocker et al., 2013), is used as a promising substitute for the current refrigerant R134a. What’s more, among its good environmental properties, ∗
Corresponding author. E-mail address:
[email protected] (M.-Q. Gong).
http://dx.doi.org/10.1016/j.ijmultiphaseflow.2017.08.015 0301-9322/© 2017 Elsevier Ltd. All rights reserved.
R1234ze(E) has an atmospheric lifetime of only 11 days, while the R134a has 13 years. Due to the good characteristics, R1234ze(E) is used as a near drop-in replacement to R134a in a lot of applications: from refrigeration to heat pump (Mota-Babiloni et al., 2014). Hence, many researches were investigated to analyze and evaluate the performance of R1234ze(E). Fukuda et al. (2014) evaluated the thermodynamic attribute of R1234ze(E) thermodynamically, experimentally and numerically. The results showed that R1234ze(E) has more potential for high-temperature heat pump systems rather than typical air conditioners or refrigeration systems. Jankovic´ et al. (2015) conducted an experiment to analyze R1234ze(E) as drop-in replacements for R134a in a small power refrigeration system. The drop-in analysis results showed that R1234ze(E) may perform better than R134a if an overridden compressor is used to match the refrigerating system cooling power. Motta et al. (2010) indicated that R1234ze(E) is a potential refrigerant for small commercial and residential refrigeration systems. They also evaluated the performance of R1234ze(E) in an actual vending system and result showed that the comparable performance to R134a can be achieved without significant hardware modification. Ansari et al. (2014) applied energy and exergy analysis method to compare R1234ze(E) with R134a theoretically. The result indicated that performance
Z.-Q. Yang et al. / International Journal of Multiphase Flow 98 (2018) 24–35
parameters of COP and exergetic efficiency for R1234ze(E) are almost same with R134a which only having a difference of 5.6%. Hence, R1234ze(E) is supposed as a good replacement to R134a if a certain modification is done in the design. As the performance of R1234ze(E) is evaluated and R1234ze(E) is verified suitable as a drop-in replacement for R134a in several applications, thus, the investigations of flow characteristics of R1234ze(E) is becoming more and more important. Ribatski and Thome (2007) pointed out that it is essential to develop an accurately predictive methods to estimate heat transfer coefficient, pressure drop, void fraction and flow patterns in order to design more efficient and compact heat exchangers. They also indicated that system thermal efficiency of heat exchangers always depends on the heat transfer coefficient and the pressure drop directly, while the flow characteristics such as pressure drop rely on the void fraction. However, these parameters in turns depend on the local flow pattern, because the different flow pattern leads to the different phase distributions which result in the distinct for heat transfer coefficients, pressure drops and void fractions. Rollmann and Spindler (2015) also indicated that flow patterns have a significant influence on the heat transfer coefficient and the pressure drop during flow boiling process. The flow characteristics of working fluid play important parts in designing the heat exchangers. Therefore, the investigation on two-phase flow pattern are essential. Over the past decades, due to the important role of two-phase flow pattern in the industrial equipment, the studies related to two-phase flow patterns are still attractive. Many researches have been done to investigate the two-phase flow patterns of different refrigerants and develop new flow pattern transitions. Taitel and Dukler (1976) put forward a theory model to predict the flow pattern transitions in an horizontal tube by taking the effect of properties of the fluids, pipe diameter, and angle of inclination into account. The theory model was developed without flow regime data and the mechanisms of flow pattern transition were based on physical concepts. After a comparison with the experimental data, this theory model showed a good predictive ability. Barnea et al. (1983) found that with decrease of pipe diameter, the deviation between the predictive models (Taitel and Dukler, 1976; Taitel et al., 1980) and experimental data was accentuated. So they modified the theoretical models by taking surface tension effects into account. Furthermore, they also drew a conclusion that surface tension play a major role in the stratified-intermittent transition in small pipes, while for large pipes the Kelvin-Helmholtz instability is the dominant factor. Kattan et al. (1998) performed tests with R134a, R123, R402A, R404A and R502 in a tube with a diameter of 12.0 mm and proposed a new flow pattern map included four improvements to the Steiner (1993) map. In the new flow pattern map, the new transition curve between stratified-wavy flow pattern and annular flow pattern was adjusted by taking account of the influence of the heat flux and onset of dryout at high vapor quality. Importantly, in order to identify the flow patterns for convenience, the map was also transformed into a mass velocity versus vapor quality format. Zürcher et al. (2002) found that void fraction is not a continuous function during the flow pattern transition. Thus, different void fraction was used for different flow pattern in the new flow transition models. Based on experimental data of flow patterns for R717, R134a, R407C covering a wide range of conditions and flow pattern model of Kattan et al. (1998), a modified flow pattern model was proposed which took the inception of dryout at the top of tube into account. Through a comparison with the experimental data, this proposed modifications showed a good agreement with flow pattern transitions for different fluids. Wojtan et al. (2005a) proposed new flow pattern transitions of annular to dryout and dryout to mist based on new heat transfer measurements and flow pattern observations. And these two
25
new transition curves were added into Kattan et al. (1998) map. According to the dynamic void fraction measured by optical void fraction measurements technique, stratified-wavy region has subdivided into three subzones: slug, slug-stratified wavy and stratified wavy. Besides, vapor qualities corresponding to the flow transition of stratified to stratified wavy flow has also been modified. These modifications of flow transitions not only promote the prediction accuracy of flow pattern transition but also improve the identification of the dryout start. Revellin and Thome (2007a) conducted a flow boiling experiment for R134a and R245fa in tubes with diameter of 0.509 and 0.790 mm under the diabatic condition. Based on the observations, flow patterns were classified into three types and a new flow pattern transition correlation was proposed. This new flow pattern transition correlation was expressed by the dimensionless numbers of liquid Reynolds number, the liquid Weber number and Boiling number. Furthermore, they also pointed out the feasible operating range of microevaporators which made with circular microchannels can also be determined by using this flow pattern map. Barbieri et al. (2008) conducted an experiment of convective boiling for R134a in smooth brass tubes with inner diameters varying from 6.2 mm to 12.6 mm. Flow patterns was obtained through a sight glass and the data of flow patterns were mapped out. They found that mass velocity, vapor quality and inner tube diameter have effects on the intermittent to annular transition. By taking these effective parameters into account, two dimensionless numbers of liquid Froude number Frl and Martinelli parameter Xtt were introduced. Furthermore, data points related to the intermittent to annular transition in terms of the liquid Froude number Frl and Martinelli parameter Xtt under the logarithmic coordinates are found grouping around a linear curve. Based on this phenomenon, a new intermittent to annular transition correlation is developed. Ong and Thome (2011a) conducted an experiment to investigate the two-phase flow patterns of R134a, R236fa and R245fa in tubes with diameters of 1.03, 2.2 and 3.04 mm. A new macro-microscale flow pattern map was proposed by taking gravity, inertia and surface tension effects into accounts. What’s more, they also found that gravity force is a dominant factor on the flow pattern transitions when confinement number less than 0.34, while it is suppressed when the confinement number larger than 1. Costa-Patry and Thome (2013) found a phenomenon that the initial vapor quality of coalescing bubble flow regime to annular flow transition is closed to inflection point where the minimum value of heat transfer coefficients occur. This phenomenon can be used to track the flow pattern transition. By using this criteria, a new coalescing bubble to annular flow transition equation was developed. Three database from Ong and Thome (2011b) and CostaPatry et al. (2011, 2012) were introduced to compare with the new flow pattern transition, and the results indicated that within the experimental resolution the prediction accuracy can reach about 95%. Although many researches on two-phase flow patterns and flow pattern transitions were conducted, most of them were developed for adiabatic conditions. Besides, an investigation on flow characteristics of R1234ze(E) is rarely reported and flow pattern transition of R1234ze(E) is still lacking. In this work, the experiment on flow characteristics was conducted under several operating conditions covering saturation pressures from 0.215 to 0.415 MPa, mass fluxes from 130 to 258 kg/m2 s, heat fluxes from 10.6 to 74.8 kW/m2 and the flow patterns were captured through high speed camera. The effect of mass flux, heat flux and saturation pressure on two-phase flow pattern transitions were studied and the transition mechanism was analyzed. Moreover, prediction models from the literature were used to compare with the experimental data. By taking inertia force, surface tension force, shear force, gravity force, evaporation momentum force into account, three dimensionless numbers were introduced. Based on the
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Refrigerant charge port
9
12 2 Refrigeration Cycle1
1
Δp
13 2
3
4
p
T
5
Δp
6 ①
T
②
p
8 p
7
T
6 ③
T
Refrigeration Cycle2
11
T
T
10
DC Regulator1 DC Regulator2
Data Acquisition and Control System
④
SENSORS T: temperature gauge p: absolute pressure sensor Δ p: differential pressure sensor
1-Heat exchanger 2-Valve 3-Magnetic gear Pump 4-Coriolis mass flow meter 5-Preheater 6-Sight glasses 7-Heat transfer test section 8-Pressure drop test section 9-Vacuum chamber 10-Vacuum pump 11-Heat exchanger 12-heating rod 13-Refrierant charge port Fig. 1. Schematic view of flow boiling experimental system.
and the preheater were packaged by aluminum foil and placed in a vacuum chamber with a vacuum consistently less than 5 Pa during the experiment. Before the experiments, a heat leakage test has been done for the heat transfer test section in the chamber when the chamber vacuum is less than 5Pa. The results indicated that the change of average vapor quality caused by heat leakage under the operating conditions is less than 0.0016 which means heat leakage has little effect on the vapor quality. Furthermore, the operating temperature (273.0/283.8/292.2K) is also close to environment temperature. Therefore, the heat leakage from the ambient to the experimental system can be neglected for the vapor quality and the similar analysis was also seen in Liu et al. (2017). In addition, more detailed description of the experimental system was presented in the previous work Yang et al. (2017). Fig. 2. Visualization section.
2.2. Experimental procedure dimensionless numbers, a new flow pattern map for R1234ze(E) was proposed. 2. Experimental setup and procedure 2.1. Test facility The experimental setup is the same as the previous work Yang et al. (2017). Fig. 1 shows the schematic view of the experimental system. The experiment system is used to study the flow boiling heat transfer, pressure drop and two-phase flow pattern characteristics of different refrigerants. From the Fig. 1, the experiment system includes two refrigeration cycles and a test loop. The test loop consists of a diabatic heat transfer test section and an adiabatic pressure drop test section. The heat transfer test section contains four individual copper blocks(1,2,3,4) and thin-film electric heaters are adhered on their surface to generate heat flux. Flow patterns were captured by high speed camera through two sight glasses which were installed in the inlet and the outlet of the diabatic heat transfer test section. The picture of visualization section is presented in the Fig. 2. In this paper, the flow pattern observed at the outlet of the diabatic heat transfer test section is used for analysis. Because of the short distance between the sight glass and the fourth copper block(4), the flow patterns observed in the outlet of the diabatic heat transfer test section were considered as the flow patterns happened in the fourth copper block(4). Moreover, in order to avoid heat gain or heat loss, test sections
Before experimental setup running, the vacuum chamber containing the test section is evacuated by a vacuum pump to less than 5.0 Pa. During the experiment, a preheater was used to adjust the test fluid inlet vapor quality. All data were recorded after system under steady state. The steady-state condition of the experiment is reached when temperature changes less than 0.1K and the flow pattern is stable within ten minutes. After the steady state is reached, then all the data exported by the platinum resistance thermometers, flow meter, pressure transducer and differential pressure transducer and so on are recorded ten times continuously by a data logger (Keithley 2700) and stored in a computer. What’s more, the steady-state is also kept in the data record process. Finally, the average of the ten sets of data is used for analysis. 3. Data reduction 3.1. Heat flux q represents the inner wall heat flux, and it is calculated by the measured total heat input by the following equation:
q=
UI
π DL
(1)
In this equation U represents the voltage of thin-film electric heater, I is current of thin-film electric heater, D is the inner diameter of the tube and L is the length of the copper block.
Z.-Q. Yang et al. / International Journal of Multiphase Flow 98 (2018) 24–35
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Table 1 Uncertainties of parameters. Parameters
Instruments
Range
Uncertainties
Temperature (K) Absolute pressure (MPa) Differential pressure (kPa) Mass flow (kg h−1 ) Voltage (V) Direct current (A)
PT100 thermometer UNIK 50 0 0 pressure transducers UNIK 50 0 0 differential pressure transducer ULTRA mass MKII Coriolis mass flow meter Keithley 2700 multimeters ZW 1659 amperometers
55–373 0–1 0–40 0–180 0–60 0–5
0.1K 0.04% 0.04% 0.1% 0.005% 0.2%
Table 2 Experimental conditions.
3.2. Vapor quality Vapor quality is an important parameter in the experiment. The inlet vapor quality of test section is obtained from the following equation:
xin =
Qpre − Cp m(Tin − Tsub ) mHlv
(2)
In the equation, Qpre represents the thermal power of preheater. m is the flow rate of test fluid. Tin is the temperature of test fluid before coming into inlet of heat transfer test section. Tsub is the temperature of test fluid before coming into inlet preheater. Hlv is the latent heat of test fluid. Cp represents the specific heat capacity at the constant pressure. Considering the thermal power of copper blocks and preheater adding to the test fluid, the vapor quality at exit of each copper block can be calculated as the following equation:
xi = xin +
Qi mHlv
(3)
In the equation, the index i represents the number of copper block. Qi represents the sum of thermal power that adding to each copper block. According to the Eq. (3), the vapor quality at the outlet of copper block 3 and 4 can be calculated.
3
Qpre − Cp m(Tin − Tsub ) 1 Qi = mHlv mHlv Q1 Q2 Q3 + + + mHlv mHlv mHlv
R1234ze(E)
Tube Internal diameter (D) Saturation pressure (psat ) Saturation temperature (K) Mass flux (G) Heat flux (q) Heating medium
Copper 6 mm 0.215/0.315/0.415 MPa 273.0/283.8/292.2 K 130/162/194/226/258 kg/m2 s 10.6/26.6/43.3/59.1/74.8 kW/m2 Electrical heating
u2 (x4_ave ) =
2 ∂f u ( Qi ) ∂ Qpre ∂ Qi 1 2 2 ∂f ∂f + u(Tin ) + u(Tsub ) ∂ Tin ∂ Tsub 2 2 2 ∂f ∂f ∂f + u (m ) + u(C ) + u(Hlv ) ∂m ∂ Cp p ∂ Hlv ∂f
2
u(Qpre )
+
4
(7) Under the operation conditions, the average uncertainty for vapor quality x4_ave is 1.75% with 95% confidence. 4. Results and discussion
x3 = xin +
(4)
4
Qpre − Cp m(Tin − Tsub ) Q1 1 Qi = + mHlv mHlv mHlv Q2 Q3 Q4 + + + mHlv mHlv mHlv
Refrigerant
In the experiment, flow boiling characteristics of R1234ze(E) have been investigated under different operation conditions, which were presented in Table 2. Then the effects of different parameters on flow pattern transitions were analyzed.
x4 = xin +
4.1. Flow regimes visualization
(5)
With the linear interpolation method, the average vapor quality x4_ave for the fourth copper block is acquired and used for flow pattern analysis.
x4_ave =
Qpre − Cp m(Tin − Tsub ) x4 + x3 Q1 Q2 = + + 2 mHlv mHlv mHlv Q3 Q4 + + mHlv 2mHlv
(6)
In the equation, Q1 , Q2 , Q3 , Q4 represent the input thermal power to copper block 1,2,3,4 respectively. 3.3. Experimental uncertainties The uncertainties of the measurements are summarized in Table 1. And the uncertainty analysis is carried out by the method Moffat (1988). The inputs to the vapor quality is expressed by Eq. (6). So the standard uncertainty of vapor quality, can be expressed by the Eq. (7):
Saisorn et al. (2010) and Rollmann and Spindler (2015) indicated that flow pattern has an significant influence on the heat transfer, so the ability to predict flow pattern transitions accurately are essential and urgent. Kim and Mudawar (2014a, b) also pointed out that flow patterns not only have effects on heat transfer coefficient but also have an influence on two-phase pressure drop. It is necessary to have a good understanding of the flow pattern transition of R1234ze(E) before using the R1234ze(E) as a candidate refrigerant to design relevant heat exchangers. Therefore, an experiment was conducted to capture the flow patterns to investigate the flow characteristics and flow patterns transition of R1234ze(E). During the experiment, a Motion Studio high speed camera which owns more than 10 0 0 0FPS shooting frequency and 1 μs of the minimum exposure time was used to observe and record the flow patterns of R1234ze(E). The flow patterns observed in the experiments were plug flow, slug flow and annular flow. In this paper, intermittent flow also refers to the plug and slug these two flow patterns. Flow patterns’ idenfication criteria here were given by Collier and Thome (1994) and the photographs of flow patterns are presented in Fig. 3.
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Fig. 3. Photographs of R1234ze(E) flow pattern underseveral conditions G = 194kg/m2 s,q = 10.6 kW/m2 (C) psat = 0.215 MPa, G = 258 kg/m2 s, q = 10.6 kW/m2 .
a
(A)
b
300
psat=0.215MPa, q=10.6kW/m2
200
150 Plug flow Slug flow Annular flow P/S transition line S/A transition line
100
50 0.0
300
G = 194 kg/m2
s,
q = 43.3 kW/m2
(B)
psat = 0.215 MPa,
psat=0.215MPa, q=43.3kW/m2
250
G(kg/m2 s)
G(kg/m2 s)
250
psat = 0.215 MPa,
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Vapor quality-x
200
150 Plug flow Slug flow Annular flow P/S transition line S/A transition line
100
50 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Vapor quality-x
Fig. 4. Effect of the mass flux on the flow pattern transitions for R1234ze(E).
4.1.1. Effect of mass flux Fig. 4 presents the effect of mass flux on the flow pattern transitions. With the increase of mass flux, the initial vapor qualities of flow pattern transitions tend to decrease. It is seen that the inception vapor quality of flow pattern transition is smaller for the mass flux of 258 kg/m2 s while it is larger for the mass flux of 130 kg/m2 s. That’s because the higher mass flux leads to higher vapor velocity and greater inertial force which results in vapor qualities corresponding to flow pattern transitions occur earlier. After a comparison is made between Fig. 4a and b, the flow pattern transition curves show the same changing tendency even at the different heat flux condition. Fig. 4 also depicts a phenomenon that with the increase of mass flux, the range of vapor quality corresponding to the plug and slug flow regimes becomes narrower while the range of vapor quality relating to annular flow regime becomes wider. This phenomenon was also similar as Barbieri et al. (2008) and Ong and Thome (2011a) observed. 4.1.2. Effect of heat flux Fig. 5 presents the effect of heat flux on the flow pattern transitions of R1234ze(E). With the increase of heat flux, inception vapor qualities of flow pattern transitions tend to decrease. What’s more, plug and slug flow occupy a narrower range of vapor qualities while the annular flow are observed in a wider range of vapor qualities when in high heat flux. However, this results are contrary
to Charnay et al. (2014). Additionally, after a comparison between Fig. 5a and b, a phenonmenon can be found that the inception vapor qualities corresponding to flow pattern transitions occur earlier and annular flow occupies smaller range of vapor quality when in high mass flux. 4.1.3. Effect of saturation pressure Fig. 6 illustrates the effect of saturation pressure on the flow pattern transitions of R1234ze(E). The thermodynamic properties of R1234ze(E) vary with saturation pressures are presented in Table 3. With the increase of saturation pressure, the vapor qualities corresponding to flow pattern transitions tend to decrease. During the flow boiling progress, the function of the surface tension is keeping the liquid hold up between the tube walls. The higher saturation pressure leads to the lower surface tension which results in the suppression of keeping the liquid hold up. Therefore, the high velocity vapor is more easily taking away the liquid film into high velocity vapor core which contributes to the higher vapor qualities corresponding to flow pattern transition. As can be seen from Table 3, the increase of saturation pressure leads to the decrease of liquid density and viscosity, while results in the increase of vapor density and viscosity. The change of thermophysical properties of R1234ze(E) results in lower vapor velocity and higher liquid velocity. Meanwhile, shear force between the two phase interface is diminished due to the decrease of the dif-
Z.-Q. Yang et al. / International Journal of Multiphase Flow 98 (2018) 24–35
a
b
110 100
Plug flow Slug flow Annular flow P/S transition line S/A transition line
psat=0.215MPa,G=130kg/m s 2
90 70
100
60 50 40
80 70 60 50 40
30
30
20
20
10
10
0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Plug flow Slug flow Annular flow P/S transition line S/A transition line
psat=0.215MPa,G=194kg/m2 s
90
q(kW/m2)
q(kW/m2)
80
110
29
0 0.0
1.0
0.1
0.2
0.3
Vapor quality-x
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Vapor quality-x
Fig. 5. Effect of the heat flux on the flow pattern transitions for R1234ze(E).
a
b
550 500
Plug flow Slug flow Annular flow P/S transition line S/A transition line
G=194kg/m s, q=10.6kW/m 2
2
400
500
350
400 350
300
300
250
250
200
200
150 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Plug flow Slug flow Annular flow P/S transition line S/A transition line
G=194kg/m2 s, q=43.3kW/m2
450
psat(kPa)
psat(kPa)
450
550
150 0.0
1.0
0.1
0.2
0.3
Vapor quality-x
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Vapor quality-x
Fig. 6. Effect of the saturation pressure on the flow pattern transitions for R1234ze(E). Table 3 Thermodynamic properties of R1234ze(E) at different saturation pressures. Fluids
Tsat (K)
psat (MPa)
ρ l (kg/m3 )
ρ v (kg/m3 )
Hlv (kJ/kg)
μl (μPa∗ s)
μv (μPa∗ s)
σ (mN/m)
R1234ze(E)
272.96 283.78 292.22
0.215 0.315 0.415
1240.7 1208.5 1182.2
11.63 16.79 21.97
184.30 177.21 171.30
269.59 236.40 213.83
11.12 11.63 11.98
12.21 10.74 9.62
ference between liquid and vapor velocity. The decrease of shear force leads to the lower vapor qualities corresponding to flow pattern transition. Therefore, with the increase of saturation pressure, the effect of surface tension on the flow pattern transition may be more stronger than the effect of shear force which leads to the transition curves tending to higher vapor quality eventually. In the Table 3, Tsat is the saturation temperature, psat is the saturation pressure, ρ l is the liquid density, ρ v the vapor density, Hlv is the latent heat, μl is the liquid viscosity, μv is the vapor viscosity, σ is the surface tension.
4.2. Comparison with existing prediction methods In this part, in order to understand mechanisms of flow pattern transition and the differences between existing flow pattern transition correlations, each flow pattern transition is reviewed briefly. Then, a detailed comparisons was made between the wellknow flow pattern maps and the flow pattern experimental data of R1234ze(E). As previously mentioned, the flow pattern data used in this study were under conditions covering saturation pressures from 0.215 to 0.415 MPa, mass fluxes from 130 to 258 kg/m2 s and heat fluxes from 10.6 to 74.8 kW/m2 .
4.2.1. Comparison with Akbar et al. (2003) Based on available two-phase flow patterns experimental data in tubes with diameter varying from 0.87 to 1.6 mm, a new Weber number based flow pattern map was developed. The entire flow pattern map was divided into four regions: surface tension dominated region consists of bubbly and plug flow patterns, inertia dominated region I represents annular flow pattern, inertia dominated region II stands for dispersed flow patterns, and transition region. Futhermore, all the flow pattern data was plotted using Wels versus Wegs coordinates. Akbar et al. (2003) correlated the data into three transition criteria. Surface tension dominated zone:
For W els ≤ 3, W egs ≤ 0.11W els 0.315
(8a)
For W els > 3, W egs ≤ 1
(8b)
where Wels is the Weber number based on liquid superficial velocity, Wels = ρ l Uls 2 D/σ and Wevs is the Weber number based on gas superficial velocity Wevs = ρ v Uvs 2 D/σ . In addition, Uvs represents the gas superficial velocity, Uvs = xG/ρ v and Uls represents liquid superficial velocity, Uls = (1-x)G/ρ l .
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Z.-Q. Yang et al. / International Journal of Multiphase Flow 98 (2018) 24–35
10000
350
Inertia dominated (Dispersed)
300
1000 Inertia dominated (Annular flow )
10 1
Plug flow Slug flow Annular flow
0.1 0.01
Transition
0.01
A
200 150 100
0.1
Slug+SW
Plug flow Slug flow Annular flow transition line
SW
50
Surface tension dominated (Bubble, Plug, Slug)
1E-3 1E-3
M D
250 Slug
G(kg/m2 s)
Wevs
100
psat=0.215MPa, q=10.6kW/m2
I
1
10
0 0.0
100
S 0.1
0.2
0.3
0.4
Wels
0.5
0.6
0.7
0.8
0.9
1.0
Vapor quality-x Fig. 8. Comparison of experimental data with Wojtan et al.flow map.
Fig. 7. Comparison of experimental data with Akbar.et.al. flow map.
Annular flow (inertia dominated zone I):
W egs ≥ 11W els 0.14 , W els < 3
(9)
Dispersion regime (the inertia dominated zone II):
W egs > 1, W els > 3
(10)
Fig. 7 presents a comparison between the Akbar et al. (2003) flow map and the experimental data under the conditions that saturation pressures from 0.215 to 0.415 MPa, mass fluxes from 130 to 258 kg/m2 s and heat fluxes from 10.6 to 74.8 kW/m2 . Fig. 7 demonstrates that the flow patterns of plug, slug and annular flow were not well classified and predicted. As for plug flow, only 58.3% of the data points fall into the surface tension dominated zone. While most of the slug flow loacte in the inertia dominated zone. For annular flow, the map predicts better in low liquid Weber number Wels region, while exhibits poor predictions in high liquid Weber number Wels region. In addition, the transition region occupies a considerable area in the flow map but there are no data points locate in this region. 4.2.2. Comparison with Wojtan et al. (2005a) This model was proposed based on Kattan et al. (1998), and several important modifications had been made to the flow pattern map. In Wojtan et al. (2005a) flow map, the stratified-wavy region has been divided into three subzones: slug, slug/stratifiedwavy and stratified-wavy by using the dynamic void fraction result from Wojtan et al. (2005b). According to the heat transfer coefficient measurements and flow pattern observations, annular to dryout and dryout to mist flow transition curves were added and integrated into the flow pattern map. What’s more, vapor qualities corresponding to the transition of stratified/stratified wavy flow were adjusted below xIA (vapor quality at transition from intermittent to annular flow). Wojtan et al. (2005a) found that these modifications show good prediction for the flow patterns below Gwavy (wavy flow transition mass flux) and improve the identification of the dryout start obviously. In order to observe the evolution of flow pattern transitions at fixed mass velocities, this map is presented by using mass velocity versus vapor quality (G vs. x) coordinates. Besides, the flow pattern transition equations are presented as follow: The stratified wavy flow pattern is classified into three zones: • • •
slug zone: G > Gwavy (xIA ); slug/stratified wavy zone: Gstrat < G < Gwavy (xIA ) and x < xIA ; stratified wavy zone: x ≥ xIA .
Gwavy =
16Avd 2 gDρl ρv
x2 π 2 1 − (2hld − 1 ) + 50
2 0. 5
×
π2 25hld
2
·
W e −1 l
F rl
0.5 +1
(11)
Herein, g is gravitational acceleration, Avd is dimensionless cross-sectional area occupied by vapor-phase, hld is dimensionless vertical height of liquid, Wel is liquid Weber number, Wel = G2 D/(ρ l σ ) and Frl is the liquid Froude number, Frl = G2 /(ρ l 2 gD) The stratified flow to stratified-wavy transition:
Gstrat =
226.32 Ald Avd 2 ρv (ρl − ρv )μl x2 (1 − x )π 2
1 / 3
(12)
Herein, Ald is the dimensionless cross-sectional area occupied by liquid-phase. The intermittent flow to annular flow transition:
xIA =
0.341/0.875
ρ −1/1.75 μ −1/7 v
l
ρl
μv
−1
+1
(13)
The annular flow to dryout transition:
Gdryout =
1 0.58 ln 0.235 x
×
D −0.17 ρv σ
+ 0.52
−0.37
1 gDρv (ρl − ρv )
ρv −0.25 q −0.7 ρl qcrit
0.926
(14) Herein, qcrit is the critical heat flux. The annular flow to mist flow transition:
Gmist =
1 0.61 ln 0.0058 x
×
1 gDρv (ρl − ρv )
D −0.38 ρv σ
+ 0.57
−0.15
ρv 0.09 q −0.27 ρl qcrit
0.943
(15) From the Fig. 8, in the flow map of Wojtan et al. (2005a), the stratified flow, the stratified wavy flow and slug/stratified wavy flow always occur under the condition of mass flux less than 150 kg/m2 s. In addition, the experimental operating range of mass fluxes are between the 130 and 258 kg/m2 s, but the stratified flow, the stratified wavy flow and slug/stratified wavy flow were not observed in the experiment. Therefore, this prediction is not in accordance with the experimantal data of flow pattern. Fig. 8 also depicts that most of data points of annular flow are located in the predicted zone. While most of data points of the plug and the slug flow pattern fall into the slug flow region. It’s obviously that the vapor qualites corresponding to intermittent/annular transition are
Z.-Q. Yang et al. / International Journal of Multiphase Flow 98 (2018) 24–35
350
1
31
psat=0.215MPa, q=10.6kW/m2
psat=0.215MPa, q=10.6kW/m2 300
Plug flow Slug flow Annular flow transition line
250
A
G(kg/m2 s)
0.1
Frl
I 0.01
1E-3 0.01
A
200 150 100
Plug flow Slug flow Annular flow transition line
0.1
1
CB
50
IB
0 0.0
10
0.1
0.2
Xtt
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Vapor quality-x
Fig. 9. Comparison of experimental data with Barbieri et al. flow transition.
Fig. 10. Comparison of experimental data with Ong and Thome flow map.
not held to occur at a constant value, with the increase of the mass flux, vapor qualites corresponding to intermittent/annular transition decrease. Therefore, the intermittent flow to annular flow transition model can not well predict the experimental data.
Based on these dimensionless numbers, new flow pattern transitions were proposed which can not only be used to predict the flow patterns happen in the macroscale channels but also the flow patterns occur in the microscale tubes. The new flow pattern transition correlations are presented as follows: Isolated bubble/coalescing bubble (IB/CB):
4.2.3. Comparison with Barbieri et al. (2008) Barbieri et al. (2008) flow map was developed based on investigation of R134a flow in channels with diameter ranging from 6.2 to 17.4 mm. In the flow map of Barbieri et al. (2008), intermittent, stratified, annular and misty flow patterns were encountered. Barbieri et al. (2008) found that the mass velocity, vapor quality and tube diameter have a significant influence on the occurrence of a particular flow pattern. In order to take these factors into accounts, two dimensionless numbers, namely the liquid Froude number, Frl , and the Martinelli parameter, Xtt have been introduced into the flow pattern transition models to group together effects related to these physical parameters. What’s more, Barbieri et al. (2008) also found intermittent to annular transition curve can be well expressed by this kind of correlation: Frl = f (Xtt ) under the logarithmic coordinates:
F rl = 3.75Xtt 2.4
(16)
where Xtt is Lockhart-Martinelli parameter, Xtt = [(1x)/x]0.9 (ρ v /ρ l )0.5 (μl /μv )0.1 . Fig. 9 depicts the comparison between the intermittent to annular transition model with experimental data. This map is presented by using liquid Froude number versus vapor Martinelli’s parameter (Frl vs. Xtt ) under logarithmic coordinates. It is obvious that the comparison between the experimental data and the transition line indicates a satisfactory agreement where the most of the experimental annular flow data points are located in the predicted annular flow region, even though the effect of the heat flux is not taken accounts of. Furthermore, the slope of the predictive flow pattern transition curve between intermittent and annular flow region is in accordance with the experimental flow pattern transition data. 4.2.4. Comparison with Ong and Thome (2011a) Using the photodiode laser signal system Revellin and Thome (2007b) and Ong and Thome (2011a) investigated flow patterns of R134a, R245fa and R236fa in tubes with diameter 1.03, 2.2, 3.04 mm. In the flow map, two-phase flow patterns were classified objectively into three types: (1) isolated bubble regime (IB) which includes bubble flow and slug-plug flow, (2) coalescing bubble regime (CB), and (3) annular regime (A). Based on this work, dimensionless numbers of Confinement number Co, Froude number Fr, Reynolds number Re and Weber number We which account for confined bubble effect, the gravity, inertia and surface tension effects have been introduced to the flow transition models.
xIB/CB = 0.36C o0.2
μ 0.65 ρ 0.9 v
v
μl
ρl
Revo 0.75 Bo0.25W el −0.91
(17)
Herein, Co is Confinement number, Co = [σ /g(ρ l -ρ v )]0.5 /D, Bo is boiling number, Bo = q/(GHlv ) and Revo is vapor Reynolds Number, Revo = GD/μv . Coalescing bubble/annular (CB/A):
xCB/A = 0.047C o0.05
μ 0 . 7 ρ 0 . 6 v
μl
v
ρl
Revo 0.8W el −0.91
(18)
Slug-plug/coalescing bubble (S-P/CB) if (xS-P/CB < xCB/A ):
xS−P/CB = 9C o0.2
ρ 0 . 9 v
ρl
F rl −1.2 Relo 0.1
(19)
where Relo is liquid Reynolds Number, Relo = GD/μl . Slug-plug/annular (S-P/A) if (xS-P/CB > xCB/A ):
xS−P/A = xCB/A
(20)
From the flow pattern transition correlations, it is clearly that mass flux, heat flux and fluid properties have effects on the flow transition from isolated bubble flow to coalescing bubble flow while there is no heat flux effect on the transition from coalescing bubble flow to annular flow. From Fig. 10, annular flow expands a wide range of vapor qualities, while the isolated bubble flow only occupy a small range of vapor qualites. What’s more, with the increase of mass flux, the isolated bubble region disappears gradually and annular flow region is getting bigger. Fig. 10 also depicts that the Ong and Thome (2011a) models over-predict the initial vapor quality of the intermittent to annular transitions. While the initial vapor quality of plug to slug transition is underestimated. 4.2.5. Comparison with Costa-Patry and Thome (2013) Based on the analysis of flow pattern and heat transfer database from Costa-Patry et al. (2011, 2012). A new flow pattern prediction method was developed. In the flow map of Costa-Patry and Thome (2013), intermittent flow regime represents the combination of the isolated bubble flow regime (IB) and coalescing bubble flow regime (CB). They found a phenomenon that vapor qualites corresponding to minimum heat transfer coefficients is close to initial vapor quality corresponding to transition of coalescing bubble regime to annular flow regime (CB-AF). Therefore, they using this inflection point in the heat transfer coefficient curves to track the
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Z.-Q. Yang et al. / International Journal of Multiphase Flow 98 (2018) 24–35
350
psat=0.215MPa, q=10.6kW/m2
300
Smooth-Annular
Plug flow Slug flow Annular flow transition line
Transition 10
Wavy-Annular
A
200
We*
G(kg/m2 s)
250
150
Slug 1
Plug
100 Plug flow Slug flow Annular flow transition line
I
50 0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.1 1E-3
1.0
0.01
0.1
1
10
Xtt
Vapor quality-x Fig. 11. Comparison of experimental data with Costa-Patry and Thome flow map.
Fig. 12. Comparison of experimental data with Zhuang et al flow map.
coalescing bubble regime to annular flow transition. Based on this consideration, they gave equation for the transition from CB to AF:
Therefore, new transition curves between different flow patterns were fitted as follow:
xCB/AF = 425
ρ 0.6 Bo1.1 v
ρl
(21)
C o0.5
From the Eq. (21), it is clear that the flow pattern transition from coalescence bubble to annular flow depends on heat flux. Fig. 11 depicts the comparison bettween the experimental data with Costa-Patry and Thome (2013) models under the mass flux versus vapor quality coordinates. From the flow map of CostaPatry and Thome (2013), it is obvious that the whole region has been divided into two flow pattern region, and the annular flow region occupy a wider range of vapor qualities than intermittent flow region. Although they took the influence of the heat flux into account, the results are still not satisfactory: most of the slug flow data fall in the annular flow region and the initial vapor quality of the experimental slug to annular transition is also underestimated. 4.2.6. Comparison with Zhuang et al. (2016) This map was developed based on the Kim and Mudawar (2012) model and flow boiling pattern data of R170 in a horizontal tube with an inner diameter of 4 mm. In this flow map, flow pattern of plug, slug, transition flow, wavy-annular flow and smooth annular flow were encountered. The physical properties of velocity, viscosity and surface tension were considered as major factors to affect the flow transition. By taking these factors into account, a modified Weber number, We∗ defined by Soliman (1986) was introduced.
W e∗ = 2.45
W e∗ = 0.85
Rev 0.64
Suv 0.3 1 + 1.09Xtt 0.039 Rev 0.79 Xtt 0.157
Suv 0.3 1 + 1.09Xtt
0.4 Rel ≤ 1250
0.039 0.4
(22)
0.084 μ v 2 ρl μl ρv
Rel > 1250
(23)
Herein, the vapor Suratman number, Suv , liquid Reynolds Number Rel and vapor Reynolds Number Rev are defined as:
S uv =
ρv σ D G(1 − x )D GxD , Rel = , Rev = μl μv μv 2
(24)
After plotting the flow regime data points under the logarithmic coordinate of modified Weber number versus Martinelli parameter. Zhuang et al. (2016) found that the flow pattern transition curves can be well expressed by this kind of correlation: We∗ = CXtt n .
Smooth - annular to wavy - annular flow: W e∗ = 29.25Xtt 0.27
(25)
Wavy - annular to transition flow: W e∗ = 18.91Xtt 0.33
(26)
Transition to slug flow: W e∗ = 9.62Xtt 0.35
(27)
Slug to plug flow: W e∗ = 4.38Xtt 0.45
(28)
Fig. 12 depicts the comparison between the experimental data with Zhuang et al. (2016) models under the logarithmic coordinates of Martinelli parameter versus modified Weber number. The experimental data plotted in the Fig. 12 were under the conditions that saturation pressures from 0.215 to 0.415 MPa, mass fluxes from 130 to 258 kg/m2 s and heat fluxes from 10.6 to 74.8 kW/m2 . From the Fig. 12, it’s clear that most of the annular flow located in the predicted zone of transition flow, wavy-annular flow and smooth annular flow. The plug to slug flow transition can be well predicted by the predictive flow transition correlation and 100% of them are properly classified and predicted. While for the slug flow, only 51% of slug flow data points locate in the predicted region. 4.3. Proposed prediction method It’s known that most of flow maps Barbieri et al. (20 08), Cheng et al. (20 08), Ong and Thome (2011a) and Wojtan et al. (2005a) are based on tests in adiabatic tube, and the flow map Costa-Patry and Thome (2013) based on tests in diabatic tube is few. However, it is common to see the flow patterns occur in the diabatic tubes in the practical applications. Besides, an investigation on flow characteristics of R1234ze(E) is rarely reported and flow pattern transition of R1234ze(E) is still lacking. So it is necessary to develop a flow map based on tests in diabatic tube for R1234ze(E). According to the analysis above, flow pattern transition is influenced by kinds of factors. While these factors are related to the forces such as inertia force, surface tension force, gravity force and shear force which have a significant influence on the P/S (plug to slug) and S/A (slug to annular) transition for R1234ze(E). After the six classical flow pattern transition models were reviewed briefly, it can be found that these transition models did not take all the influence forces into account. Akbar et al. (2003) took the Weber numbers Wels and Wegs for analysis. As it is known, Weber number only represents the combined influence of surface tension force and shear force. So the Akbar et al. (2003) can not predicted the experimental data of R1234ze(E) well. As for the transition of
Z.-Q. Yang et al. / International Journal of Multiphase Flow 98 (2018) 24–35
a
b
100 80
0.4
Slug flow Annular flow Slug-Annular transition line
0.35
60
33
0.3
K1-0.8385K21.1388K3-0.3993=14.87Xtt1.269
0.25
KP-S
KS-A
40
0.2 20 Plug flow Slug flow Plug-Slug transition line
1
10
0.15 K1-0.2963K20.3620K30.1941=0.3044Xtt0.5671
100
1E-3
0.01
0.1
Xtt
1
Xtt
Fig. 13. Flow pattern data for R1234ze(E) compared with the new transition lines.
stratified-wavy in Wojtan et al. (2005a) flow pattern maps, which took the Weber number Wel, Froude number Frl , as well as the density into account, but no inertial force (or viscosity) was encountered. What’s more, the initial transition vapor quality of intermittent flow to annular flow is a constant value for certain pressure even mass flux is changing which is not accordance with the experimental data. Barbieri et al. (2008) found intermittent to annular transition can be expressed by this kind of correlation: Frl = f (Xtt ), but the surface tension force and shear force is lacking. Thus, this model overestimated the intermittent/annular transition eventually. Ong and Thome (2011a) took inertia force, surface tension force, gravity force and shear force into accounts for the coalescing bubble to annular (CB/A) transition, but the influence of heat flux was not reflected in the model. The results indicated that transition model of Ong and Thome (2011a) overestimated the experimental data. As a contrary, Costa-Patry and Thome (2013) took the influence of heat flux into consideration, however, inertia force and shear force were excluded for the flow pattern transition of coalescing bubble to annular flow. The results showed that the slug to annular transition was underestimated. Zhuang et al. (2016) analyzed the effects of mass flux and saturation pressure on the flow pattern transitions and took physical properties of velocity, viscosity and surface tension into account. However, gravity force and shear force are absent in their correlation. Therefore, only the plug flow of R1234ze(E) is properly classified and predicted. In addition, many researches such as Yang and Shieh (2001), Chen et al. (2006) and Zhang et al. (2011) pointed out that gravity plays an important role in macroscale flows, but it is suppressed in miniscale flows due to the increasingly stronger effect of surface tension. Rollmann and Spindler (2015) indicated shear stress force is important at the phase interface which have an effect on the flow pattern transition especially for stratified to stratified-wavy flow transition. Ong and Thome (2011a) and Zhuang et al. (2016) showed that not only inertia force and shear force but also surface tension force were found to affect the flow pattern transitions. Therefore, in order to develop a model which can well predict the two phase flow pattern transition in a smooth horizontal tube with an inner diameter of 6 mm, it is essential to take all these forces into account. According to Kandlikar (2010), there are five forces: inertia force, surface tension force, shear force, gravity force, evaporation momentum force come into play in the flow boiling process. Kandlikar (2010) also pointed out that these forces per unit area are useful to investigate the effect on flow patterns and flow instability. The expressions of these forces on per unit area are presented below:
Inertia force:
G2
Fi ∼
(29)
ρl
Surface tension force:
Fσ ∼
σ
(30)
D
Shear force:
Fτ ∼
μl G ρl D
(31)
Gravity force:
Fg ∼ (ρl − ρv )gD
(32)
Evaporation momentum force:
q 2 1 hlv ρ v
FM ∼
(33)
where evaporation momentum force is exerted at the evaporating interface due to the change in momentum caused by the increase in velocity as the liquid phase changes into vapor phase. This force depends on applied heat flux, acts on the evaporating interface and plays a major role in its motion. In order to take account of inertia force, surface tension force, evaporation momentum force factors for flow pattern transition, two dimensionless numbers K1 and K2 defined by Kandlikar (2003) were introduced. Furthermore, a new dimensionless number K3 is also defined and introduced to reflect the influence of shear force and gravity force.
q 2
K1 =
hlv
=
q 2 ρ l Ghlv ρ v
(34)
=
q 2 D hlv ρ vσ
(35)
1
ρv
G2
ρl
q 2 K2 =
hlv
σ
1
ρv
D
K3 =
μl G ρl D
(ρl − ρv )gD
=
μl G (ρl − ρv )ρl gD2
(36)
where dimensionless number K1 represents the ratio of the evaporation momentum force to the inertia force, dimensionless number K2 represents the ratio of the evaporation momentum force to the surface tension force, and dimensionless number K3 represents the ratio of the shear force to the gravity force. Fig. 13 shows all data points in a plot of dimensionless number K versus Martinelli parameter Xtt based on the flow pattern
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Z.-Q. Yang et al. / International Journal of Multiphase Flow 98 (2018) 24–35
transition data of R1234ze(E). From the Fig. 13a and b, a linear relationship between the K with the Xtt was found under the logarithmic coordinates, and the relationship can be expressed as K = f (Xtt ). Based on the analysis above and R1234ze(E) flow visualization data, the following lines are fitted for boundaries between different flow regimes:
Plug to Slug: K = KP−S = K1 −0.8385 K2 1.1388 K3 −0.3993 = 14.87Xtt 1.269
(37)
Slug to Annular: K = KS−A = K1 −0.2963 K2 0.3620 K3 0.1941 = 0.3044Xtt 0.5671
(38)
The new transition curves of the equations are displayed in Fig. 13 at various experimental conditions. It is found that the new transition lines agree well with the experimental data. 5. Conclusion In this work, an experiment study of two-phase flow patterns R1234ze(E) was conducted under several operating conditions covering saturation pressures from 0.215 to 0.415 MPa, mass fluxes from 130 to 258 kg/m2 s and heat fluxes from 10.6 to 74.8 kW/m2 . The following conclusions could be drawn from this study: (1) In the flow pattern map of R1234ze(E), the plug to slug and slug to annular transition are influenced by mass flux, heat flux and saturation pressure. The higher mass flux and heat flux the lower the initial vapor quality of flow pattern transition occurs. While the higher saturation pressure contributes to the flow regime transition lines tending to higher initial vapor qualities. (2) The flow pattern maps of R1234ze(E) have been compared with six predictive models, the results show that the transition curve given by Zhuang et al. (2016) can predicted the plug to slug flow transition well and the trend of Barbieri et al. (2008) transition line consistents best with the slug to annular flow transition. However, there is no general model can predict all flow pattern transition boundaries accurately. (3) Three dimensionless numbers K1 , K2 , K3 which take inertia force, surface tension force, shear force, gravity force, evaporation momentum force into account were introduced. Based on dimensionless numbers K1 , K2 , K3 and Xtt , a new flow pattern map for R1234ze(E) was proposed in this paper which could predict the experimental data used in this study very well. Acknowledgment This work was supported by the National Science Fund for Distinguished Young Scholars of China (No. 51625603). References Akbar, M.K., Plummer, D.A., Ghiaasiaan, S.M., 2003. On gas–liquid two-phase flow regimes in microchannels. Int. J. Multiphase Flow 29, 855–865. Ansari, N.A., Yadav, B., Kumar, J., 2013. Theoretical exergy analysis of HFO-1234yf and HFO-1234ze as an alternative replacement of HFC-134a in simple vapour compression refrigeration system. Int. J. Sci. Eng. Res. 4 (8), 137–144. Barbieri, P., Jabardo, J., Bandarra Filho, E., 2008. Flow patterns in convective boiling of refrigerant R-134a in smooth tubes of several diameters. In: Proceedings of the 5th European Thermal-Sciences Conference, Eindhoven, The Netherlands. Barnea, D., Luninski, Y., Taitel, Y., 1983. Flow pattern in horizontal and vertical two phase flow in small diameter pipes. Can. J. Chem. Eng. 61, 617–620. Charnay, R., Bonjour, J., Revellin, R., 2014. Experimental investigation of R-245fa flow boiling in minichannels at high saturation temperatures: Flow patterns and flow pattern maps. Int. J. Heat Fluid Flow 46, 1–16. Chen, L., Tian, Y.S., Karayiannis, T.G., 2006. The effect of tube diameter on vertical two-phase flow regimes in small tubes. Int. J. Heat Mass. Tranf. 49, 4220–4230.
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