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Measurement of the void fraction of R-134a flowing through a horizontal tube
International Communications in Heat and Mass Transfer 56 (2014) 8–14
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Measurement of the void fraction of R-134a flowing through a horizontal tube☆ R. Srisomba a, O. Mahian b, A.S. Dalkilic c, S. Wongwises a,⁎ a Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Lab. (FUTURE), Department of Mechanical Engineering, Faculty of Engineering, King Mongkut's University of Technology Thonburi, Bangmod, Bangkok 10140, Thailand b Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran c Heat and Thermodynamics Division, Department of Mechanical Engineering, Yildiz Technical University, Yildiz, Besiktas, Istanbul 34349, Turkey
a r t i c l e
i n f o
Available online 2 May 2014 Keywords: Two-phase flow Void fraction Optical observation technique Void fraction correlation Quick closing valve method
a b s t r a c t This experiment aims to measure the void fraction of R-134a refrigerant flowing through a horizontal tube, using a quick-closing valve and optical observation techniques. The tube is transparent, circular, 115 mm long with an inside 8 mm thick, and has two actuator ball valves installed at both ends. The experiment was conducted in conditions where vapor quality ranged from 1% to 82%, saturated temperature was from 23 to 30 °C, and mass flux was from 644 to 1455 kg/m2 s. The results of the experiment indicate that raising the saturated temperature decreased the void fraction, whereas increasing mass flux had no significant effect on it. Moreover, results also show three flow regimes: intermittent, wavy, and annular. Each flow regime led to different predicted void fractions. © 2014 Elsevier Ltd. All rights reserved.
1. Introduction Two-phase gas-liquid flow has various applications, including petroleum intake, air conditioning systems, refrigerators, and nuclear power reactors [1]. An investigation of flow mechanism that sets parameters for such flow is necessary to develop better heat equipment for these systems. 1.1. Void fraction measurements Void fraction is an important parameter for two-phase flow works, like preparation of flow regime map, calculation of gravitation, and acceleration terms for total pressure drop analysis. Generally, the void fraction can be defined by the ratio of vapor to volume. The simplest measurement technique of the void fraction is the quick-closing valve method, still used at present. This method traps liquid in a tube to measure its mass and liquid volume. Several researchers have used it individually [2–7] and in calibration with other techniques [8–11]. Optical observation is another void fraction measurement technique under appropriate assumption. Several researchers have used it, since it is a non-intrusive technique that maintains flow regime.
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (S. Wongwises).
http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.04.004 0735-1933/© 2014 Elsevier Ltd. All rights reserved.
Maurus et al. [12,13] optically observed the void fraction in a subcooled flow of boiling water through a horizontal rectangular channel. A high-speed camera's top and side views of vapor shape helped estimate the void fraction. They found that void fraction decreased with an increase of mass flux. Ursenbacher et al. [14] and Wojtan et al. [15] also optically observed the cross-sectional void fraction of a twophase stratified flow. The experiments used two refrigerants (R-22 and R-410a) with a 13.6 mm circular horizontal transparent tube. Bowers and Hrnjak [16] optically observed the void fraction measurement of R-134a stratified flow through three different tube diameters, 7.2, 8.7, and 15.3 mm. They stated that void fraction depended on tube size diameter, while mass velocity had little effect on it. Pulli and Rajvanshi [17] developed an image analysis technique to measure the void fraction in subcooled, boiling, distilled water. They estimated the void fraction from the ratio of vapor pixels to pixels. Winkler et al. [18] used image analysis to measure the void fraction of R-134a's condensing process while flowing through a minichannel ranging from 2.00 to 4.91 mm. Their results show that neither mass flux nor channel size had a significant effect on the void fraction of a wavy flow pattern. 1.2. Models and correlations A model and correlations can also help calculate the void fraction. A homogeneous model is the simplest type for such predictions: it assumes that vapor and liquid velocities are equal. However, it completely neglects interfacial shears between vapor and liquid phases, compromising its accuracy. Thus, we used several separated
R. Srisomba et al. / International Communications in Heat and Mass Transfer 56 (2014) 8–14
Nomenclature A a, b Co Cp Di G Hv h I J L m Q S T u V Vvi X x
cross-sectional area, m2 the empirical constant parameters distribution parameter in drift-flux model specific heat capacity, kJ/kg °C inner tube size diameter, mm mass flux, kg/m2s height of refrigerant vapor, m enthalpy, kJ/kg electric current, A superficial velocity, m/s length, m mass flow rate, kg/s heat transfer rate, W slip ratio model temperature, °C actual velocity of, m/s AC voltage, V weight mean different velocity, m/s Lockhart–Matinelli parameter vapor quality
Greek letters α void fraction β chord angle, °
Subscripts ann annular flow regime int intermittent flow regime v vapor phase l liquid phase t total L latent heat ref refrigerant ph pre-heater in inlet out outlet s sensible heat tt turbulent flow of two-phase flow (turbulent liquidturbulent vapor) wav wavy flow regime
flow models and correlations, including slip ratio and drift flux. We will summarize past models and correlations based on refrigerant properties below. Rouhani and Axelsson [19] proposed a distribution parameter, C0, and weight mean different velocity, Vvj, for the drift flux model, which included mass flux, buoyancy, and gravity. Later, Steiner [20] modified these models for application in the horizontal flow direction. Yashar et al. [4] proposed a void fraction correlation based on their experimental data with refrigerant which included the effects of viscous distribution and gravitational distribution. El Hajal et al. [21] developed a new correlation for the void fraction to propose a new flow regime mapping of refrigerant flowing in a horizontal channel. Their correlation was created by using a logarithm mean void fraction different from the homogeneous model and the model of Rouhani and Axelsson [19]. Lastly, Winkler et al. [18] proposed void fraction correlations from the slip ratio and drift flux models to calculate the void fraction for the
9
refrigerant condensation process in a mini-channel. Their proposed correlations were based on different flow regimes. Table 1 summarizes all these proposed correlations. Although some techniques and models mentioned above are still in current use, they are mostly appropriate for only a few flow regimes, such as slug and stratified flows. This study aims to propose a technique that combines the quick-closing valve with optical observation techniques to measure the void fraction for different flow regimes, using R-134a and a circular horizontal tube, and considering the effects of mass flux and saturated temperature. Correlations for predicting the void fraction related to various flow regimes, which have never been seen before, are also proposed.
2. Experimental apparatus and procedure Fig. 1 schematically diagrams the experimental apparatus to measure the R-134a void fraction. Its main components are the test section, refrigerant loop, pre-heater system, cooling water loop, and data acquisition system. Since two techniques are combined in this study, the test section was designed to support both. The main components of the test section are a transparent, high-pressure glass circular tube, digital camera (Nikon D90 with AF-S NIKKOR 18–105 mm lens), and ball valve actuators, as shown in Fig. 2. The tube's inner diameter is 8 mm, and its length is 115 mm. The two ball valve actuators at either end of it trap the refrigerant. The experimental procedure started by pumping liquid R-134a with a micro gear pump to make it flow through a filter/dryer, a Rotameter, a pre-heater, a test section, a plate heat exchanger, and a receiver tank, back to the pump to complete the loop. The Rotameter measured the volume flow rate. A hot runner at the pre-heater heated the liquid refrigerant to control inlet vapor quality before the vapor entered the test section. A DC power supply determined the voltage and electric current values of the required heat flux for the pre-heater section. After leaving the test section, the refrigerant entered the plate heat exchanger in a cooling water loop to dissipate heat until it became subcooled liquid. This study's experiments varied three parameters; inlet vapor quality, saturated temperature, and refrigerant flow rates. While the refrigerant flow rate was adjusted, inlet vapor quality and saturated temperatures were kept constant. All three parameters were identically treated throughout the test. When the system reached a steady state, the two ball valves simultaneously closed to trap the refrigerant in the test section. At the same time, the bypass valve opened to force refrigerant to flow so the system could continue to work normally. The digital camera captured the side view of the test section (Fig. 2) to illustrate clear separation between vapor and liquid phases. We estimated the height of vapor from the interface to the top of the inner tube for void fraction calculation, with results presented below. Table 2 illustrates the ranges of experimental conditions. Refrigerant temperature was measured with T-type thermocouples (with an accuracy of ±0.1 °C). A data acquisition system recorded all data. Bourdon tube pressure gauges measured saturated pressures at the inlet and outlet of the test section. Rubber foam with a thermal conductivity of 0.04 W/m K insulated the test section, preventing heat loss. A Multimeter (Fluke 336 meter) measured voltage and electric current with an accuracy of ± 1.0% + 5 for DC voltage and ±1.5% + 5 for DC current. We estimated uncertainty of the void fraction as 1.2%.
3. Data reduction This section presents the calculation of the void fraction and inlet vapor quality. The physical properties of refrigerant used in this study are extracted from REFPROP, Version 6.01 (1998) [22].
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Table 1 Correlations proposed in literature. Model and correlation Authors
Model and correlation
Homogeneous model
αH ¼
1
1þð1−x x Þ
ρg ρl
;S ¼ 1
l
Rouhani and Axelsson [19]
Ranges of Dh, x, Tsat and G Measurement techniques
Notes
−
−
−
−
- All flow regimes
Dh = 7.3, 8.9 (mm) x = 5–80% G = 75–700 (kg/m2s) Tsat = 5, 35 (°C) x = 0–18% G = 665–1597 (kg/m2s) Tsat = 0–73.4 (°C)
Quick-closing vales method
- Evaporation and condensation - Effects of gravity, fluid properties and viscous dissipation are elucidated - Evaporation - Effects of surface tension, vapor quality, mass velocity, tube size and physical properties are analyzed
Dh = 8 (mm) x = 15–88% G = 65–750 (kg/m2s) Tsat = 28–52 (°C) Dh = 2–4.91 (mm) x = 1–96% G = 140–800 (kg/m2s) Tsat = 52.42 (°C)
–
- Condensation - Effect of mass flux and surface tension is discussed.
Image analysis technique
- Condensation - G and Dh have no significance in the wavy flow regime
S
−0:321 þ X tt Ft ¼ α ¼ 1 þ F −1 t 1−x0:9 ρv 0:5 μ l 0:1 X tt ¼ x ρ μ
Yashar et al. [4]
Flow regime
x3 G2 ρ2g gdð1−xÞ
0:5
v
h i V −1 þ Gvj C o x þ 1−x α¼ ρl ρv 0:25 pffiffiffi ðgσ ðρ −ρ ÞÞ V vj ¼ 1:18 l v ρ
- Stratified flow
x ρv
l
−
Steiner [17] version
Co = 1 + 0.12(1 − x) α ¼ αH−αRouhani
El HaJal et al. [21]
ln
Winkler et al. [18]
- All flow regimes
αH α Rouhani
- Intermittent, intermittent–wavy overlap region and wavy
Slip ratio: 0:349 −1 H α ¼ 1 þ 0:604 1−α αH Drift flux models: αH α ¼ 1:153þ0:071= j αH α ¼ 1:151−0:059= j
where Al and Av are the cross-sectional areas of the liquid and vapor phase, respectively, which can be obtained from Eqs. (2) and (3).
3.1. Void fraction We estimated the void fraction from a cross-sectional area ratio between the vapor phase cross-sectional area and the total crosssectional area, based on the optical technique. α¼
Av A v þ Al
2
Al ¼
D ðβ− sinβÞ 8
ð2Þ
ð1Þ
Av ¼ At −Al
ð3Þ
Digital camera
P
P
Pre-heater
P
Lighter source
Test section
Data acquisition system Thermocouple type-T
Air regulator Digital multimeters
Air compressor
Power supply
Plate heat exchanger T
Volumetric flow meter
Condensing unit
T DC power supply
Filter/dryer
Receiver
Micro gear pump
Water pump Subcooled water tank
Fig. 1. Schematic diagram of the experimental apparatus.
R. Srisomba et al. / International Communications in Heat and Mass Transfer 56 (2014) 8–14
11
8 mm
1 Ball valves 2 Actuators
Vapor 3 Tube fitting
Hv
4 Transparent tube
β
2
Liquid 3 1
A
SECTION A-A 4
Vapor
A
Liquid 102 mm L=115 mm
Fig. 2. Schematic diagram of the test section.
where At is the total cross-section area of the tube (πDi 2 =4) and β is a chord angle (in degrees) which can be obtained from: −1
β ¼ 2 cos
D−Hv 1− ðD=2Þ
ð4Þ
where IV@ ph is the electrical power from a heater to the refrigerant flowing through the pre-heater and QS is a sensible heat transfer rate in the pre-heater: Q S ¼ mref cp;ref T ref ;out −T ref ;in
ð8Þ
ph
where Hv is the height of the vapor phase within the transparent tube shown in Fig. 2 and Di is the inside of the tube diameter. 4. Results and discussion
3.2. Vapor quality
4.1. Experimental results x¼
hph;out −h f @T ph;out hfg@T ph;out
ð5Þ
The h f @T ph;out and hfg@T ph;out are the enthalpy of the saturated liquid and of vaporization which is based on the outlet temperature of the preheater, respectively. The hph,out is the enthalpy of refrigerant at the outlet of the pre-heater, which can be gained from: hph;out ¼ h f @ T
ph;out
þ
QL mref
Fig. 3 shows a variation of the measured void fraction plotted against vapor quality. The intermittent, flow regime generally consists of an elongated vapor bubble (plug flow) and slug flows observable at low vapor quality. The flow regime changed from intermittent to wavy when the vapor quality increased because of the increase in the elongated vapor bubble. The void fraction rapidly increased with the increase of vapor quality. Annular flow could be observed from the liquid annular film flowing around the inner tube while the vapor flew inside the core.
ð6Þ
1.0 0.9
where h f @T ph;out is the enthalpy of saturated liquid which is based on the outlet temperature of the pre-heater, mref is the mass flow rate of refrigerant and QL is the latent heat transfer rate in the pre-heater: ð7Þ
0.7 Wavy Flow
0.6 0.5 0.4 0.3
Table 2 Ranges of experimental conditions.
Intermittent Flo w
0.2
Experimental conditions Vapor quality Mass flux (kg/m2s) Saturation temperature (°C) Refrigerant Inner diameter (mm)
Void fraction, α
Q L ¼ IV @ph −Q S
Annular Flow
0.8
Annular flow regime Wavy flow regime Intermittent flow regime
0.1 0.01–0.82 644–1455 23–30 R 134a 8
0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Vapor quality, x Fig. 3. Void fraction vs. vapor quality.
0.8
0.9
1.0
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1.0
1.0
0.9 0.8
Predicted void fraction
Void fraction, α
0.6
Wavy Flow
0.5 0.4 0.3 Intermittent Flow
0.1 0.1
0.2
0.3
0.4
0.7 -20%
0.6 0.5 0.4 0.3
Homogeneous model Yashar et al. [4] Rouhani & Axelsson [19] El Hajal et al. [21] Winkler et al. [18]
Di = 8 mm
G = 644 kg/m2s G = 1051 kg/m2s
Tsat = 25 oC
G = 1455 kg/m2s
0.1
0.8
0.0 0.0
R-134a
0.2
0.5
0.6
0.7
0.9
0.2
1.0
0.1
0.2
Vapor quality, x
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Measured void fraction
Fig. 4. The void fraction data at different mass fluxes for a saturated temperature of 25 °C.
4.1.1. Effect of mass flux Fig. 4 presents the effect of mass flux on the void fraction, plotted against vapor quality at three different mass fluxes of 644, 1051 and 1455 kg/m2s at the saturated temperature of 25 °C. Results show that increase of mass flux had little effect on the void fraction. Graham et al. [23] also remarked that the mass flux had little effect on the void fraction of evaporative conditions, but affected the void fraction during condensation. 4.1.2. Effect of saturated temperature Fig. 5 presents a relationship between the measured void fraction and vapor qualities of 644 kg/m2s mass flux at different saturated temperatures between 23 and 30 °C. The void fraction decreased when the saturated temperature increased. This is because the void fraction directly depends on the refrigerant's specific volume ratio between vapor and liquid (vv/vl). When the saturated temperature of refrigerant increases, the specific volume of the vapor phase decreases, leading to the decease of the vapor volume fraction. 4.2. Comparisons of the experimental void fraction with existing correlations We compared the experimental void fraction of each flow regime with existing correlations available in Table 1. Fig. 6 shows a comparison of the void fraction for the intermittent flow regime. It can be seen that
Fig. 6. Comparison of the measured void fraction with the existing correlations for the intermittent flow regime.
the predicted void fraction of other existing correlations is mostly higher than +20%. Fig. 7 shows a comparison of the void fraction for the wavy flow regime. Those other correlations could be used to predict the void fraction at high vapor quality. The comparison of the void fraction for the annular flow regime is shown in Fig. 8. A good prediction of existing correlations is obvious when compared with experimental data. However, that prediction is clearly not satisfactory for all flow regimes. 4.3. Development of a new correlation for predicting the void fraction A new correlation is proposed to apply for different three flow regimes, based on R-134a properties, modified from the slip ratio model for intermittent, wavy and annular flow regimes. The form of the slip ratio proposed by Winkler et al. [18] is as follows: b
ð9Þ
S ¼ aX tt
where a and b are the empirical constant parameters obtained from a least-square linear regression. Fig. 9 shows a relativity of the slip ratio and Lockhart–Martinelli turbulent two-phase multiplier with different flow regimes. Hence, we propose empirical constant parameters as different flow regimes:
1.0
1.00
0.9
0.95
Annular Flow
0.8
Wavy flow regime
+20%
Predicted void fraction
0.90
0.7 0.6 Wavy Flow
0.5 0.4 Tsat = 23 oC
0.3 Intermittent Flow
0.2
Tsat = 25 oC
R-134a Di = 8 mm
0.1 0.0 0.0
+20%
0.8
0.7
0.0 0.0
Intermittent flow regime
0.9
Annular Flow
2
G = 644 kg/m s
0.85 0.80 0.75 -20%
0.70 0.65 0.60
Tsat = 27 oC
0.55
Tsat = 30 oC
0.50
Homogenous model Yashar et al. [4] Rouhani & Axelsson [19] El Hajal et al. [21] Winkler et al. [18]
0.45 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Vapor quality, x Fig. 5. The void fraction data at different saturated temperatures for a mass flux of 644 kg/m2s.
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
Measured void fraction Fig. 7. Comparison of the measured void fraction with the existing correlations for the wavy flow regime.
R. Srisomba et al. / International Communications in Heat and Mass Transfer 56 (2014) 8–14
13
1.0
1.00 Annular flow regime
0.98
+20%
0.9
+10%
+5%
Predicted void fraction
Predicted void fraction
0.8 0.96 0.94 0.92
-5%
0.90 Homogeneous model Yashar et al.[4] Rouhani & Axelsson [19] El Hajal et al. [21] Winkler et al. [18]
0.88 0.86 0.84 0.84
0.86
0.88
0.90
-10%
0.7
-20%
0.6 0.5 0.4 Annular flow Wavy flow Intermittent flow
0.3 0.2
Flow regimes Intermittent Proposed correlation Wavy 82.7 % of the data within 20% Annular
0.1 0.92
0.94
0.96
0.98
1.00
b -0.55 0.49 0.656
0.0 0.0
0.1
0.2
0.3
Measured void fraction
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Measured void fraction
Fig. 8. Comparison of the measured void fraction with the existing correlations for the annular flow regime.
Intermittent flow regime:
Fig. 10. Comparison between the measured void fraction and the predicted void fraction for the intermittent, wavy and annular flow regimes.
Intermittent flow regime:
−1 1−x 0:505 ρv 0:725 μ l −0:055 α int ¼ 1 þ 5:102 ρl μv x
a ¼ 5:102; b ¼ −0:55 Wavy flow regime:
ð11Þ
Wavy flow regime:
−1 1−x 1:44 ρv 1:25 μ l 0:044 α wav ¼ 1 þ 3:191 ρl μv x
a ¼ 3:191; b ¼ 0:49 Annular flow regime:
ð12Þ
Annular flow regime:
a ¼ 4:331; b ¼ 0:66 Xtt is the Lockhart–Martinelli parameter for turbulent flow in both phases, given by:
X tt ¼
a 5.102 3.191 4.331
1−x 0:9 ρv 0:5 μ l 0:1 ρl μv x
ð10Þ
Thus, the last version of the void fraction correlations [24] for intermittent, wavy and annular flow regimes can be taken in the following form in Eqs. (11)–(13), respectively. 10
S=aX ttb
−1 1−x 1:073 ρv 1:041 μ l 0:008 α ann ¼ 1 þ 4:331 ρl μv x
ð13Þ
N α exp;i −α cor;i 1X Mean relative error ¼ 100% α exp;i N i¼1
ð14Þ
Fig. 10 compares experimental and predicted void fractions using these newly presented correlations. The annular and wavy flow regimes are in good agreement: their mean absolute errors are only 0.93% and 5.25%, respectively. A higher error could be observed in the intermittent flow regime (~18.6%), but it is still lower than the data from other correlations (Table 3). It indicates that the presented correlations could be used for predicting the void fraction within the range of ±20%. 5. Conclusion
S
The quick-closing valves and optical observation techniques are combined to measure the void fraction of R-134 refrigerant flowing 1
Flow regimes Intermittent Wavy Annular
0.1 0.01
a 5.102 3.191 4.331
b -0.55 0.49 0.656
Table 3 Mean absolute errors.
Annular flow regime Wavy flow regime Intermittent flow regime Regression line (Ann) Regression line (Wav) Regression line (Int)
R2 0.81 0.22 0.23
0.1
1
Model and correlation
10
Xtt Fig. 9. Relationship between the slip ratio and Lockhart–Martinelli parameter for the intermittent, wavy and annular flow regimes.
Homogeneous Yashar et al. [4] Rouhani and Axelsson [19] El haJal et al. [21] Winkler et al. [18] Proposed correlations
Mean absolute error (%) Annular
Wavy
Intermittent
All flow regimes
1.05 2.37 3.49 1.68 12.49 0.93
13.71 8.34 9.45 10.92 11.47 5.25
59.90 43.68 45.10 52.34 48.71 18.60
29.17 20.70 19.81 23.77 33.00 14.79
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through a circular horizontal tube with an inner diameter of 8 mm. The amount of the void fraction is measured in various test conditions, with saturated temperatures of 23, 25, 27, and 30 °C and mass flux of 644, 1051, and 1455 kg/m2 s. Experimental results are as follows: − The mass flux has no significance on the variation of the void fraction, while the saturated temperature has a significant effect on the void fraction. − The new correlations for predicting the void fraction are developed by combining the effect of vapor quality, physical properties of R-134a, and different flow regimes.
Acknowledgments The authors would like to express their appreciation to the Thailand Research Fund (DPG5380003), NSTDA Chair Professor Grant (2013) and the National Research University Project (2013–2014) for providing financial support for this study. The second and third authors would like to thank Professor Somchai Wongwises for the supporting during their research in the Department of Mechanical Engineering, King Mongkut’s University of Technology Thonburi. References [1] L. Guangyao, R. Junsheng, H. Wenyou, X. Wenyuan, Z. Chengang, L. Yonghong, in: Soon Heung Chang (Ed.), Investigation on two-phase flow characteristics in nuclear power equipment, nuclear power plants, InTech, ISBN: 978-953-51-0408-7, 2012. [2] A. Colombo, A. Era, A. Hassid, A. Premoli, B. Spadoni, R. Zavattarelli, Density measurements with two-phase mixtures in adiabatic and heated channels at high pressure by means of a quick-closing valve method, 225, CISE (Centro Informazioni Studi Esperienze), 1967. 29. [3] K.H. Chien, T.T. Chen, B.S. Pei, W.K. Lin, Void fraction measurement by using the side-tube method, Flow Meas. Instrum. 8 (1997) 103–112. [4] D.A. Yashar, M.J. Wilson, H.R. Kopke, D.M. Graham, J.C. Chato, T.A. Newell, An investigation of refrigerant void fraction in horizontal, microfin tubes, HVAC R Res. 7 (2001) 67–82. [5] P.L. Spedding, G.S. Woods, R.S. Raghunathan, J.K. Watterson, Vertical two-phase flow part II: experimental semi-annular flow and hold-up, Inst. Chem. Eng. Trans. IChemE, Part A 76 (1998) [July]. [6] E. Bjork, A simple technique for refrigerant mass measurement, Appl. Therm. Eng. 25 (2005) 1115–1125.
[7] S. Wonwises, M. Pipathattakul, Flow pattern, pressure drop and void fraction of two-phase flow gas–liquid flow in an inclined narrow annular channel, Exp. Thermal Fluid Sci. 30 (2006) 345–354. [8] A. Teyssedou, A. Tapucu, M. Lortie, Impedance prove to measure local void fraction profiles, Rev. Sci. Instrum. 59 (1988) 631. [9] G. Costigan, P.B. Whalley, Slug flow regime identification from dynamic void fraction measurements in vertical air–water flows, Int. J. Multiphase Flow 23 (1996) 263–282 (No. 2). [10] K.J. Elkow, K.S. Rezkallah, Void fraction measurements in gas–liquid flows under l-g and μ-g conditions using capacitance sensors, Int. J. Multiphase Flow 23 (5) (1997) 815–829. [11] J. Ye, Y. Feng, L.J. Guo, Phase fraction measurement in multiphase flow using an improved electrical method, 7th International conference on multiphase flow ICMF 2010, Tampa, FL USA, May 30-June 4, 2010. [12] R. Maurus, V. Ilchenko, T. Sattelmayer, Study of the bubble characteristics and the local void fraction in subcooled flow boiling using digital imaging and analysing techniques, Exp. Thermal Fluid Sci. 26 (2002) 147–155. [13] R. Maurus, V. Ilchenko, T. Sattelmayer, Automated high-speed video analysis of the bubble dynamics in subcooled flow boiling, Int. J. Heat Fluid Flow 25 (2004) 149–158. [14] T. Ursenbacher, L. Wojtan, J.R. Thome, Interfacial measurements in stratified types of flow. Part I: new optical measurement technique and dry angle measurements, Int. J. Multiphase Flow 30 (2004) 107–124. [15] L. Wojtan, T. Ursenbacher, J.R. Thome, Interfacial measurements in stratified types of flow. Part II: Measurements for R-22 and R-410a, Int. J. Multiphase Flow 30 (2004) 125–137. [16] C.D. Bowers, S.P. Hrnjak, Determination of void fraction in separated two-phase flows using optical techniques, International Refrigeration and Air Conditioning Conference, 2010, Paper 1083, 2010, (http://docs.lib.purdue.edu/iracc/1083 ). [17] U. Puli, A.K. Rajvansh, An image analysis technique for determination of void fraction in subcooled flow boiling of water in horizontal annulus at high pressures, Int. J. Heat Fluid Flow 38 (2012) 180–189. [18] J. Winkler, J. Killion, S. Garimella, Void fractions for condensing refrigerant flow in small channels. Part II: void fraction measurement and modeling, Int. J. Refrig. 35 (2012) 246–262. [19] S.Z. Rouhani, E. Axelsson, Calculation of void volume fraction in subcooled and quality boiling regions, Int. J. Heat Mass Transfer 13 (1970) 383–393. [20] D. Steiner, Heat transfer to boiling saturated liquids, VDI-Warmeatlas (VDI Heat Atlas), Editor: Verein Deutscher Ingenieure, VDI-Gassellschaft Verfahrenstechnikund Chemie-ingenieurwesen (GCV), Translator: J.W. Fullarton, Dusseldorf, 1993. [21] J. El Hajal, J.R. Thome, A. Cavallini, Condensation in horizontal tubes part 1: twophase flow pattern map, Int. J. Heat Mass Transfer 46 (2003) 3349–3363. [22] REFPROP, INST, Refrigerant Properties Database 23, Gaithersburg, MD, 1998. (Version 6.01). [23] D.M. Graham, H.R. Kopke, M.J. Wilson, D.A. Yashar, J.C. Chato, T.A. Newell, An investigation of void fraction in the stratified/annular flow regions in smooth, horizontal tubes, ACRC-144, Air Conditioning and Refrigeration Center, University of Illinois, Urbana-Champaign, IL, 1999. [24] D. Butterworth, A comparison of some void-fraction relationships for co-current gas-liquid flow, Int. J. Multiphase Flow 1 (1975) 845–850.
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International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Measurement of the void fraction of R-134a flowing through a horizontal tube☆ R. Srisomba a, O. Mahian b, A.S. Dalkilic c, S. Wongwises a,⁎ a Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Lab. (FUTURE), Department of Mechanical Engineering, Faculty of Engineering, King Mongkut's University of Technology Thonburi, Bangmod, Bangkok 10140, Thailand b Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran c Heat and Thermodynamics Division, Department of Mechanical Engineering, Yildiz Technical University, Yildiz, Besiktas, Istanbul 34349, Turkey
a r t i c l e
i n f o
Available online 2 May 2014 Keywords: Two-phase flow Void fraction Optical observation technique Void fraction correlation Quick closing valve method
a b s t r a c t This experiment aims to measure the void fraction of R-134a refrigerant flowing through a horizontal tube, using a quick-closing valve and optical observation techniques. The tube is transparent, circular, 115 mm long with an inside 8 mm thick, and has two actuator ball valves installed at both ends. The experiment was conducted in conditions where vapor quality ranged from 1% to 82%, saturated temperature was from 23 to 30 °C, and mass flux was from 644 to 1455 kg/m2 s. The results of the experiment indicate that raising the saturated temperature decreased the void fraction, whereas increasing mass flux had no significant effect on it. Moreover, results also show three flow regimes: intermittent, wavy, and annular. Each flow regime led to different predicted void fractions. © 2014 Elsevier Ltd. All rights reserved.
1. Introduction Two-phase gas-liquid flow has various applications, including petroleum intake, air conditioning systems, refrigerators, and nuclear power reactors [1]. An investigation of flow mechanism that sets parameters for such flow is necessary to develop better heat equipment for these systems. 1.1. Void fraction measurements Void fraction is an important parameter for two-phase flow works, like preparation of flow regime map, calculation of gravitation, and acceleration terms for total pressure drop analysis. Generally, the void fraction can be defined by the ratio of vapor to volume. The simplest measurement technique of the void fraction is the quick-closing valve method, still used at present. This method traps liquid in a tube to measure its mass and liquid volume. Several researchers have used it individually [2–7] and in calibration with other techniques [8–11]. Optical observation is another void fraction measurement technique under appropriate assumption. Several researchers have used it, since it is a non-intrusive technique that maintains flow regime.
☆ Communicated by W.J. Minkowycz. ⁎ Corresponding author. E-mail address: [email protected] (S. Wongwises).
http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.04.004 0735-1933/© 2014 Elsevier Ltd. All rights reserved.
Maurus et al. [12,13] optically observed the void fraction in a subcooled flow of boiling water through a horizontal rectangular channel. A high-speed camera's top and side views of vapor shape helped estimate the void fraction. They found that void fraction decreased with an increase of mass flux. Ursenbacher et al. [14] and Wojtan et al. [15] also optically observed the cross-sectional void fraction of a twophase stratified flow. The experiments used two refrigerants (R-22 and R-410a) with a 13.6 mm circular horizontal transparent tube. Bowers and Hrnjak [16] optically observed the void fraction measurement of R-134a stratified flow through three different tube diameters, 7.2, 8.7, and 15.3 mm. They stated that void fraction depended on tube size diameter, while mass velocity had little effect on it. Pulli and Rajvanshi [17] developed an image analysis technique to measure the void fraction in subcooled, boiling, distilled water. They estimated the void fraction from the ratio of vapor pixels to pixels. Winkler et al. [18] used image analysis to measure the void fraction of R-134a's condensing process while flowing through a minichannel ranging from 2.00 to 4.91 mm. Their results show that neither mass flux nor channel size had a significant effect on the void fraction of a wavy flow pattern. 1.2. Models and correlations A model and correlations can also help calculate the void fraction. A homogeneous model is the simplest type for such predictions: it assumes that vapor and liquid velocities are equal. However, it completely neglects interfacial shears between vapor and liquid phases, compromising its accuracy. Thus, we used several separated
R. Srisomba et al. / International Communications in Heat and Mass Transfer 56 (2014) 8–14
Nomenclature A a, b Co Cp Di G Hv h I J L m Q S T u V Vvi X x
cross-sectional area, m2 the empirical constant parameters distribution parameter in drift-flux model specific heat capacity, kJ/kg °C inner tube size diameter, mm mass flux, kg/m2s height of refrigerant vapor, m enthalpy, kJ/kg electric current, A superficial velocity, m/s length, m mass flow rate, kg/s heat transfer rate, W slip ratio model temperature, °C actual velocity of, m/s AC voltage, V weight mean different velocity, m/s Lockhart–Matinelli parameter vapor quality
Greek letters α void fraction β chord angle, °
Subscripts ann annular flow regime int intermittent flow regime v vapor phase l liquid phase t total L latent heat ref refrigerant ph pre-heater in inlet out outlet s sensible heat tt turbulent flow of two-phase flow (turbulent liquidturbulent vapor) wav wavy flow regime
flow models and correlations, including slip ratio and drift flux. We will summarize past models and correlations based on refrigerant properties below. Rouhani and Axelsson [19] proposed a distribution parameter, C0, and weight mean different velocity, Vvj, for the drift flux model, which included mass flux, buoyancy, and gravity. Later, Steiner [20] modified these models for application in the horizontal flow direction. Yashar et al. [4] proposed a void fraction correlation based on their experimental data with refrigerant which included the effects of viscous distribution and gravitational distribution. El Hajal et al. [21] developed a new correlation for the void fraction to propose a new flow regime mapping of refrigerant flowing in a horizontal channel. Their correlation was created by using a logarithm mean void fraction different from the homogeneous model and the model of Rouhani and Axelsson [19]. Lastly, Winkler et al. [18] proposed void fraction correlations from the slip ratio and drift flux models to calculate the void fraction for the
9
refrigerant condensation process in a mini-channel. Their proposed correlations were based on different flow regimes. Table 1 summarizes all these proposed correlations. Although some techniques and models mentioned above are still in current use, they are mostly appropriate for only a few flow regimes, such as slug and stratified flows. This study aims to propose a technique that combines the quick-closing valve with optical observation techniques to measure the void fraction for different flow regimes, using R-134a and a circular horizontal tube, and considering the effects of mass flux and saturated temperature. Correlations for predicting the void fraction related to various flow regimes, which have never been seen before, are also proposed.
2. Experimental apparatus and procedure Fig. 1 schematically diagrams the experimental apparatus to measure the R-134a void fraction. Its main components are the test section, refrigerant loop, pre-heater system, cooling water loop, and data acquisition system. Since two techniques are combined in this study, the test section was designed to support both. The main components of the test section are a transparent, high-pressure glass circular tube, digital camera (Nikon D90 with AF-S NIKKOR 18–105 mm lens), and ball valve actuators, as shown in Fig. 2. The tube's inner diameter is 8 mm, and its length is 115 mm. The two ball valve actuators at either end of it trap the refrigerant. The experimental procedure started by pumping liquid R-134a with a micro gear pump to make it flow through a filter/dryer, a Rotameter, a pre-heater, a test section, a plate heat exchanger, and a receiver tank, back to the pump to complete the loop. The Rotameter measured the volume flow rate. A hot runner at the pre-heater heated the liquid refrigerant to control inlet vapor quality before the vapor entered the test section. A DC power supply determined the voltage and electric current values of the required heat flux for the pre-heater section. After leaving the test section, the refrigerant entered the plate heat exchanger in a cooling water loop to dissipate heat until it became subcooled liquid. This study's experiments varied three parameters; inlet vapor quality, saturated temperature, and refrigerant flow rates. While the refrigerant flow rate was adjusted, inlet vapor quality and saturated temperatures were kept constant. All three parameters were identically treated throughout the test. When the system reached a steady state, the two ball valves simultaneously closed to trap the refrigerant in the test section. At the same time, the bypass valve opened to force refrigerant to flow so the system could continue to work normally. The digital camera captured the side view of the test section (Fig. 2) to illustrate clear separation between vapor and liquid phases. We estimated the height of vapor from the interface to the top of the inner tube for void fraction calculation, with results presented below. Table 2 illustrates the ranges of experimental conditions. Refrigerant temperature was measured with T-type thermocouples (with an accuracy of ±0.1 °C). A data acquisition system recorded all data. Bourdon tube pressure gauges measured saturated pressures at the inlet and outlet of the test section. Rubber foam with a thermal conductivity of 0.04 W/m K insulated the test section, preventing heat loss. A Multimeter (Fluke 336 meter) measured voltage and electric current with an accuracy of ± 1.0% + 5 for DC voltage and ±1.5% + 5 for DC current. We estimated uncertainty of the void fraction as 1.2%.
3. Data reduction This section presents the calculation of the void fraction and inlet vapor quality. The physical properties of refrigerant used in this study are extracted from REFPROP, Version 6.01 (1998) [22].
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Table 1 Correlations proposed in literature. Model and correlation Authors
Model and correlation
Homogeneous model
αH ¼
1
1þð1−x x Þ
ρg ρl
;S ¼ 1
l
Rouhani and Axelsson [19]
Ranges of Dh, x, Tsat and G Measurement techniques
Notes
−
−
−
−
- All flow regimes
Dh = 7.3, 8.9 (mm) x = 5–80% G = 75–700 (kg/m2s) Tsat = 5, 35 (°C) x = 0–18% G = 665–1597 (kg/m2s) Tsat = 0–73.4 (°C)
Quick-closing vales method
- Evaporation and condensation - Effects of gravity, fluid properties and viscous dissipation are elucidated - Evaporation - Effects of surface tension, vapor quality, mass velocity, tube size and physical properties are analyzed
Dh = 8 (mm) x = 15–88% G = 65–750 (kg/m2s) Tsat = 28–52 (°C) Dh = 2–4.91 (mm) x = 1–96% G = 140–800 (kg/m2s) Tsat = 52.42 (°C)
–
- Condensation - Effect of mass flux and surface tension is discussed.
Image analysis technique
- Condensation - G and Dh have no significance in the wavy flow regime
S
−0:321 þ X tt Ft ¼ α ¼ 1 þ F −1 t 1−x0:9 ρv 0:5 μ l 0:1 X tt ¼ x ρ μ
Yashar et al. [4]
Flow regime
x3 G2 ρ2g gdð1−xÞ
0:5
v
h i V −1 þ Gvj C o x þ 1−x α¼ ρl ρv 0:25 pffiffiffi ðgσ ðρ −ρ ÞÞ V vj ¼ 1:18 l v ρ
- Stratified flow
x ρv
l
−
Steiner [17] version
Co = 1 + 0.12(1 − x) α ¼ αH−αRouhani
El HaJal et al. [21]
ln
Winkler et al. [18]
- All flow regimes
αH α Rouhani
- Intermittent, intermittent–wavy overlap region and wavy
Slip ratio: 0:349 −1 H α ¼ 1 þ 0:604 1−α αH Drift flux models: αH α ¼ 1:153þ0:071= j αH α ¼ 1:151−0:059= j
where Al and Av are the cross-sectional areas of the liquid and vapor phase, respectively, which can be obtained from Eqs. (2) and (3).
3.1. Void fraction We estimated the void fraction from a cross-sectional area ratio between the vapor phase cross-sectional area and the total crosssectional area, based on the optical technique. α¼
Av A v þ Al
2
Al ¼
D ðβ− sinβÞ 8
ð2Þ
ð1Þ
Av ¼ At −Al
ð3Þ
Digital camera
P
P
Pre-heater
P
Lighter source
Test section
Data acquisition system Thermocouple type-T
Air regulator Digital multimeters
Air compressor
Power supply
Plate heat exchanger T
Volumetric flow meter
Condensing unit
T DC power supply
Filter/dryer
Receiver
Micro gear pump
Water pump Subcooled water tank
Fig. 1. Schematic diagram of the experimental apparatus.
R. Srisomba et al. / International Communications in Heat and Mass Transfer 56 (2014) 8–14
11
8 mm
1 Ball valves 2 Actuators
Vapor 3 Tube fitting
Hv
4 Transparent tube
β
2
Liquid 3 1
A
SECTION A-A 4
Vapor
A
Liquid 102 mm L=115 mm
Fig. 2. Schematic diagram of the test section.
where At is the total cross-section area of the tube (πDi 2 =4) and β is a chord angle (in degrees) which can be obtained from: −1
β ¼ 2 cos
D−Hv 1− ðD=2Þ
ð4Þ
where IV@ ph is the electrical power from a heater to the refrigerant flowing through the pre-heater and QS is a sensible heat transfer rate in the pre-heater: Q S ¼ mref cp;ref T ref ;out −T ref ;in
ð8Þ
ph
where Hv is the height of the vapor phase within the transparent tube shown in Fig. 2 and Di is the inside of the tube diameter. 4. Results and discussion
3.2. Vapor quality
4.1. Experimental results x¼
hph;out −h f @T ph;out hfg@T ph;out
ð5Þ
The h f @T ph;out and hfg@T ph;out are the enthalpy of the saturated liquid and of vaporization which is based on the outlet temperature of the preheater, respectively. The hph,out is the enthalpy of refrigerant at the outlet of the pre-heater, which can be gained from: hph;out ¼ h f @ T
ph;out
þ
QL mref
Fig. 3 shows a variation of the measured void fraction plotted against vapor quality. The intermittent, flow regime generally consists of an elongated vapor bubble (plug flow) and slug flows observable at low vapor quality. The flow regime changed from intermittent to wavy when the vapor quality increased because of the increase in the elongated vapor bubble. The void fraction rapidly increased with the increase of vapor quality. Annular flow could be observed from the liquid annular film flowing around the inner tube while the vapor flew inside the core.
ð6Þ
1.0 0.9
where h f @T ph;out is the enthalpy of saturated liquid which is based on the outlet temperature of the pre-heater, mref is the mass flow rate of refrigerant and QL is the latent heat transfer rate in the pre-heater: ð7Þ
0.7 Wavy Flow
0.6 0.5 0.4 0.3
Table 2 Ranges of experimental conditions.
Intermittent Flo w
0.2
Experimental conditions Vapor quality Mass flux (kg/m2s) Saturation temperature (°C) Refrigerant Inner diameter (mm)
Void fraction, α
Q L ¼ IV @ph −Q S
Annular Flow
0.8
Annular flow regime Wavy flow regime Intermittent flow regime
0.1 0.01–0.82 644–1455 23–30 R 134a 8
0.0 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Vapor quality, x Fig. 3. Void fraction vs. vapor quality.
0.8
0.9
1.0
12
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1.0
1.0
0.9 0.8
Predicted void fraction
Void fraction, α
0.6
Wavy Flow
0.5 0.4 0.3 Intermittent Flow
0.1 0.1
0.2
0.3
0.4
0.7 -20%
0.6 0.5 0.4 0.3
Homogeneous model Yashar et al. [4] Rouhani & Axelsson [19] El Hajal et al. [21] Winkler et al. [18]
Di = 8 mm
G = 644 kg/m2s G = 1051 kg/m2s
Tsat = 25 oC
G = 1455 kg/m2s
0.1
0.8
0.0 0.0
R-134a
0.2
0.5
0.6
0.7
0.9
0.2
1.0
0.1
0.2
Vapor quality, x
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Measured void fraction
Fig. 4. The void fraction data at different mass fluxes for a saturated temperature of 25 °C.
4.1.1. Effect of mass flux Fig. 4 presents the effect of mass flux on the void fraction, plotted against vapor quality at three different mass fluxes of 644, 1051 and 1455 kg/m2s at the saturated temperature of 25 °C. Results show that increase of mass flux had little effect on the void fraction. Graham et al. [23] also remarked that the mass flux had little effect on the void fraction of evaporative conditions, but affected the void fraction during condensation. 4.1.2. Effect of saturated temperature Fig. 5 presents a relationship between the measured void fraction and vapor qualities of 644 kg/m2s mass flux at different saturated temperatures between 23 and 30 °C. The void fraction decreased when the saturated temperature increased. This is because the void fraction directly depends on the refrigerant's specific volume ratio between vapor and liquid (vv/vl). When the saturated temperature of refrigerant increases, the specific volume of the vapor phase decreases, leading to the decease of the vapor volume fraction. 4.2. Comparisons of the experimental void fraction with existing correlations We compared the experimental void fraction of each flow regime with existing correlations available in Table 1. Fig. 6 shows a comparison of the void fraction for the intermittent flow regime. It can be seen that
Fig. 6. Comparison of the measured void fraction with the existing correlations for the intermittent flow regime.
the predicted void fraction of other existing correlations is mostly higher than +20%. Fig. 7 shows a comparison of the void fraction for the wavy flow regime. Those other correlations could be used to predict the void fraction at high vapor quality. The comparison of the void fraction for the annular flow regime is shown in Fig. 8. A good prediction of existing correlations is obvious when compared with experimental data. However, that prediction is clearly not satisfactory for all flow regimes. 4.3. Development of a new correlation for predicting the void fraction A new correlation is proposed to apply for different three flow regimes, based on R-134a properties, modified from the slip ratio model for intermittent, wavy and annular flow regimes. The form of the slip ratio proposed by Winkler et al. [18] is as follows: b
ð9Þ
S ¼ aX tt
where a and b are the empirical constant parameters obtained from a least-square linear regression. Fig. 9 shows a relativity of the slip ratio and Lockhart–Martinelli turbulent two-phase multiplier with different flow regimes. Hence, we propose empirical constant parameters as different flow regimes:
1.0
1.00
0.9
0.95
Annular Flow
0.8
Wavy flow regime
+20%
Predicted void fraction
0.90
0.7 0.6 Wavy Flow
0.5 0.4 Tsat = 23 oC
0.3 Intermittent Flow
0.2
Tsat = 25 oC
R-134a Di = 8 mm
0.1 0.0 0.0
+20%
0.8
0.7
0.0 0.0
Intermittent flow regime
0.9
Annular Flow
2
G = 644 kg/m s
0.85 0.80 0.75 -20%
0.70 0.65 0.60
Tsat = 27 oC
0.55
Tsat = 30 oC
0.50
Homogenous model Yashar et al. [4] Rouhani & Axelsson [19] El Hajal et al. [21] Winkler et al. [18]
0.45 0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Vapor quality, x Fig. 5. The void fraction data at different saturated temperatures for a mass flux of 644 kg/m2s.
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
0.95
1.00
Measured void fraction Fig. 7. Comparison of the measured void fraction with the existing correlations for the wavy flow regime.
R. Srisomba et al. / International Communications in Heat and Mass Transfer 56 (2014) 8–14
13
1.0
1.00 Annular flow regime
0.98
+20%
0.9
+10%
+5%
Predicted void fraction
Predicted void fraction
0.8 0.96 0.94 0.92
-5%
0.90 Homogeneous model Yashar et al.[4] Rouhani & Axelsson [19] El Hajal et al. [21] Winkler et al. [18]
0.88 0.86 0.84 0.84
0.86
0.88
0.90
-10%
0.7
-20%
0.6 0.5 0.4 Annular flow Wavy flow Intermittent flow
0.3 0.2
Flow regimes Intermittent Proposed correlation Wavy 82.7 % of the data within 20% Annular
0.1 0.92
0.94
0.96
0.98
1.00
b -0.55 0.49 0.656
0.0 0.0
0.1
0.2
0.3
Measured void fraction
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Measured void fraction
Fig. 8. Comparison of the measured void fraction with the existing correlations for the annular flow regime.
Intermittent flow regime:
Fig. 10. Comparison between the measured void fraction and the predicted void fraction for the intermittent, wavy and annular flow regimes.
Intermittent flow regime:
−1 1−x 0:505 ρv 0:725 μ l −0:055 α int ¼ 1 þ 5:102 ρl μv x
a ¼ 5:102; b ¼ −0:55 Wavy flow regime:
ð11Þ
Wavy flow regime:
−1 1−x 1:44 ρv 1:25 μ l 0:044 α wav ¼ 1 þ 3:191 ρl μv x
a ¼ 3:191; b ¼ 0:49 Annular flow regime:
ð12Þ
Annular flow regime:
a ¼ 4:331; b ¼ 0:66 Xtt is the Lockhart–Martinelli parameter for turbulent flow in both phases, given by:
X tt ¼
a 5.102 3.191 4.331
1−x 0:9 ρv 0:5 μ l 0:1 ρl μv x
ð10Þ
Thus, the last version of the void fraction correlations [24] for intermittent, wavy and annular flow regimes can be taken in the following form in Eqs. (11)–(13), respectively. 10
S=aX ttb
−1 1−x 1:073 ρv 1:041 μ l 0:008 α ann ¼ 1 þ 4:331 ρl μv x
ð13Þ
N α exp;i −α cor;i 1X Mean relative error ¼ 100% α exp;i N i¼1
ð14Þ
Fig. 10 compares experimental and predicted void fractions using these newly presented correlations. The annular and wavy flow regimes are in good agreement: their mean absolute errors are only 0.93% and 5.25%, respectively. A higher error could be observed in the intermittent flow regime (~18.6%), but it is still lower than the data from other correlations (Table 3). It indicates that the presented correlations could be used for predicting the void fraction within the range of ±20%. 5. Conclusion
S
The quick-closing valves and optical observation techniques are combined to measure the void fraction of R-134 refrigerant flowing 1
Flow regimes Intermittent Wavy Annular
0.1 0.01
a 5.102 3.191 4.331
b -0.55 0.49 0.656
Table 3 Mean absolute errors.
Annular flow regime Wavy flow regime Intermittent flow regime Regression line (Ann) Regression line (Wav) Regression line (Int)
R2 0.81 0.22 0.23
0.1
1
Model and correlation
10
Xtt Fig. 9. Relationship between the slip ratio and Lockhart–Martinelli parameter for the intermittent, wavy and annular flow regimes.
Homogeneous Yashar et al. [4] Rouhani and Axelsson [19] El haJal et al. [21] Winkler et al. [18] Proposed correlations
Mean absolute error (%) Annular
Wavy
Intermittent
All flow regimes
1.05 2.37 3.49 1.68 12.49 0.93
13.71 8.34 9.45 10.92 11.47 5.25
59.90 43.68 45.10 52.34 48.71 18.60
29.17 20.70 19.81 23.77 33.00 14.79
14
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through a circular horizontal tube with an inner diameter of 8 mm. The amount of the void fraction is measured in various test conditions, with saturated temperatures of 23, 25, 27, and 30 °C and mass flux of 644, 1051, and 1455 kg/m2 s. Experimental results are as follows: − The mass flux has no significance on the variation of the void fraction, while the saturated temperature has a significant effect on the void fraction. − The new correlations for predicting the void fraction are developed by combining the effect of vapor quality, physical properties of R-134a, and different flow regimes.
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