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Metastable flow in capillary tubes: An experimental evaluation
Experimental Thermal and Fluid Science 31 (2007) 957–966 www.elsevier.com/locate/etfs
Metastable flow in capillary tubes: An experimental evaluation Alex Alberto Silva Huerta a,b, Fla´vio Augusto Sanzovo Fiorelli Ota´vio de Mattos Silvares a,c
c,* ,
a Maua´ Institute of Technology, Prac¸a Maua´ no. 1, 09580-900 – Sa˜o Caetano do Sul (SP), Brazil IMENSU – Mairipora˜ Institute of Technology, Rodovia Ferna˜o Dias Km 67, 076000-000 – Mairipora˜ (SP), Brazil University of Sa˜o Paulo, Mechanical Engineering Department, Av. Prof. Mello Moraes, 2231 – Cidade Universita´ria, 05508-900 – Sa˜o Paulo (SP), Brazil
b c
Received 8 June 2006; received in revised form 2 October 2006; accepted 5 October 2006
Abstract This work presents the results of an experimental study with pure refrigerants R-134a and R-600a and refrigerant–oil mixtures flowing through capillary tubes in order to analyse the metastable flow. A large number of experiments were carried out to verify the influence of several variables on the underpressure of vaporization, mainly the inlet subcooling, internal diameter and inlet pressure. Capillary tubes with internal diameter of 0.69 mm and 0.82 mm were tested for condensation temperatures between 40 C and 50 C and subcooling degrees between 3 C and 12 C. Measurements for oil concentrations of 1% and 3% were conducted and compared with those for pure refrigerant R-134a. The oil influence on the metastable flow was tested and the effect on the underpressure of vaporization is addressed for lower oil concentrations. 2006 Elsevier Inc. All rights reserved. Keywords: Refrigeration; Metastable flow; Capillary tubes; Experimental analysis
1. Introduction In refrigeration systems, capillary tubes are used as expansion devices and their correct sizing and analysis require knowledge on the metastable flow that occurs during transition from liquid to the vapour state. This phase change is called ‘‘flashing flow’’, since the process occurs solely as result of a reduction in the system pressure. Before vaporization starts, as saturation conditions are achieved, there is a region where liquid becomes superheated, generating the metastable flow. Once proper conditions are obtained, further pressure reductions will start the nucleation process. There is neither a reliable explanation for the metastable flow occurrence nor exact criteria proposed for determining the flashing point inception. The scattered data encoun*
Corresponding author. Tel.: +55 11 3091 9661; fax: +55 11 3091 9681. E-mail addresses: [email protected] (A.A. Silva Huerta), fi[email protected] (F.A. Sanzovo Fiorelli), [email protected] (O. de Mattos Silvares). 0894-1777/$ - see front matter 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2006.10.002
tered in experimental studies carried out by Huerta and Silvares [1] in glass capillary tubes show that the flashing point is very sensible and change continuously. However, the dominating process is certainly the wall heterogeneous nucleation, due to the lower superheating required. Several theoretical and empirical models were proposed in order to predict the performance of capillary tubes, but results were not accurate, due to the inability to predict the exact point where flashing process starts. The underpressure of vaporization (Dpvap) originated as consequence of superheated liquid flow is responsible for increasing the total liquid length and mass flow rate. The superheating degree required for initiating the flashing process depends on some parameters such as: inlet pres_ subcooling degree (DTsub), sure (pin), mass flow rate (mÞ, capillary tube internal diameter (Dct) and length (Lct), roughness and surfaces local irregularities, which may act as nucleation sites. Another aspect of practical interest is the presence of the lubricant oil. The refrigerant–oil mixture has different
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Nomenclature d L m m_ p T C ct evap l
diameter, mm length, m mass, kg mass flow rate, kg/h pressure, kPa temperature, C concentration, % capillary tube evaporating, evaporation liquid
thermophysical properties, which modifies the flashing point position when compared with the results encountered for pure refrigerant. This work presents the results of an experimental investigation on pure and refrigerant–oil mixtures flow, in order to analyse metastable flow in capillary tubes. The influence of oil concentration, subcooling degree, inlet pressure, diameter, and other parameters on the underpressure of vaporization and capillary tube performance are addressed. 2. Literature review Cooper et al. [2] and Mikol and Dudley [3] conducted the first studies about metastable flow in capillary tubes. Mikol and Dudley verified, by means of photographic observations in a glass capillary tube, that vaporization always occurred at one specific point at tube wall, and that point of inception of vaporization moves by discrete jumps rather than in a continuous manner as operating variables are changed. Koizumi and Yokoyama [4] measured pressure and temperature distributions for refrigerant R-22 flow in adiabatic capillary tubes, verifying the occurrence of the delay of vaporization. The authors proposed a simple calculation method to find the length of the liquid region. Such method was developed for adiabatic flow, based on integration of the momentum equation and assuming two-phase homogeneous flow. The experimental results showed a delay of vaporization ranging from 2 C to 4 C and a maximum superheated liquid length of 0.60 m, and calculations agree with experimental data within ±3%. Kuijpers and Janssen [5] studied the effects of non-equilibrium metastable flow of R-12 in capillary tubes and verified that delay of vaporization has a clearly systematic influence on mass flow rate. Deviations of measured mass flow rates to calculated ones, considering equilibrium conditions, where up to 12%, with an average value of 8%. Using the observed delay as an input value for calculations and a relationship between the superheating temperature and the volume fraction, the average deviation was reduced to 0.3%. Authors also presented some experimental results for the dependence of superheating degree on capillary tube inlet
ms o r sub
metastable oil refrigerant subcooling
Subscripts sup superheating cond condensing, condensation vap vaporization
pressure and subcooling degree, and tried to derive a relationship for such dependence, but comparison of experimental results to calculations was not satisfactory. Maczek et al. [6] studied the delay of vaporization and proposed a mathematical model based on theory of creation and expansion of a nucleate bubble inside a superheated fluid, as well as mass, momentum and energy balances. According to the authors, comparison with experimental data for delay of vaporization was not fully satisfactory, but the proposed model was a better approximation of experimental capillary tube lengths than the homogeneous model, and further investigations would be necessary. Kuhel and Goldschmidt [7,8], working with R-22, also verified the occurrence of metastable flow in capillary tubes. In order to take this effect into account in a capillary tube simulation model, the authors calculated an average value for the underpressure of vaporization and added such value to the inlet pressure in simulation model input. This procedure reduced the difference between experimental and simulation results. Paiva et al. [9], Fiorelli et al. [10] and Fiorelli and Silvares [11] used the same approach for R-12, R-134a and zeotropic/near-azeotropic refrigerant mixtures. Li et al. [12] investigated the effects of the diameter, backpressure, subcooling degree and mass flow rate on metastability for R-12. It was found a decrease of the length of the metastable flow region as the capillary tube diameter increased. The mass flow rate increased as consequence of a larger Dpvap, and an increase in DTsub caused a decrease in Dpvap. It was also verified that the position of the flashing inception is not affected by backpressure variations. Chen et al. [13] developed a correlation for the delay of vaporization for R-12 flow through capillary tubes based on the nucleation theory initially developed by Alamgir and Lienhard [14] and with experimental data of Li et al. [12]. Although such correlation predicts underpressure of vaporization within a relative error of 26%, it was successfully used by several authors as part of capillary tube simulation models for the same range of operational and geometric parameters. For instance, Dirik et al. [15] verified that Chen’s correlation was suitable for R-134a flow
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through capillary tubes, and Bittle and Pate [16] used such correlation for R-22, R-134a, R152a and R-410A. Chang and Ro [17], as part of a study on two-phase flow pressure drop in capillary tubes, analysed the temperature and pressure profiles along capillary tubes and proposed a empirical correlation for the underpressure of vaporization as function of subcooling degree and mass flow rate for R-134a, R-32, R-125 and some mixtures of R-32/ R-134a and R-32/R-125. Fiorelli et al. [10] tried to use such correlations in their study for R-410A and R-407C, but results were not satisfactory. Meyer and Dunn [18] showed that metastability might be more predictable than reported in the literature. The authors developed an experimental study on metastable flow of HCFC 22 in adiabatic capillary tubes, in which subcooling degree was continuously reduced and increased. A hysteresis effect in the mass flow rate was found, and the sudden flow variations only occurred in the sense of reducing flow rate. Chen and Li [19] investigated the underpressure of vaporization for adiabatic capillary tubes (configuration in which suction line and capillary tube are mounted as a counter-flow heat exchanger), showing that Dpvap decreases as the heat transfer between the capillary tube and the suction line increases. Bittle et al. [20] experimentally analysed the behavior of the metastable liquid region. The authors showed that the variation in the flashing point location could be controlled, and in this way it is possible to improve the accuracy of theoretical flow models used to simulate capillary tube performance. 3. Experimental apparatus and operation Fig. 1 shows a schematic diagram of the experimental apparatus built to this study. Such apparatus uses a blow-down batch process in order to provide a more accu-
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rate and independent control of the process parameters that could be achieved in a conventional refrigeration unit. Refrigerant is initially stored upstream the test section in a high-pressure reservoir (50-l neoprene bladder accumulator). This high pressure is provided by nitrogen filling of accumulator, controlled by a pressure regulator. The test section exit is connected to a low-pressure reservoir (a condenser–receiver). Low pressure is obtained by refrigerant condensation provided by a chilled ethylene-glycol/water mixture flowing through a coil inside the reservoir. During each run, refrigerant flows to from the high-pressure to the low-pressure reservoir through the test section where the capillary tube is placed. At the end of a run, refrigerant is returned to bladder accumulator by pressure difference. A 3 kW electric resistance heats the refrigerant stored in the condenser–receiver in order to raise its pressure, while pressure is lowered in the bladder by releasing nitrogen to atmosphere. A PID-controlled electric heating tape wrapped around the tube provides subcooling degree control. Refrigerant flow rate is measured in the liquid line by a Coriolis-type flowmeter (±0.1 kg/h uncertainty). Ten pressure transducers (±0.5 kPa uncertainty) measure pressure profile along the test section. Small pressure taps (0.5 mm diameter) was mounted along capillary tube. 20T-type thermocouples (±0.2 C uncertainty) measure capillary tube temperature profile. Thermocouples were soldered to capillary tube wall. Tables 1 and 2 show the pressure transducer and thermocouples positioning along the test section for refrigerant R-134a. A Pt-100 thermometer (±0.1 C uncertainty) measures capillary tube inlet temperature. Two sight glasses are installed, one at capillary tube inlet, and the other one at its outlet. A computer-based acquisition system is used to record data for later analysis. The refrigerant pressure at the test section exit was controlled by adjusting the mass flow rate of chilled water–
Fig. 1. Capillary tube test facility.
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Table 1 Pressure transducers position along the capillary tube Pressure transducer
Position from tube inlet (m)
#1 #2 #3 #4 #5 #6 #7 #8 #9 #10
0.06 0.31 0.51 0.81 1.01 1.21 1.41 1.61 1.81 1.93
Table 2 Thermocouples position along the capillary tube Thermocouple
Position from tube inlet (m)
#1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 #17 #18 #19 #20
0.10 0.20 0.40 0.50 0.65 0.75 0.87 0.96 1.06 1.16 1.26 1.35 1.46 1.56 1.67 1.77 1.87 1.90 1.98 2.00
refrigerant is vaporized and released by heating the sampling vessel When the vaporization is complete a third weight measurement is performed (m3). Thus, oil concentration can be evaluated by Eq. (1): C o ¼ 100
m3 m1 m_ o ¼ 100 m2 m1 m_ o þ m_ r
ð1Þ
3.2. Test conditions and procedure Tests were conducted for a copper capillary tube with the following geometries: • R-134a: Dct = 0.66 mm and 0.82 mm; Lct = 2.02 m; • R-600a (propane): Dct = 0.83 mm; Lct = 2.30 m. The operational conditions adopted for this study were: • condensing temperature: 40–50 C (R-134a) and 30– 40 C (R-600a); • evaporating temperature: below 20 C to assure critical (choked) flow conditions at capillary tube outlet; • subcooling degree: 3–12 C; • oil concentration: 1.0–5.0%. At each run the pressure corresponding to a given condensing temperature is set and data for different subcooling degrees were obtained. For test with refrigerant–oil mixtures a given oil concentration is also set. More details on the experimental procedure can be found in Huerta [21]. The operation time of the experimental apparatus is based on the refrigerant content stored in the accumulator, which is measured by a dynamometer installed at top and
glycol solution entering the condenser–receiver. Refrigerant–oil mixture leaving the test section is distilled by vaporization of the refrigerant at the temperature of 110 C in a reservoir heated by a 2.5 kW electric resistance. Thus, only pure refrigerant leaves this reservoir to the condenser– receiver. 3.1. Oil injection and concentration measurement Like pure refrigerant, the oil injection into system was also performed by a bladder accumulator. The test procedure begins with a pure refrigerant flow. Once such flow is stablished and refrigerant mass flow rate measured, oil mass flow rate is set as function of refrigerant flow rate by regulating a needle valve in oil feeding line in order to achieve the desired oil concentration. Actual concentration is measured by mixture sample weighting, based on ASHRAE standard 41–4. The first step is to measure the weight of an evacuated sampling vessel (m1). After sampling, a second measurement is made to get the total weight of vessel and sample (m2). Then the
Fig. 2. Experimental values obtained for inlet pressure along 30 min during test.
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Table 3 Experimental measurements for pure R-134a (Lct = 2.03 m; dct = 0.82 mm; Tevap = 25 C)
Fig. 3. Experimental values for mass flow rate and subcooling degree as function of test time.
holding up the accumulator. Typical duration of a test is near two hours, which allows obtaining three different operational conditions. Figs. 2 and 3 show an example of the experimental values for inlet pressure, subcooling temperature and mass flow rate as function of time for one of such operational conditions.
Tcond
DTsub
m_
Dpvap
DTit
40
4 5 6 7 8 9 10 11 12 13
6.56 6.69 6.82 7.11 7.32 7.58 7.72 7.79 7.87 8.03
95 78 70 55 60 42 32 25 23 21
4.0 3.5 2.8 2.3 2.0 1.8 1.7 1.5 1.4 1.1
0.60 0.50 0.42 0.38 0.25 0.20 0.18 0.15 0.12 0.10
44
4 5 6 7 8 9 10 11 12 13
7.41 7.54 7.87 7.92 7.97 8.02 8.08 8.16 8.24 8.34
90 80 70 75 60 42 35 25 27 18
4.5 3.3 4.0 3.5 3.0 2.0 1.8 1.0 1.2 0.5
0.50 0.42 0.47 0.45 0.30 0.20 0.15 0.10 0.12 0.07
50
4 5 6 7 8 9 10 11 12 13
7.29 7.51 7.84 8.21 8.38 8.66 8.73 8.89 8.99 9.09
80 60 50 42 40 60 50 50 50 40
4.0 3.7 3.2 3.0 2.8 2.5 2.0 1.8 1.5 1.2
0.52 0.44 0.35 0.30 0.26 0.25 0.18 0.16 0.12 0.10
sup,l
Lms
3.3. Visual observation of flow A pyrex glass capillary tube with Dct 1.0 mm and Lct = 2.2 m was used for observing the flashing point inception in refrigerant flow and examining the continuous developing of the two-phase flow process. The experiments were carried out using refrigerant R600a (isobutane) in several conditions. A copper wire was introduced into the capillary tube for helping in the nucleation sites formation, since glass has a smaller roughness than copper. It was observed that the subcooling degree and the mass flow rate are the most important parameters that affects flashing inception location. A significant dispersion on such location was also observed. 4. Results and discussions Table 3 presents the experimental results for pure refrigerant R-134a for several test conditions. It is shown mass flow rates, underpressure of vaporization and liquid superheating degree for condensation temperatures ranging from 40 C to 50 C and subcooling degrees from 4 C to 13 C. The maximum value for Dpvap found in this work was 95 kPa, with an uncertainty of ±6.0 kPa, and uncertainty for DTsup,l is ±0.3 C. Table 3 shows that Dpvap
Fig. 4. Pressure profile along capillary tube for Dct = 0.82 mm, Tcond = 40 C and DTsub = 12 C.
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Fig. 5. Pressure profile along capillary tube for Dct = 0.66 mm, Tcond = 48 C and DTsub = 12 C.
decreases as DTsub increases, and that Tcond has a small influence on underpressure of vaporization. Figs. 4 and 5 show the measured pressure profiles and calculated saturation pressure profiles along a capillary tube of Dct = 0.82 mm for Tcond = 40 C and Dct = 0.66 mm for Tcond = 48 C, both with DTsub = 12 C. Saturation pressures were calculated from measured temperatures along the capillary tube using a equation of state for the refrigerant. In such figures it can be verified the
Fig. 6. Temperature profile along capillary tube (Dct = 0.82 mm, Tcond = 40 C, DTsub = 4 C).
Fig. 7. Temperature profile along capillary tube (Dct = 0.82 mm, Tcond = 40 C, DTsub = 12 C).
occurrence and the magnitude of the underpressure of vaporization. Phase change, expected to occur when the measured and saturation pressure are coincident, starts only when the necessary liquid superheating to initiate the flashing process is attained. Figs. 6 and 7 show similar results in terms of temperature profiles for Tcond = 40 C, with DTsub of 4 C and 12 C, respectively. It can be seen from these figures that the metastable region length for DTsub = 4 C is higher than for DTsub = 12 C.
Fig. 8. DTsup,l as function of mass flow rate.
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4.1. Effect of mass flow rate on Dpvap and DTsup,l Fig. 8 shows the liquid superheating degree (DTsup,l) as function of mass flow rate for Tcond = 40 C and 50 C, respectively. It is observed DTsup,l decreases as mass flow rate increases. The minimum value found for DTsup,l was approximately 1 C for higher mass flow rates. A similar effect can be verified for the underpressure of vaporization Dpvap on Fig. 9. It can be noticed, as expected, that there is a direct relation between these two parameters, as it can be seen in Fig. 10. Since DTsup,l represents the penetration of liquid in metastable state, it is expected that the underpressure of vaporization Dpvap has the same behavior. In fact these two parameters are different ways of expressing the same effect, the metastable flow ‘‘intensity’’. 4.2. Effect of DTsub The effect of DTsub on DTsup,l for different capillary tube inlet and condensing temperatures can be verified in Fig. 11. Such figure shows that the liquid superheating degree increases as inlet temperature increases. Fig. 12 shows DTsup,l behavior for DTsub ranging between 4 C and 13 C for several condensation temperatures. As DTsub increases (and Tin decreases), DTsup,l decreases. At last Fig. 13 shows a similar behavior of the metastable region length Lms for the same DTsub range (4–13 C).
Fig. 10. DTsup,l as function of Dpvap.
4.3. Effect of lubricant oil on metastable flow In this work, it were carried out tests whit inlet oil concentrations ranging 1% and 3%, which are typical values expected in refrigeration systems (depending on
Fig. 11. DTsup,l as function of Ti,ct and DTsub.
Fig. 9. Dpvap as function of mass flow rate.
the compressor type). These values refer to oil concentrations at capillary tube inlet. As the refrigerant begins to vaporize the oil local concentration rises since the refrigerant is more volatile than oil. As stated before, the underpressure of vaporization depends on the subcooling degree, condensing temperature, and mass flow rate. The phenomenon becomes more complex when the oil effects are to be considered. It is expected that the oil presence should affect the flashing process and the liquid superheating degree required for the process to take place.
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Fig. 12. DTsup,l as function of DTsub and Tcond.
Fig. 14. Pressure profile along capillary tube.
the mass flow rate as the oil concentration increases. Fig. 14 compares the pressure profiles for pure R134a and R-134/oil mixture. It can be noticed that it is necessary a lower DTsup,l for refrigerant–oil mixture than for the pure refrigerant. A possible explanation for this behavior is the variation of fluid thermophysical properties caused by oil presence. Fig. 14 also shows the difference on the theoretical flashing point inception.
Fig. 13. Lms as function DTsub.
The bubble temperature for a refrigerant–oil mixture changes with oil concentration. According to Thome [22] there is an increase of approximately 0.1–0.2 K in this temperature as oil concentration increases 1%. Oil presence also affects the thermophysical properties of the mixture. Viscosity seems to be an important variable in flashing flow. Refrigerant–oil mixture viscosity is higher than pure fluid one, so a larger pressure drop of the liquid refrigerant–oil mixture will be partially compensated by a change in the bubble point, so that there is a decrease in
Fig. 15. Oil influence on DTsup,l as function of DTsub.
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flow inception of mixture compared with refrigerant R-134a pure. This result was verified mainly for low subcooling where a little liquid superheating is required to begin the nucleation. Acknowledgement The authors would like to acknowledge the support of FAPESP (Research Support Foundation of the State of Sa˜o Paulo, Brazil). References
Fig. 16. Dpvap for R-134a pure and refrigerant–oil mixtures.
The superheating of liquid necessary to start the flashing process is lower for refrigerant–oil mixtures when compared to pure refrigerant, as shown in Fig. 15. It can be seen that there is a small variation as the oil concentration increases. The underpressure of vaporization as a function of mass flow rate is shown in Fig. 16. Again there is a slight oil influence, and a tendency to increase this effect as the oil concentration is increased. 5. Conclusions The objective of this study was to verify the behavior of flashing process that occurs in capillary tubes and to analyse the influence of oil and other variables on the vaporization delay. Based on the experimental study developed, the data show a variable but predictable behavior of flash point inception. It is very important to consider an adequate control on the subcooling degree in the process. The mass flow rate and the subcooling degree are the two most important parameters affecting the underpressure of vaporization. Additional data are needed for investigate the influence of roughness in flashing inception. The capillary tube outlet pressure has no appreciable effect on the flashing point inception. The average length metastable liquid region is approximately 0.4 m for the test condition performed in this work. The maximum values encountered for liquid superheating and vaporization delay were about 4.5 C and 90 kPa for a subcooling degree of 4 C. The oil influence on the metastable flow was tested and its effects on the underpressure of vaporization may be verified also for lower oil concentrations. Oil presence increases the metastable liquid region retarding the flashing
[1] A.A.S. Huerta, O.M. Silvares, A Theoretical and experimental study on underpressure of vaporization in capillary tubes with refrigerant– oil mixtures, Post-Doctoral Thesis, University of Sa˜o Paulo, 2003 (in Portughese). [2] L. Cooper, C.K. Chu, W.R. Brisken, Simple capillaries selection method derived from physical flow conditions, Refrig. Eng. 7 (65) (1957) 37–41. [3] E.P. Mikol, J.C. Dudley, Visual and photographic study of the inception of vaporization in adiabatic flow, Trans. ASME (1964) 257– 264. [4] H. Koizumi, K. Yokoyama, Characteristics of refrigerant flow in a capillary tube, ASHRAE Trans. 86 (2) (1980) 19–27. [5] L.J.M. Kuijpers, M.J.P. Janssen, Influence of thermal non-equilibrium on capillary tube mass flow, in: Proc. 16th Int. Congr. Refrigeration, 1983, pp. 307-315. [6] K. Maczek, Z. Krolicki, E. Sochanecka, Model of throttling capillary tube with metastable process, in: Proc. 16th Int. Congr. Refrigeration, 1983, pp. 154–161. [7] S.J. Kuhel, V.W. Goldschmidt, Steady flows of R-22 through capillary tubes: test data, ASHRAE Trans. 96 (1) (1990) 719–728. [8] S.J. Kuhel, V.W. Goldschmidt, Modeling of steady flows of R-22 through capillary tubes, ASHRAE Trans. 97 (1) (1991) 139–148. [9] M.A.S. Paiva, F.A.S. Fiorelli, R.A. Peixoto, P. Vodianitskaia, A. Hernandez Neto, O.M. Silvares, Experimental and numerical study of the flow through non adiabatic capillary tubes with lateral and concentric capillary tube-suction line heat exchanger configuration, in: Proc. 19th Int. Congr. Refrigeration, 1995, pp. 429–436. [10] F.A.S. Fiorelli, A.A.S. Huerta, O.M. Silvares, Experimental analysis of refrigerant mixtures flow through adiabatic capillary tubes, Exp. Thermal Fluid Sci. 26 (5) (2002) 499–512. [11] F.A.S. Fiorelli, O.M. Silvares, Homogeneous capillary tube simulation model with refrigerant mixtures flow: experimental validation, in: Proc. 2002 Int. Refrigeration Conf. Purdue, 2002, Cd-rom. [12] R.Y. Li, Z.H. Chen, S. Lin, Z.Y. Chen, Metastable flow of R-12 through capillary tubes, Int. J. Refrig. 13 (3) (1990) 181–186. [13] Z.H. Chen, R.Y. Li, Z.Y. Chen, A correlation for metastable flow of refrigerant R-12 through capillary tubes, ASHRAE Trans. 96 (1990) 550–554. [14] M.D. Alamgir, J.H. Lienhard, Correlation of pressure undershoot during hot water depressurization, J. Heat Transfer 103 (1981) 52–55. [15] E. Dirik, C. Inan, Y. Tanes, Numerical and experimental studies on adiabatic and non adiabatic capillary tubes with HFC-134a, in: Proc. 1994 Int. Refrigeration Conf. Purdue, 1994, pp. 365–370. [16] R.R. Bittle, M.B. Pate, A theoretical model for predicting adiabatic capillary tube performance with alternative refrigerants, ASHRAE Trans. 102 (2) (1996) 52–64. [17] S. Chang, S.T. Ro, Pressure drop of pure HFC refrigerants and their mixtures flowing in capillary tubes, Int. J. Multiphase Flow 22 (3) (1996) 551–561. [18] J.J. Meyer, W.E. Dunn, New insights into the behavior of the metastable region of an operating capillary tube, HVAC&R Res. 4 (1) (1998) 105–115.
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[19] D. Chen, S. Li, Underpressure of vaporization of refrigerant R-134a through a diabatic capillary tube, Int. J. Refrig. 24 (2001) 261–271. [20] R.R. Bittle, J.A. Carter, J.V. Oiliver, Extended insight into metastable liquid region behavior in an adiabatic capillary tube, HVAC&R Res. 7 (2) (2001) 107–123.
[21] A.A.S. Huerta, Theoretical and experimental study in capillary tubes with refrigerant–oil mixtures, Ph.D. Thesis, University of Sa˜o Paulo, 2000. (in Portughese). [22] J.R. Thome, Enhanced Boiling Heat Transfer, Hemisphere Publishing Corporation, 1990.
Metastable flow in capillary tubes: An experimental evaluation Alex Alberto Silva Huerta a,b, Fla´vio Augusto Sanzovo Fiorelli Ota´vio de Mattos Silvares a,c
c,* ,
a Maua´ Institute of Technology, Prac¸a Maua´ no. 1, 09580-900 – Sa˜o Caetano do Sul (SP), Brazil IMENSU – Mairipora˜ Institute of Technology, Rodovia Ferna˜o Dias Km 67, 076000-000 – Mairipora˜ (SP), Brazil University of Sa˜o Paulo, Mechanical Engineering Department, Av. Prof. Mello Moraes, 2231 – Cidade Universita´ria, 05508-900 – Sa˜o Paulo (SP), Brazil
b c
Received 8 June 2006; received in revised form 2 October 2006; accepted 5 October 2006
Abstract This work presents the results of an experimental study with pure refrigerants R-134a and R-600a and refrigerant–oil mixtures flowing through capillary tubes in order to analyse the metastable flow. A large number of experiments were carried out to verify the influence of several variables on the underpressure of vaporization, mainly the inlet subcooling, internal diameter and inlet pressure. Capillary tubes with internal diameter of 0.69 mm and 0.82 mm were tested for condensation temperatures between 40 C and 50 C and subcooling degrees between 3 C and 12 C. Measurements for oil concentrations of 1% and 3% were conducted and compared with those for pure refrigerant R-134a. The oil influence on the metastable flow was tested and the effect on the underpressure of vaporization is addressed for lower oil concentrations. 2006 Elsevier Inc. All rights reserved. Keywords: Refrigeration; Metastable flow; Capillary tubes; Experimental analysis
1. Introduction In refrigeration systems, capillary tubes are used as expansion devices and their correct sizing and analysis require knowledge on the metastable flow that occurs during transition from liquid to the vapour state. This phase change is called ‘‘flashing flow’’, since the process occurs solely as result of a reduction in the system pressure. Before vaporization starts, as saturation conditions are achieved, there is a region where liquid becomes superheated, generating the metastable flow. Once proper conditions are obtained, further pressure reductions will start the nucleation process. There is neither a reliable explanation for the metastable flow occurrence nor exact criteria proposed for determining the flashing point inception. The scattered data encoun*
Corresponding author. Tel.: +55 11 3091 9661; fax: +55 11 3091 9681. E-mail addresses: [email protected] (A.A. Silva Huerta), fi[email protected] (F.A. Sanzovo Fiorelli), [email protected] (O. de Mattos Silvares). 0894-1777/$ - see front matter 2006 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2006.10.002
tered in experimental studies carried out by Huerta and Silvares [1] in glass capillary tubes show that the flashing point is very sensible and change continuously. However, the dominating process is certainly the wall heterogeneous nucleation, due to the lower superheating required. Several theoretical and empirical models were proposed in order to predict the performance of capillary tubes, but results were not accurate, due to the inability to predict the exact point where flashing process starts. The underpressure of vaporization (Dpvap) originated as consequence of superheated liquid flow is responsible for increasing the total liquid length and mass flow rate. The superheating degree required for initiating the flashing process depends on some parameters such as: inlet pres_ subcooling degree (DTsub), sure (pin), mass flow rate (mÞ, capillary tube internal diameter (Dct) and length (Lct), roughness and surfaces local irregularities, which may act as nucleation sites. Another aspect of practical interest is the presence of the lubricant oil. The refrigerant–oil mixture has different
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Nomenclature d L m m_ p T C ct evap l
diameter, mm length, m mass, kg mass flow rate, kg/h pressure, kPa temperature, C concentration, % capillary tube evaporating, evaporation liquid
thermophysical properties, which modifies the flashing point position when compared with the results encountered for pure refrigerant. This work presents the results of an experimental investigation on pure and refrigerant–oil mixtures flow, in order to analyse metastable flow in capillary tubes. The influence of oil concentration, subcooling degree, inlet pressure, diameter, and other parameters on the underpressure of vaporization and capillary tube performance are addressed. 2. Literature review Cooper et al. [2] and Mikol and Dudley [3] conducted the first studies about metastable flow in capillary tubes. Mikol and Dudley verified, by means of photographic observations in a glass capillary tube, that vaporization always occurred at one specific point at tube wall, and that point of inception of vaporization moves by discrete jumps rather than in a continuous manner as operating variables are changed. Koizumi and Yokoyama [4] measured pressure and temperature distributions for refrigerant R-22 flow in adiabatic capillary tubes, verifying the occurrence of the delay of vaporization. The authors proposed a simple calculation method to find the length of the liquid region. Such method was developed for adiabatic flow, based on integration of the momentum equation and assuming two-phase homogeneous flow. The experimental results showed a delay of vaporization ranging from 2 C to 4 C and a maximum superheated liquid length of 0.60 m, and calculations agree with experimental data within ±3%. Kuijpers and Janssen [5] studied the effects of non-equilibrium metastable flow of R-12 in capillary tubes and verified that delay of vaporization has a clearly systematic influence on mass flow rate. Deviations of measured mass flow rates to calculated ones, considering equilibrium conditions, where up to 12%, with an average value of 8%. Using the observed delay as an input value for calculations and a relationship between the superheating temperature and the volume fraction, the average deviation was reduced to 0.3%. Authors also presented some experimental results for the dependence of superheating degree on capillary tube inlet
ms o r sub
metastable oil refrigerant subcooling
Subscripts sup superheating cond condensing, condensation vap vaporization
pressure and subcooling degree, and tried to derive a relationship for such dependence, but comparison of experimental results to calculations was not satisfactory. Maczek et al. [6] studied the delay of vaporization and proposed a mathematical model based on theory of creation and expansion of a nucleate bubble inside a superheated fluid, as well as mass, momentum and energy balances. According to the authors, comparison with experimental data for delay of vaporization was not fully satisfactory, but the proposed model was a better approximation of experimental capillary tube lengths than the homogeneous model, and further investigations would be necessary. Kuhel and Goldschmidt [7,8], working with R-22, also verified the occurrence of metastable flow in capillary tubes. In order to take this effect into account in a capillary tube simulation model, the authors calculated an average value for the underpressure of vaporization and added such value to the inlet pressure in simulation model input. This procedure reduced the difference between experimental and simulation results. Paiva et al. [9], Fiorelli et al. [10] and Fiorelli and Silvares [11] used the same approach for R-12, R-134a and zeotropic/near-azeotropic refrigerant mixtures. Li et al. [12] investigated the effects of the diameter, backpressure, subcooling degree and mass flow rate on metastability for R-12. It was found a decrease of the length of the metastable flow region as the capillary tube diameter increased. The mass flow rate increased as consequence of a larger Dpvap, and an increase in DTsub caused a decrease in Dpvap. It was also verified that the position of the flashing inception is not affected by backpressure variations. Chen et al. [13] developed a correlation for the delay of vaporization for R-12 flow through capillary tubes based on the nucleation theory initially developed by Alamgir and Lienhard [14] and with experimental data of Li et al. [12]. Although such correlation predicts underpressure of vaporization within a relative error of 26%, it was successfully used by several authors as part of capillary tube simulation models for the same range of operational and geometric parameters. For instance, Dirik et al. [15] verified that Chen’s correlation was suitable for R-134a flow
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through capillary tubes, and Bittle and Pate [16] used such correlation for R-22, R-134a, R152a and R-410A. Chang and Ro [17], as part of a study on two-phase flow pressure drop in capillary tubes, analysed the temperature and pressure profiles along capillary tubes and proposed a empirical correlation for the underpressure of vaporization as function of subcooling degree and mass flow rate for R-134a, R-32, R-125 and some mixtures of R-32/ R-134a and R-32/R-125. Fiorelli et al. [10] tried to use such correlations in their study for R-410A and R-407C, but results were not satisfactory. Meyer and Dunn [18] showed that metastability might be more predictable than reported in the literature. The authors developed an experimental study on metastable flow of HCFC 22 in adiabatic capillary tubes, in which subcooling degree was continuously reduced and increased. A hysteresis effect in the mass flow rate was found, and the sudden flow variations only occurred in the sense of reducing flow rate. Chen and Li [19] investigated the underpressure of vaporization for adiabatic capillary tubes (configuration in which suction line and capillary tube are mounted as a counter-flow heat exchanger), showing that Dpvap decreases as the heat transfer between the capillary tube and the suction line increases. Bittle et al. [20] experimentally analysed the behavior of the metastable liquid region. The authors showed that the variation in the flashing point location could be controlled, and in this way it is possible to improve the accuracy of theoretical flow models used to simulate capillary tube performance. 3. Experimental apparatus and operation Fig. 1 shows a schematic diagram of the experimental apparatus built to this study. Such apparatus uses a blow-down batch process in order to provide a more accu-
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rate and independent control of the process parameters that could be achieved in a conventional refrigeration unit. Refrigerant is initially stored upstream the test section in a high-pressure reservoir (50-l neoprene bladder accumulator). This high pressure is provided by nitrogen filling of accumulator, controlled by a pressure regulator. The test section exit is connected to a low-pressure reservoir (a condenser–receiver). Low pressure is obtained by refrigerant condensation provided by a chilled ethylene-glycol/water mixture flowing through a coil inside the reservoir. During each run, refrigerant flows to from the high-pressure to the low-pressure reservoir through the test section where the capillary tube is placed. At the end of a run, refrigerant is returned to bladder accumulator by pressure difference. A 3 kW electric resistance heats the refrigerant stored in the condenser–receiver in order to raise its pressure, while pressure is lowered in the bladder by releasing nitrogen to atmosphere. A PID-controlled electric heating tape wrapped around the tube provides subcooling degree control. Refrigerant flow rate is measured in the liquid line by a Coriolis-type flowmeter (±0.1 kg/h uncertainty). Ten pressure transducers (±0.5 kPa uncertainty) measure pressure profile along the test section. Small pressure taps (0.5 mm diameter) was mounted along capillary tube. 20T-type thermocouples (±0.2 C uncertainty) measure capillary tube temperature profile. Thermocouples were soldered to capillary tube wall. Tables 1 and 2 show the pressure transducer and thermocouples positioning along the test section for refrigerant R-134a. A Pt-100 thermometer (±0.1 C uncertainty) measures capillary tube inlet temperature. Two sight glasses are installed, one at capillary tube inlet, and the other one at its outlet. A computer-based acquisition system is used to record data for later analysis. The refrigerant pressure at the test section exit was controlled by adjusting the mass flow rate of chilled water–
Fig. 1. Capillary tube test facility.
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Table 1 Pressure transducers position along the capillary tube Pressure transducer
Position from tube inlet (m)
#1 #2 #3 #4 #5 #6 #7 #8 #9 #10
0.06 0.31 0.51 0.81 1.01 1.21 1.41 1.61 1.81 1.93
Table 2 Thermocouples position along the capillary tube Thermocouple
Position from tube inlet (m)
#1 #2 #3 #4 #5 #6 #7 #8 #9 #10 #11 #12 #13 #14 #15 #16 #17 #18 #19 #20
0.10 0.20 0.40 0.50 0.65 0.75 0.87 0.96 1.06 1.16 1.26 1.35 1.46 1.56 1.67 1.77 1.87 1.90 1.98 2.00
refrigerant is vaporized and released by heating the sampling vessel When the vaporization is complete a third weight measurement is performed (m3). Thus, oil concentration can be evaluated by Eq. (1): C o ¼ 100
m3 m1 m_ o ¼ 100 m2 m1 m_ o þ m_ r
ð1Þ
3.2. Test conditions and procedure Tests were conducted for a copper capillary tube with the following geometries: • R-134a: Dct = 0.66 mm and 0.82 mm; Lct = 2.02 m; • R-600a (propane): Dct = 0.83 mm; Lct = 2.30 m. The operational conditions adopted for this study were: • condensing temperature: 40–50 C (R-134a) and 30– 40 C (R-600a); • evaporating temperature: below 20 C to assure critical (choked) flow conditions at capillary tube outlet; • subcooling degree: 3–12 C; • oil concentration: 1.0–5.0%. At each run the pressure corresponding to a given condensing temperature is set and data for different subcooling degrees were obtained. For test with refrigerant–oil mixtures a given oil concentration is also set. More details on the experimental procedure can be found in Huerta [21]. The operation time of the experimental apparatus is based on the refrigerant content stored in the accumulator, which is measured by a dynamometer installed at top and
glycol solution entering the condenser–receiver. Refrigerant–oil mixture leaving the test section is distilled by vaporization of the refrigerant at the temperature of 110 C in a reservoir heated by a 2.5 kW electric resistance. Thus, only pure refrigerant leaves this reservoir to the condenser– receiver. 3.1. Oil injection and concentration measurement Like pure refrigerant, the oil injection into system was also performed by a bladder accumulator. The test procedure begins with a pure refrigerant flow. Once such flow is stablished and refrigerant mass flow rate measured, oil mass flow rate is set as function of refrigerant flow rate by regulating a needle valve in oil feeding line in order to achieve the desired oil concentration. Actual concentration is measured by mixture sample weighting, based on ASHRAE standard 41–4. The first step is to measure the weight of an evacuated sampling vessel (m1). After sampling, a second measurement is made to get the total weight of vessel and sample (m2). Then the
Fig. 2. Experimental values obtained for inlet pressure along 30 min during test.
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Table 3 Experimental measurements for pure R-134a (Lct = 2.03 m; dct = 0.82 mm; Tevap = 25 C)
Fig. 3. Experimental values for mass flow rate and subcooling degree as function of test time.
holding up the accumulator. Typical duration of a test is near two hours, which allows obtaining three different operational conditions. Figs. 2 and 3 show an example of the experimental values for inlet pressure, subcooling temperature and mass flow rate as function of time for one of such operational conditions.
Tcond
DTsub
m_
Dpvap
DTit
40
4 5 6 7 8 9 10 11 12 13
6.56 6.69 6.82 7.11 7.32 7.58 7.72 7.79 7.87 8.03
95 78 70 55 60 42 32 25 23 21
4.0 3.5 2.8 2.3 2.0 1.8 1.7 1.5 1.4 1.1
0.60 0.50 0.42 0.38 0.25 0.20 0.18 0.15 0.12 0.10
44
4 5 6 7 8 9 10 11 12 13
7.41 7.54 7.87 7.92 7.97 8.02 8.08 8.16 8.24 8.34
90 80 70 75 60 42 35 25 27 18
4.5 3.3 4.0 3.5 3.0 2.0 1.8 1.0 1.2 0.5
0.50 0.42 0.47 0.45 0.30 0.20 0.15 0.10 0.12 0.07
50
4 5 6 7 8 9 10 11 12 13
7.29 7.51 7.84 8.21 8.38 8.66 8.73 8.89 8.99 9.09
80 60 50 42 40 60 50 50 50 40
4.0 3.7 3.2 3.0 2.8 2.5 2.0 1.8 1.5 1.2
0.52 0.44 0.35 0.30 0.26 0.25 0.18 0.16 0.12 0.10
sup,l
Lms
3.3. Visual observation of flow A pyrex glass capillary tube with Dct 1.0 mm and Lct = 2.2 m was used for observing the flashing point inception in refrigerant flow and examining the continuous developing of the two-phase flow process. The experiments were carried out using refrigerant R600a (isobutane) in several conditions. A copper wire was introduced into the capillary tube for helping in the nucleation sites formation, since glass has a smaller roughness than copper. It was observed that the subcooling degree and the mass flow rate are the most important parameters that affects flashing inception location. A significant dispersion on such location was also observed. 4. Results and discussions Table 3 presents the experimental results for pure refrigerant R-134a for several test conditions. It is shown mass flow rates, underpressure of vaporization and liquid superheating degree for condensation temperatures ranging from 40 C to 50 C and subcooling degrees from 4 C to 13 C. The maximum value for Dpvap found in this work was 95 kPa, with an uncertainty of ±6.0 kPa, and uncertainty for DTsup,l is ±0.3 C. Table 3 shows that Dpvap
Fig. 4. Pressure profile along capillary tube for Dct = 0.82 mm, Tcond = 40 C and DTsub = 12 C.
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Fig. 5. Pressure profile along capillary tube for Dct = 0.66 mm, Tcond = 48 C and DTsub = 12 C.
decreases as DTsub increases, and that Tcond has a small influence on underpressure of vaporization. Figs. 4 and 5 show the measured pressure profiles and calculated saturation pressure profiles along a capillary tube of Dct = 0.82 mm for Tcond = 40 C and Dct = 0.66 mm for Tcond = 48 C, both with DTsub = 12 C. Saturation pressures were calculated from measured temperatures along the capillary tube using a equation of state for the refrigerant. In such figures it can be verified the
Fig. 6. Temperature profile along capillary tube (Dct = 0.82 mm, Tcond = 40 C, DTsub = 4 C).
Fig. 7. Temperature profile along capillary tube (Dct = 0.82 mm, Tcond = 40 C, DTsub = 12 C).
occurrence and the magnitude of the underpressure of vaporization. Phase change, expected to occur when the measured and saturation pressure are coincident, starts only when the necessary liquid superheating to initiate the flashing process is attained. Figs. 6 and 7 show similar results in terms of temperature profiles for Tcond = 40 C, with DTsub of 4 C and 12 C, respectively. It can be seen from these figures that the metastable region length for DTsub = 4 C is higher than for DTsub = 12 C.
Fig. 8. DTsup,l as function of mass flow rate.
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4.1. Effect of mass flow rate on Dpvap and DTsup,l Fig. 8 shows the liquid superheating degree (DTsup,l) as function of mass flow rate for Tcond = 40 C and 50 C, respectively. It is observed DTsup,l decreases as mass flow rate increases. The minimum value found for DTsup,l was approximately 1 C for higher mass flow rates. A similar effect can be verified for the underpressure of vaporization Dpvap on Fig. 9. It can be noticed, as expected, that there is a direct relation between these two parameters, as it can be seen in Fig. 10. Since DTsup,l represents the penetration of liquid in metastable state, it is expected that the underpressure of vaporization Dpvap has the same behavior. In fact these two parameters are different ways of expressing the same effect, the metastable flow ‘‘intensity’’. 4.2. Effect of DTsub The effect of DTsub on DTsup,l for different capillary tube inlet and condensing temperatures can be verified in Fig. 11. Such figure shows that the liquid superheating degree increases as inlet temperature increases. Fig. 12 shows DTsup,l behavior for DTsub ranging between 4 C and 13 C for several condensation temperatures. As DTsub increases (and Tin decreases), DTsup,l decreases. At last Fig. 13 shows a similar behavior of the metastable region length Lms for the same DTsub range (4–13 C).
Fig. 10. DTsup,l as function of Dpvap.
4.3. Effect of lubricant oil on metastable flow In this work, it were carried out tests whit inlet oil concentrations ranging 1% and 3%, which are typical values expected in refrigeration systems (depending on
Fig. 11. DTsup,l as function of Ti,ct and DTsub.
Fig. 9. Dpvap as function of mass flow rate.
the compressor type). These values refer to oil concentrations at capillary tube inlet. As the refrigerant begins to vaporize the oil local concentration rises since the refrigerant is more volatile than oil. As stated before, the underpressure of vaporization depends on the subcooling degree, condensing temperature, and mass flow rate. The phenomenon becomes more complex when the oil effects are to be considered. It is expected that the oil presence should affect the flashing process and the liquid superheating degree required for the process to take place.
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Fig. 12. DTsup,l as function of DTsub and Tcond.
Fig. 14. Pressure profile along capillary tube.
the mass flow rate as the oil concentration increases. Fig. 14 compares the pressure profiles for pure R134a and R-134/oil mixture. It can be noticed that it is necessary a lower DTsup,l for refrigerant–oil mixture than for the pure refrigerant. A possible explanation for this behavior is the variation of fluid thermophysical properties caused by oil presence. Fig. 14 also shows the difference on the theoretical flashing point inception.
Fig. 13. Lms as function DTsub.
The bubble temperature for a refrigerant–oil mixture changes with oil concentration. According to Thome [22] there is an increase of approximately 0.1–0.2 K in this temperature as oil concentration increases 1%. Oil presence also affects the thermophysical properties of the mixture. Viscosity seems to be an important variable in flashing flow. Refrigerant–oil mixture viscosity is higher than pure fluid one, so a larger pressure drop of the liquid refrigerant–oil mixture will be partially compensated by a change in the bubble point, so that there is a decrease in
Fig. 15. Oil influence on DTsup,l as function of DTsub.
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flow inception of mixture compared with refrigerant R-134a pure. This result was verified mainly for low subcooling where a little liquid superheating is required to begin the nucleation. Acknowledgement The authors would like to acknowledge the support of FAPESP (Research Support Foundation of the State of Sa˜o Paulo, Brazil). References
Fig. 16. Dpvap for R-134a pure and refrigerant–oil mixtures.
The superheating of liquid necessary to start the flashing process is lower for refrigerant–oil mixtures when compared to pure refrigerant, as shown in Fig. 15. It can be seen that there is a small variation as the oil concentration increases. The underpressure of vaporization as a function of mass flow rate is shown in Fig. 16. Again there is a slight oil influence, and a tendency to increase this effect as the oil concentration is increased. 5. Conclusions The objective of this study was to verify the behavior of flashing process that occurs in capillary tubes and to analyse the influence of oil and other variables on the vaporization delay. Based on the experimental study developed, the data show a variable but predictable behavior of flash point inception. It is very important to consider an adequate control on the subcooling degree in the process. The mass flow rate and the subcooling degree are the two most important parameters affecting the underpressure of vaporization. Additional data are needed for investigate the influence of roughness in flashing inception. The capillary tube outlet pressure has no appreciable effect on the flashing point inception. The average length metastable liquid region is approximately 0.4 m for the test condition performed in this work. The maximum values encountered for liquid superheating and vaporization delay were about 4.5 C and 90 kPa for a subcooling degree of 4 C. The oil influence on the metastable flow was tested and its effects on the underpressure of vaporization may be verified also for lower oil concentrations. Oil presence increases the metastable liquid region retarding the flashing
[1] A.A.S. Huerta, O.M. Silvares, A Theoretical and experimental study on underpressure of vaporization in capillary tubes with refrigerant– oil mixtures, Post-Doctoral Thesis, University of Sa˜o Paulo, 2003 (in Portughese). [2] L. Cooper, C.K. Chu, W.R. Brisken, Simple capillaries selection method derived from physical flow conditions, Refrig. Eng. 7 (65) (1957) 37–41. [3] E.P. Mikol, J.C. Dudley, Visual and photographic study of the inception of vaporization in adiabatic flow, Trans. ASME (1964) 257– 264. [4] H. Koizumi, K. Yokoyama, Characteristics of refrigerant flow in a capillary tube, ASHRAE Trans. 86 (2) (1980) 19–27. [5] L.J.M. Kuijpers, M.J.P. Janssen, Influence of thermal non-equilibrium on capillary tube mass flow, in: Proc. 16th Int. Congr. Refrigeration, 1983, pp. 307-315. [6] K. Maczek, Z. Krolicki, E. Sochanecka, Model of throttling capillary tube with metastable process, in: Proc. 16th Int. Congr. Refrigeration, 1983, pp. 154–161. [7] S.J. Kuhel, V.W. Goldschmidt, Steady flows of R-22 through capillary tubes: test data, ASHRAE Trans. 96 (1) (1990) 719–728. [8] S.J. Kuhel, V.W. Goldschmidt, Modeling of steady flows of R-22 through capillary tubes, ASHRAE Trans. 97 (1) (1991) 139–148. [9] M.A.S. Paiva, F.A.S. Fiorelli, R.A. Peixoto, P. Vodianitskaia, A. Hernandez Neto, O.M. Silvares, Experimental and numerical study of the flow through non adiabatic capillary tubes with lateral and concentric capillary tube-suction line heat exchanger configuration, in: Proc. 19th Int. Congr. Refrigeration, 1995, pp. 429–436. [10] F.A.S. Fiorelli, A.A.S. Huerta, O.M. Silvares, Experimental analysis of refrigerant mixtures flow through adiabatic capillary tubes, Exp. Thermal Fluid Sci. 26 (5) (2002) 499–512. [11] F.A.S. Fiorelli, O.M. Silvares, Homogeneous capillary tube simulation model with refrigerant mixtures flow: experimental validation, in: Proc. 2002 Int. Refrigeration Conf. Purdue, 2002, Cd-rom. [12] R.Y. Li, Z.H. Chen, S. Lin, Z.Y. Chen, Metastable flow of R-12 through capillary tubes, Int. J. Refrig. 13 (3) (1990) 181–186. [13] Z.H. Chen, R.Y. Li, Z.Y. Chen, A correlation for metastable flow of refrigerant R-12 through capillary tubes, ASHRAE Trans. 96 (1990) 550–554. [14] M.D. Alamgir, J.H. Lienhard, Correlation of pressure undershoot during hot water depressurization, J. Heat Transfer 103 (1981) 52–55. [15] E. Dirik, C. Inan, Y. Tanes, Numerical and experimental studies on adiabatic and non adiabatic capillary tubes with HFC-134a, in: Proc. 1994 Int. Refrigeration Conf. Purdue, 1994, pp. 365–370. [16] R.R. Bittle, M.B. Pate, A theoretical model for predicting adiabatic capillary tube performance with alternative refrigerants, ASHRAE Trans. 102 (2) (1996) 52–64. [17] S. Chang, S.T. Ro, Pressure drop of pure HFC refrigerants and their mixtures flowing in capillary tubes, Int. J. Multiphase Flow 22 (3) (1996) 551–561. [18] J.J. Meyer, W.E. Dunn, New insights into the behavior of the metastable region of an operating capillary tube, HVAC&R Res. 4 (1) (1998) 105–115.
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[19] D. Chen, S. Li, Underpressure of vaporization of refrigerant R-134a through a diabatic capillary tube, Int. J. Refrig. 24 (2001) 261–271. [20] R.R. Bittle, J.A. Carter, J.V. Oiliver, Extended insight into metastable liquid region behavior in an adiabatic capillary tube, HVAC&R Res. 7 (2) (2001) 107–123.
[21] A.A.S. Huerta, Theoretical and experimental study in capillary tubes with refrigerant–oil mixtures, Ph.D. Thesis, University of Sa˜o Paulo, 2000. (in Portughese). [22] J.R. Thome, Enhanced Boiling Heat Transfer, Hemisphere Publishing Corporation, 1990.