# Experimental and numerical investigation of R-134a flow through a lateral type diabatic capillary tube.

INTRODUCTIONThe capillary tubes are drawn copper tubes with internal diameters of 0.5-2.0 mm and lengths of 2-6 m. They are used in low-capacity refrigeration systems, such as household refrigerators and window-type air conditioners. The capillary tubes offer a number of advantages: they are simple in construction, low-cost, and require no maintenance. Further, a system employing a capillary tube requires a low-starting-torque motor, as during off-cycle the pressure difference across the capillary tube equalizes. Capillary tubes are available in a range of sizes and their proper selection is a necessity for satisfactory performance of a system. Figure 1a shows the vapor compression system employing a diabatic capillary tube. In a diabatic capillary tube, the capillary tube is bonded with the cold compressor suction line to form a counter flow heat exchanger. The thermal contact between the capillary tube and the compressor suction line can be attained by bonding the capillary tube with the compressor suction line by means of a solder or brazing joint, as shown in Figure 1b. The heat transfer from the capillary to suction-line results in a higher refrigerating effect and, thus, a better performance is achieved. On the other hand, after receiving heat from the capillary tube, the low-temperature saturated refrigerant vapors in the suction line are superheated, which reduces the chance of liquid refrigerant entering the compressor.

[FIGURE 1 OMITTED]

Capillary tubes of different geometries (e.g., straight, helical, and spiral shapes) and flow conditions (e.g., adiabatic and diabatic arrangements) are used extensively in the refrigeration industry. It is a known fact that coiling of capillary tubes results in system compactness, whereas use of diabatic capillary tubes enhances the refrigerating effect of a refrigeration system. An exhaustive review of the literature reveals that most of the work on capillary tubes focuses on adiabatic capillary tubes with a straight geometry. Only a few researchers have investigated diabatic capillary tubes with a straight geometry.

A majority of the experimental research on diabatic capillary tubes was conducted on lateral arrangement. The experimental work on diabatic capillary tubes was pioneered by Staeblar (1948). The capacity balance characteristics to determine the length of a diabatic capillary tube for R-12 and R-22 were presented. It was concluded that the effect of changes in evaporator pressure on the refrigerant mass flow rate was insignificant. Pate and Tree (1984b) studied the diabatic flow of R-12 through the capillary tube with air flowing in the suction line in counter flow direction, forming an open loop. They did not observe metastable flow in a diabatic arrangement, although the metastability was observed during adiabatic flow. Melo et al. (2002) conducted experiments on the concentric diabatic capillary tubes with R-600a as a working fluid. Based on their experimental results, they proposed separate empirical correlations using a factorial design of experiments technique for the determination of refrigerant mass flow and the suction-line outlet temperature. The research work on coiled capillary tubes was pioneered by Kuehl and Goldschmidt (1990). It was found that coiling reduces the mass flow rate through the capillary tube by as much as 5% only. However, some researchers also reported a higher drop in refrigerant mass flow rate in helically coiled capillary tubes. For instance, Kim et al. (2002) found that the refrigerant mass flow rate through a helically coiled capillary tube was reduced by 9%. Zhou and Zhang (2006) also found that the mass flow rate through a helical capillary tube was reduced by 10%. Park et al. (2007) reported a slightly higher reduction in mass flow rates for the coiled capillary tubes, i.e., 5%-16%, compared to straight capillary tubes. Khan et al. (2008a) carried out an experimental study on adiabatic spiral capillary tubes and proposed a correlation for the prediction mass flow rate of R-134a.

Various investigators also developed numerical models for the flow refrigerant through coiled capillary tubes. A numerical model was developed by Zhou and Zhang (2006) for adiabatic helical capillary tubes and validated with their own experimental data. Khan et al. (2008b) developed a numerical model for adiabatic helical capillary tubes based on homogeneous two-phase flow theory. They compared the results of their numerical model with the experimental data of Zhou and Zhang (2006) and Kim et al. (2002). Further, they compared their model with that of Zhou and Zhang (2006). The predictions of the Khan et al. (2008b) model were found to be very close to those of the Zhou and Zhang (2006) model. In addition, Khan et al. (2007) also developed a numerical model for adiabatic spiral capillary tubes and compared the performance of spiral capillary tubes with adiabatic straight capillary tubes.

A number of numerical investigations were made for the flow through diabatic capillary tubes. Pate and Tree (1984a) proposed a linear quality model for the flow of R-12 through diabatic capillary tubes operating in an open loop--i.e., cold air in the suction line and refrigerant R-12 in the capillary tube. The proposed numerical model was validated with their own experimental data. Sinpiboon and Wongwises (2002) developed a simple mathematical model for the refrigerant flow through a lateral diabatic capillary tube. The linear quality model of Pate and Tree (1984a) in the analysis of the heat exchange region of the diabatic capillary tube was used. Xu and Bansal (2002) developed a numerical model by dividing the flow domain into numerous control volumes along the length of capillary tubes. They observed that when the effect of heat transfer was stronger than the pressure drop effect, the refrigerant was condensed within the heat exchanger region; whereas, if the pressure drop effect was stronger, the refrigerant flashed within the heat exchange region. Bansal and Xu (2003) also conducted a parametric study on the diabatic flow of R-134a through a capillary tube. Bansal and Yang (2005) proposed a model for the flow of refrigerant through a diabatic capillary tube. It was observed that the rate of heat transfer from the capillary tube to suction decreases by 8%-10% if the inlet diabatic arrangement was considered, compared to adiabatic inlet conditions. The control volume formulation for the flow through a diabatic capillary tube was adopted by a number of researchers. Escanes et al. (1995) developed a numerical simulation model based on the control volume formulation on 4.0 m of capillary tube length assuming that the first 1.3 m length of capillary tube is diabatic and rest of the tube is adiabatic. The solution was carried out using an implicit step-by-step numerical scheme. The calculation of mass flow rate for both critical and noncritical flow was made iteratively by means of the Newton-Raphson algorithm. A reasonably low computational cost resulted. Valladares et al. (2002a) developed a numerical simulation similar to the simulation model by Escanes et al. (1995). This model was based on the finite volume formulation of the governing equations. As a sequel to the numerical simulation, Valladares et al. (2002b) validated their simulation model with the experimental data of previous researchers. Parametric studies for the concentric capillary-tube suction-line heat exchangers were also presented. Valladares (2004) presented a review of, and, most recently (Valladares 2007a, 2007b), extended the numerical work of Valladares et al. (2002a; 2002b) on diabatic capillary tubes considering separated flow model and metastable regions. He validated his renewed model with the existing experimental data.

Consequently, there is a need to conduct more experimental and numerical research on the diabatic capillary tubes to evaluate their performance for different input conditions. Therefore, the present work carries out experimental as well as numerical investigations on diabatic capillary tubes. In fact, in the present experimental investigation, a novel configuration of capillary tubes is proposed that includes the advantages of coiling in helical form as well as those of a diabatic flow arrangement. The experimental part of this paper may be perceived as an extension of our own experimental work (Khan et al. 2008c) on the flow of R-134a through an adiabatic helically coiled capillary tube. Further, an attempt has also been made to develop a numerical model for a diabatic straight capillary tube. The developed numerical model was compared with previous and present experimental data.

EXPERIMENTAL SETUP AND PROCEDURE

The experimental setup shown in Figure 2 has been designed to carry out experiments on the adiabatic and diabatic flows of R-134a through a helical capillary tube. The refrigerant was expanded from the high-pressure condenser side to low-pressure evaporator side in the helical test section (1). The test section was a capillary tube brazed on a 6.35 mm compressor-suction line forming a counter-flow heat exchanger. The evaporator (2) consisted of a copper coil submerged in a water tank. An electric heater (3) was fitted in the evaporator tank to provide heating load to the evaporator. The heating load was controlled by a variac (4). An agitator (5) was also fitted in the tank to maintain the uniform bulk temperature of water. The refrigerant vapors, after producing a refrigerating effect inside the evaporator (2), passed through the liquid accumulator (6) in order to prevent liquid refrigerant from entering the compressor. The compressor (7) was run by means of a three-phase electric motor (8) using a belt and pulley arrangement. Superheated refrigerant vapors from the compressor (7) were passed through the oil separator (9) to remove lubricating oil. The oil-free vapors were condensed in a water-cooled condenser (10) where the tap water was circulated by means of a pump (11). The high-pressure saturated liquid from the condenser was then collected in a receiver (12) to ensure a continuous supply of refrigerant into the test section. The unwanted solid particles and moisture in the refrigerant were removed in the drier-cum-filter (13). The mass flow rate of the high-pressure liquid refrigerant was measured by four rotameters (14) of different ranges of flow measurement. The bank of four rotameters was facilitated to cover the entire range of refrigerant flow rate with accurate measurement. To vary the refrigerant subcooling at the capillary tube inlet, a subcooler and preheater arrangement was employed. The chilled water to the subcooler (15) was supplied by means of a separate chiller unit. The chiller was composed of a hermetically sealed compressor (16), an air-cooled condenser (17), and a tank for cooling water. Another pump (18) was used to circulate chilled water through the subcooler (15). Input to the preheater (19) was controlled by a variac (20) to obtain a wide range of inlet subcooling. A sight glass (21) was provided directly after the preheater to visualize the state of flowing refrigerant. For bypassing the excess refrigerant, a hand-operated expansion valve (22) was also provided. The temperature measurements were made at different locations of the setup and the test section by means of type T (copper constantan) thermocouples (24), while the pressure of the refrigerant was measured by pressure gauges (26) and pressure transducers (27) through pressure headers (25).

[FIGURE 2 OMITTED]

Valves V1, V2, and V3, shown in Figure 2, were used to operate the experimental setup in adiabatic or diabatic mode. The same test-section acted as an adiabatic capillary tube by setting valves V1 and V2 closed and V3 open; whereas it acted like diabatic capillary tube by setting the valves V1 and V2 open and V3 closed.

Figure 3 shows the helical test section and its cross section. The test section consisted of a capillary tube brazed over a helically coiled compressor suction line. Further, a copper tape was wrapped around the two brazed tubes to promote heat exchange between the capillary tube and compressor suction line. The cross section of the test section was a capillary tube brazed over the compressor suction line wrapped together with copper tape. After copper tape was wrapped around the two tubes, the tubes were embedded in the helical groove carved on the wooden log. The test section was completely insulated by a layer of ceramic wool.

[FIGURE 3 OMITTED]

For the fabrication of a helical capillary tube test section, three wooden logs (cylindrical patterns) for three different coil pitches (20, 40, and 60 mm) were used. All three of the wooden patterns with different coil pitches are shown in Figure 4. The diameter of the cylindrical pattern was kept equal to the coil diameter of the helical capillary tube test section. For the present study, the coil diameter was kept at 140 mm. The groove was large enough to accommodate the suction line of 6.35 mm diameter.

[FIGURE 4 OMITTED]

Table 1 shows the range of parameters for the present experimental investigation, which was mainly conducted on the flow of R-134a through instrumented (with pressure taps) capillary tubes of all three diameters. However, to see whether pressure taps have any effect on the refrigerant mass flow rate, experiments were also conducted on 1.40 mm of noninstrumented capillary tube. The data for a straight capillary tube was also collected for the sake of comparison. It should be noted that for a diabatic capillary tube, two more parameters must be considered: suction-line inlet superheat and heat exchange length. It should also be noted that suction-line inlet superheat in the present study is not a controlled variable; whereas, the heat exchange length is 0.8 m less than the total capillary tube length. The evaporator temperature and pressure are not controlled in the present investigation. However, the evaporator pressure in all the tests is kept below the critical or choking pressure. The evaporator temperature was recorded in the range of -1[degrees]C to -26[degrees]C; whereas the evaporator pressure was in the range 35 to 150 kPa. The capillary inlet pressure and coil diameter were kept constant during the present investigation. The uncertainties in the measuring instruments are shown in Table 2.

Table 1. Range of Input Parameters Selected Range Parameters Straight Capillary Helical Capillary Tube Tube d, mm 1.12, 1.40, 1.63 1.12, 1.40, 1.63 L *, m 6.4-2.4 6.4-2.4 [L.sub.hx], m 5.6-1.6 5.6-1.6 P, mm -- 20, 40, 60 [DELTA][T.sub.sub], [degrees]C 0.5-25 0.5-25 [P.sub.in], kPa 740 740 D, mm -- 140 * A total of six capillary lengths, viz., 6.4, 5.6, 4.8, 4.0, 3.2, 2.4, have been taken for each test section. Table 2. Uncertainties in the Measured Parameters Parameters Instruments Uncertainty Temperature Thermocouple (type T) [+ or -] 0.1[degrees]C Pressure Pressure gauge (4 Nos.) 6.87 kPa Pressure transducer (4 Nos.) 0.25% FS (2 MPa) Mass flow rate Analog rotameters (3 Nos.) 0.5 LPH Digital rotameter (1 No.) 1%FS(50LPH) Capillary tube Steel rule 1.0 mm length Capillary tube Toolmaker's microscope 0.01 mm diameter Internal surface Surface profilometer 0.01 [mu]m roughness Coil pitch Vernier callipers 0.01 mm Coil diameter Vernier callipers 0.01 mm

Initially, 5.6 m of the 6.4 m capillary tube was brazed from the middle over the compressor suction line and embedded in the helical groove of the required pitch such that the initial and final adiabatic lengths of the capillary tube were 0.4 m each. The refrigerant mass flow rate was recorded for a given capillary tube length and length diameter, first for the adiabatic test section and then for the diabatic test-section, by means of operating valves as described earlier. For each length and diameter of capillary tube, the refrigerant mass flow rate was recorded for four to five levels of inlet subcooling in the range of 0.5[degrees]C to 25[degrees]C. The procedure was repeated for five other capillary tube lengths for each capillary tube diameter.

EXPERIMENTAL RESULTS

Khan et al. (2008a) showed that the effect of pressure taps on refrigerant mass flow is insignificant. Therefore, the results for the instrumented capillary tube can be used for noninstrumented capillary tubes as well.

Figures 5-7 were drawn to find the effect of the inlet subcooling, capillary tube length, and coil pitch on refrigerant mass flow rate through the diabatic helical capillary tubes with diameters of 1.12, 1.40, and 1.63 mm, respectively. The coil diameter was fixed at 140 mm, while the coil pitch was varied from 20, 40, and 60 mm. The following observations were made from Figures 5-7:

* The mass flow rate of R-134a increases with the rise in inlet subcooling, as the liquid length of the capillary tube is higher for higher inlet subcooling. Consequently, the two-phase length becomes less. The reason for higher mass flow for high inlet subcooling is that liquid offers a lesser resistance to the flow as compared to the resistance offered by the two-phase liquid-vapor mixture.

* The refrigerant mass flow rate through a diabatic helical capillary tube increases with the increase in tube diameter. Also, there is an increase in mass flow rate with the reduction in tube length due to the fact that flow capacity of a capillary tube increases with the increase in tube diameter or with the reduction in capillary tube length.

* Coil pitch has an interfering effect on refrigerant mass flow rate from the suction-line inlet superheat. It is noted that the suction-line superheat was not controlled during the experiments and, hence, the experimental runs resulted in different suction-line inlet superheats. The effect of low suction-line superheat is so pronounced that in some of the curves of these figures, mass flow rate of R-134a through helically coiled capillary tubes exceeds that of the straight capillary tube. In fact, for high suction-line superheat, the refrigerant mass flow rate through straight or coiled tubes with 60 mm pitch even falls below those of the 20 mm pitch coiled capillary tubes.

* This behavior of diabatic tubes is entirely different from that of adiabatic capillary tubes where, in any manner, the suction-line inlet superheat does not influence the flow of R-134a through capillary tubes. It is noted that because of the interfering effect of suction-line superheat, these figures were drawn to depict only the trend of change in refrigerant mass flow rate with inlet subcooling. The interfering effect of suction-line superheat on mass flow rate of R-134a for a 1.63 mm diameter capillary tube of 3.2 m length is discussed in the next paragraph.

It was observed in the case of adiabatic capillary tubes that the mass flow rate of R-134a increases with an increase in coil pitch, and for any capillary tube geometry, the refrigerant mass flow rate through coiled capillary tubes does not exceed that of the straight capillary tubes. However, in the case of diabatic capillary tubes, it is interesting to observe that the effect of coil pitch on the refrigerant mass flow rate in some cases is totally suppressed due to the interfering effect of suction-line inlet superheat.

Figure 8 was drawn to show the effect of inlet superheat the case of a capillary tube with a length of 3.2 m and a diameter of 1.63 mm. Figure 8 also shows the error bars for uncertainty in the flow measurement. Data are also provided at the right-hand side of the figure in order to explain the discrepancies in the flow behavior of R-134a through capillary tubes. In the table adjoining Figure 8, the suction-line inlet superheat corresponding to each test run is shown. In Figure 8, for some of the test runs, the refrigerant mass flow rate through a 20 mm coil pitch capillary tube exceeds the refrigerant mass flow rate through a straight capillary tube. These test runs are labeled A, B, and C. Point D signifies the case when refrigerant mass flow rate through a 60 mm coil pitch capillary tube falls far below that through a 20 mm coil pitch capillary tube.

[FIGURE 8 OMITTED]

Table 3 was drawn for the data shown in Figure 8. As seen in Table 3, the suction-line inlet superheats corresponding to runs A, B, and C are comparatively lower than that of the straight capillary tube. Similarly, for run D for a 60 mm coil pitch capillary tube, the suction-line inlet superheat is quite higher than that of a 20 mm pitch capillary tube, resulting in a lower mass flow rate of R-134a through a 60 mm coil pitch tube as compared to that of a 20 mm coil pitch tube. As a matter of fact, when the suction-line superheat is low, the suction-line is cooler and more heat transfer from the capillary to the suction line takes place. As a result, recondensation occurs, the point of vaporization shifts downstream, and the length of the liquid region of the capillary tube increases; thus, an increase in the refrigerant mass flow rate takes place. Recondensation depends not only on the inlet adiabatic length but also on the capillary inlet subcooling, heat exchange length, and the suction-line inlet superheat (or a combination of all three). For a given inlet subcooling and capillary tube diameter, if the adiabatic length is more, the refrigerant enters the heat exchange region in a saturated state or in a two-phase condition (depending upon the inlet subcooling and on the pressure drop). Now, if the temperature of vapors flowing inside the suction line is much lower than the temperature of the vaporizing refrigerant flowing inside the capillary tube, recondensation may take place.

Table 3. Sample Data for Figure 8 Coil Pitch, p, Inlet Subcooling, Suction-Line Mass Flow mm [DELTA][T.sub.sub], Superheat, Rate, m, [degrees]C [DELTA][T.sub.sup], kg/h [degrees]C 20 19.6 1.5 27.7 [black C 14.9 1.0 29.2 [circle] 13.4 1.5 27.1 B 10.0 2.5 26.5 A 4.0 3.5 22.9 0.2 6.9 15.5 40 20.7 4.6 26.6 [white 15.3 5.5 25.9 circle] 12.9 5.7 25.8 9.7 6.9 24.7 3.0 8.9 21.1 60 22.5 4.7 28.6 [black 18.5 8.1 26.8 triangel] D 15.6 9.9 24.6 11.9 8.4 25.7 3.1 8.9 21.0 Straight 21.8 3.5 29.3 [white 16.7 4.4 27.8 triangle] 12.1 5.5 25.9 8.7 6.7 24.6 0.5 4.9 19.5

In Figure 9, the characteristics curves of diabatic capillary tubes for all diameters and for a 4.8 m length are drawn side-by-side for the sake of comparison with those of adiabatic capillary tubes. The following observations can be made:

* The refrigerant mass flow rate increases with the rise in capillary inlet subcooling in diabatic and adiabatic capillary tubes as well. However, the slope of the curve in the case of adiabatic capillary tubes is higher. In other words, the effect of capillary inlet subcooling in diabatic capillary tubes is not as strong as it is in the case of adiabatic capillary tubes. The increase in refrigerant mass flow rate in diabatic capillary tubes is restricted by the effect of suction-line inlet superheat.

[FIGURE 9 OMITTED]

* The effect of capillary tube length and diameter on the refrigerant mass flow rate through diabatic capillary tubes is similar to that through adiabatic capillary tubes. It is a known fact that the flow capacity of a capillary tube increases with either the increase in tube diameter or with the reduction in tube length.

* In adiabatic coiled capillary tubes, it is clearly observed that the refrigerant mass flow rate increases with an increase in the coil pitch of the coiled capillary tubes, namely helical and spiral. However, the effect of coil pitch from the mass flow characteristics of spiral capillary tubes is difficult to ascertain from Figure 8. The effect of coil pitch seems to be suppressed by the effect of suction-line inlet superheat. The effect of coil pitch on refrigerant mass flow rate in the case of adiabatic coiled capillary tubes is clear and significant--i.e., with the rise in coil pitch, the mass flow rate of R-134a increases, and it is the highest for straight capillary tube of same diameter and length. For diabatic capillary tubes, there is an interference of the effect of suction-line inlet superheat on the refrigerant mass flow rate. In some test runs, low suction-line inlet superheat resulted in a refrigerant mass flow rate higher than that for the straight capillary tube. Further, for certain test runs with high suction-line inlet superheat, the mass flow rate of R-134a is lower through the tubes with higher coil pitch as compared to that through the capillary tubes with lower pitch.

DEVELOPMENT OF CORRELATION

A combined mass flow rate correlation for diabatic capillary tubes of straight and helical geometries was developed. The refrigerant mass flow rate through a diabatic helical capillary tube is a function of capillary tube diameter, capillary tube length, heat exchange length, coil pitch, inlet subcooling, and suction-line inlet superheat:

m = f(L, [L.sub.hx], d, p, [P.sub.in], [P.sub.s,in], [DELTA][T.sub.sub], [DELTA][T.sub.sup], [[rho].sub.f], [[mu].sub.f], [c.sub.pf]) (1)

The thermophysical properties that appear in Equation 1 were evaluated by REFPROP 7 refrigerant database (McLinden et al. 2002). The total number of variables in Equation 1 is twelve for a helical capillary tube and eleven for a straight capillary tube.

Out of these parameters, d, [[rho].sub.f], [[mu].sub.f], and [c.sub.pf] are selected as repeating variables. Therefore, the nondimensional [pi] groups are eight (12-4) in the case of a helical capillary tube and seven (11-4) for a straight capillary tube. All the non-dimensional terms have been summarized in Table 4.

Table 4. Nondimensional [pi] Groups [pi]-Group Original Parameter Description [[pi].sub.1] m/[d[[mu].sub.f]] Mass flow rate [[pi].sub.2] [[d.sup.2][[rho].sub.f][P.sub.in]]/ Capillary [[mu].sub.f.sup.2] inlet pressure [[pi].sub.3] [[d.sup.2][[rho].sub.f][P.sub.s,in]]/ Suction-line [[mu].sub.f.sup.2] inlet pressure [[pi].sub.4] L/d Total length [[pi].sub.5] [L.sub.hx]/d Heat exchange length [[pi].sub.6] [[d.sup.2][[rho].sub.f.sup.2] Capillary [c.sub.pf][DELTA][T.sub.sub]]/ inlet [[mu].sub.f.sup.2] subcooling [[pi].sub.7] [[d.sup.2][[rho].sub.f.sup.2] Suction-line [c.sub.pf][DELTA][T.sub.sup]]/ inlet [[mu].sub.f.sup.2] superheating [[pi].sub.8] p/d Coil pitch

Hence, Equation 1 can be reduced to the following form:

[[pi].sub.1] = [f.sub.1]([[pi].sub.2], [[pi].sub.3], [[pi].sub.4], [[pi].sub.5], [[pi].sub.6], [[pi].sub.7], [[pi].sub.8]) (2)

Equation 2, in nonlinear power law form, can be written as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

In a generalized form, Equation 3 can be rewritten as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

The multiple variable regression technique was applied to the 376 data sets of all the three capillary tube geometries to obtain the constants that appear in Equation 4. The following equation was evolved as a result of data analysis:

[[pi].sub.1] = C[([[pi].sub.2]).sup.0.6547][([[pi].sub.3]).sup.[-0.0018]][([[pi].sub.4]).sup.[-0.3985]][([[pi].sub.5]).sup.0.1004][([[pi].sub.6]).sup.0.1013][([[pi].sub.7]).sup.[-0.0762]]F (5)

For straight tube: C = 0.0093; F = 1 for 102 data sets

For helical tube: C = 0.008; F = [([[pi].sub.8]).sup.0.033] for 274 data sets

Figure 10 was drawn to compare the refrigerant mass flow rate predicted by the proposed correlation given by Equation 5 and the measured mass flow rate for both diabatic helical and straight capillary tubes. The proposed correlation predicts the refrigerant mass flow rate in the error band of [+ or -]5%. Therefore, it can be concluded that the correlation is in very good agreement with the measured experimental mass flow rate. The proposed correlation was compared with the mass flow rate correlation proposed by Wolf and Pate (2002):

[[pi].sub.1] = 0.07602[([[pi].sub.2]).sup.0.7342][([[pi].sub.3]).sup.[-0.1204]][([[pi].sub.4]).sup.[-0.4583]][([[pi].sub.5]).sup.0.07751][([[pi].sub.6]).sup.0.03774][([[pi].sub.7]).sup.[-0.04085]] (6)

[FIGURE 10 OMITTED]

The proposed correlation was compared to the correlation in Figure 11 proposed by Wolf and Pate (2002). As seen in the figure, the refrigerant mass flow rate predicted by Wolf and Pate lies in the error band of [+ or -]25%. In fact, for lower mass flow rates up to 15 kg/h, the mass flow rate data predicted by Wolf and Pate is equally dispersed about the zero error line, while for higher mass flow rates, the data predicted by Wolf and Pate lies below the zero error line. For lower refrigerant mass flow rates, Wolf and Pate (2002) predict the refrigerant mass flow rate in the error band of [+ or -]25%, and for higher refrigerant mass flow rates, this correlation underpredicts the data in the error band of 0%-30%. However, the proposed correlation predicts the experimental data in an error band of [+ or -]5%. The predictions of the developed correlation and those of the correlation of Wolf and Pate (2002) do not agree on the same error band. Table 5 shows the comparison of the ranges of operating parameters for the present study and for Wolf and Pate's (2002) study. There is an agreement between the two correlations to a certain extent for low refrigerant mass flow rates, as the upper limit of tube diameter for the Wolf and Pate (2002) study lies in the operating range of the present experimental study.

Table 5. Comparison of the Ranges of Operating Parameters Investigators d, mm L, m [L.sub.hx], [DELTA][T.sub.sub], M [degrees]C Present 1.12-1.63 2.4-6.4 1.6-5.6 0.5-25 investigation Wolf and Pate 0.5-1.25 Up to 3.0 0.5-2.5 1-17 (2002) Investigators [DELTA][T.sub.sup], [degrees]C Present 1-19 investigation Wolf and Pate 3-22 (2002)

[FIGURE 11 OMITTED]

MATHEMATICAL MODELING

In a lateral configuration, the capillary tube is brazed on the suction line and then the assembly is wrapped with copper tape. The capillary tube-suction-line heat exchanger is insulated to avoid heat transfer to the surroundings. For the purpose of analysis, a capillary tube has been divided into three regions: the initial adiabatic length ([L.sub.in]), the intermediary region length or the heat exchange region length ([L.sub.hx]), and the final adiabatic length ([L.sub.f]).

The developed mathematical model is based on the following assumptions:

* the capillary tube is straight, horizontal, and has uniform cross section and roughness

* there is negligible thermal resistance at the contact of the capillary tube and suction line

* there is a one-dimensional and steady turbulent flow through the capillary tube

* flow is homogenous in the two-phase region

* metastability is ignored

Table 6 shows the governing equations for both capillary tube and suction-line fluid flow using the principles of mass, momentum, and energy conservations.

[TABLE 6 OMITTED]

Heat balance at the tube wall can be expressed by considering the fluid flow in the capillary tube and suction line. Therefore,

[h.sub.c][pi][d.sub.c]([T.sub.c] - [T.sub.w]) = [h.sub.s][pi][d.sub.s]([T.sub.w] - [T.sub.s]), (7)

where heat transfer coefficients [h.sub.c] and [h.sub.s] can be determined from the following equation:

h = [[Nuk]/d] (8)

where Nu is the Nusselt number given by Gnielinski's (1976) correlation:

Nu = [[(f/8)(Re - 1000)Pr]/[1 + 12.7[square root of [f/8([Pr.sup.[2/3]] - 1)]]]] (9)

where Pr is the Prandtl number given by the following relationship:

Pr = [[[c.sub.p][mu]]/k] (10)

The friction factor, f, is evaluated using Churchill's correlation (1977) given by the following:

f = 8[[[(8/[Re]).sup.12] + (1/[[(A + B)].sup.1.5])].sup.[1/12]] (11)

where

A = 2.457ln[(1/[[[(7/Re)].sup.0.9] + 0.27(e/d)]).sup.16]; B = [(37530/[Re]).sup.16] (12)

For the saturated or superheated vapor flowing through the suction line, neglecting the elevation difference and external work in the capillary tube, the conservation of energy is expressed by the suction-line energy equation depicted in Table 6 without the term

[[G.sub.s.sup.2]/2][[[dv.sup.2]]/[dz]].

The thermophysical properties of the refrigerant were determined by the REFPROP 7 database (McLinden et al. 2002). Inside the suction line, thermophysical properties of superheated vapor were not assumed constant; they are the function of suction-line temperature. For different suction-line temperatures, thermophysical properties are determined using REFPROP 7 and then plotted as a function of suction-line temperature. The best-fit line was fitted, and the equation for each thermophysical property was evolved and then used in the computer program.

The governing differential equations of momentum and energy were converted into the difference equations using forward difference formula of the finite difference method (FDM). These difference equations were solved simultaneously to obtain the pressure and temperature distribution along the capillary tube. In the adiabatic regions of the capillary tube, refrigerant temperature is constant when the flow is single-phase flow, while it falls sharply in the two-phase flow.

Three different cases, as shown in Figure 12, similar to those described by Sinpiboon and Wongwises (2002), were considered for the analysis.

[FIGURE 12 OMITTED]

Case 1: The Heat-Exchange Process Starts in the Single-Phase Flow Region ([L.sub.in] < [L.sub.sp])

Figure 12a shows the schematic diagram of the capillary tube and suction-line heat exchanger where the heat transfer starts in the single-phase region. As seen in Figure 12a, the refrigerant enters the capillary tube in a subcooled liquid state. There is a drop in pressure at the inlet of the capillary tube due to sudden contraction. The pressure at point 2 is given by

[P.sub.2] = [P.sub.1] - k[[[G.sub.c.sup.2]v]/2], (13)

where k is the entrance-loss coefficient and its value is taken as 1.5 (Zhou and Zhang 2006).

The pressure drop in the initial length is evaluated using the momentum equation; therefore, pressure at point 3 can be written as

[P.sub.3] = [P.sub.2] - [[[f.sub.sp]v[G.sub.c.sup.2][L.sub.in]]/[2[d.sub.c]]]. (14)

Since the flow in the capillary tube is adiabatic in the section 1-3, the refrigerant temperature will be constant in section 1-3.

[T.sub.3] = [T.sub.1] (15)

In section 3-4, the flow is diabatic, and the temperature is not constant and will vary along the length of the capillary tube and the suction line, depending on the rate of heat transfer. Since it is not known whether the flash point location will lie in the heat exchange region, the single-phase heat exchange region is discretized into N number of infinitesimal elements of constant length ([DELTA]z = [z.sub.[i+1]] - [z.sub.i]). One such element is shown in Figure 13. Therefore, after each elemental length, the computer program checks the state of the refrigerant. Later, all these infinitesimal elements are summed to obtain the single-phase heat exchange length.

[FIGURE 13 OMITTED]

The pressure after each elemental length can be evaluated by converting the differential momentum equation into the difference equation using the forward difference formulation as follows:

- [[[P.sub.[i + 1]] - [P.sub.i]]/[[Z.sub.[i + 1]] - [z.sub.i]]] = f[[[G.sub.c.sup.2][v.sub.i]]/[2[d.sub.c]]] + [G.sub.c.sup.2][[[v.sub.[i + 1]] - [v.sub.i]]/[[z.sub.[i + 1]] - [z.sub.i]]] (16)

The refrigerant temperature inside the capillary tube and the suction line can be calculated by applying the energy equation (see Table 6). As the energy equations are in differential form, they are first converted to difference equations as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

The wall temperature, [T.sub.w], was calculated by the wall heat balance Equation 1 as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

Equations 11-13 were solved simultaneously to obtain the distribution of temperature along the capillary tube-suction-line heat exchanger. The temperature at the end of the heat exchange region, i.e., [T.sub.4], is known in this way. From 4 to 4s, the single-phase flow is again adiabatic. Therefore,

[T.sub.4s] = [T.sub.4]. (20)

In the section 4s-5, the flow of the refrigerant is two-phase adiabatic; this section is again discretized into n number of infinitesimal elements with a constant pressure difference across them.

The pressure at any section i is given by

[P.sub.i] = [P.sub.4s] - idP, (21)

where [P.sub.4s] is the saturation pressure corresponding to the refrigerant temperature inside the capillary tube at the end heat exchange region, i.e., [T.sub.4]. For pressure, [P.sub.i], [x.sub.i] can be calculated from Equation 18.

Applying the continuity equation between sections 4s and 5,

m = [[[V.sub.4s]A]/[v.sub.4s]] = [[[V.sub.5]A]/[v.sub.5]]. (22)

Applying a steady flow energy equation with no external work, heat transfer, or potential energy between sections 4 and 5,

[h.sub.4s] + [[V.sub.[4s].sup.2]/2] = [h.sub.f] + x[h.sub.fg] + [[G.sup.2]/2][[([v.sub.f] + [xv.sub.fg])].sup.2]. (23)

Equation 17 is quadratic in x and, therefore, quality x is expressed as follows:

x = [[ - [h.sub.fg] - [G.sup.2][v.sub.f][v.sub.fg] + [square root of ([[[([G.sup.2][v.sub.f][v.sub.fg] + [h.sub.fg])].sup.2] - 2[G.sup.2][v.sub.[fg].sup.2]([[G.sup.2][v.sub.f.sup.2]]/2 - [h.sub.4s] - [[V.sub.[4s].sup.2]/2] + hf)]]]/[[G.sup.2][v.sub.[fg].sup.2]]] (24)

The two-phase friction factor, [f.sub.tp], is calculated using Churchill's correlation (1977). The Reynolds number in the two-phase region is determined by

[Re.sub.tp] = [[Vd]/[[[mu].sub.tp][v.sub.tp]]]. (25)

The entropy at the i-th section can be determined from the following:

[s.sub.i] = [s.sub.f] + [x.sub.i][s.sub.fg] (26)

The incremental length, dL, is calculated from section after section. For each section, pressure, temperature, vapor quality, friction factor, and entropy are calculated. It was found that the entropy increased until it attained a certain value and then decreased. The calculations are made up to the point of maximum entropy. The pressure of the elemental section where entropy is maximum ([P.sub.i,smax]) is then compared to the evaporator pressure ([P.sub.o]):

if [P.sub.i,smax] = [P.sub.o] then [P.sub.5] = [P.sub.o]

if [P.sub.i,smax][not equal to][P.sub.o] then [P.sub.5] = [P.sub.i,smax]

Integrating Equation 2 for section 4s-5,

[L.sub.tp] = 2d([ - 1]/[G.sup.2][[P.sub.smax].[integral].[P.sub.4s]][[rho]/[f.sub.tp]]dP + [[P.sub.smax].[integral].[P.sub.4s]][d[rho]]/[[rho][f.sub.tp]]). (27)

The incremental length of each section is calculated using

[DELTA][L.sub.i] = [[2d]/[f.sub.tp,i]]([ - [[rho].sub.i][DELTA]P]/[G.sup.2] + [[DELTA][rho]]/[[rho].sub.i]). (28)

The total length of two-phase region is

[L.sub.4s5] = [L.sub.tp] = [n.summation over (i = 1)][DELTA][L.sub.i]. (29)

The total length of capillary tubes is the sum of single and two-phase lengths, i.e.,

L = [L.sub.13] + [L.sub.34] + [L.sub.44s] + [L.sub.4s5]. (30)

Case 2: The Heat-Exchange Process Starts at the End of Single-Phase Flow Region ([L.sub.in] = [L.sub.sp])

The heat exchange process occurs between points 3 and 4, and the flow of refrigerant in this region is two-phase, as shown in Figure 12b. Equations 13-15 are applicable in this case also. The proposed model assumes that quality is linearly increased along the capillary tube and the refrigerant does not recondense in the heat exchanger (Pate and Tree 1984a).

The linear quality can be expressed as follows:

[[dx]/[dz]] = constant (31)

Therefore, quality at the end of each elemental length is given by the following equation:

[x.sub.[i + 1]] - [x.sub.i] = [[[x.sub.4] - [x.sub.3]]/[L.sub.hx]]([z.sub.[i + 1]] - [z.sub.i]) (32)

Section 3-4 was discretized into N number of infinitesimal elements with fixed elemental length [DELTA]z. The pressure at each elemental length can be evaluated in a similar fashion as done in Case 1-i.e, from Equation 16. The energy equations for capillary tube and suction line are as follows:

Capillary tube energy equation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (33)

Suction-line energy equation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (34)

The wall temperature can be calculated from Equation 19. The heat transfer coefficients are evaluated from the Gnielinski Nusselt number correlation (1976). Equations 33, 34, and 19 are solved simultaneously to compute the temperatures at each elemental length.

The length of adiabatic two-phase region is

[L.sub.45] = [L.sub.tp] = [n.summation over (i = 1)][DELTA][L.sub.i]. (35)

The total length of capillary tubes is the sum of single and two-phase lengths, i.e.,

L = [L.sub.in] + [L.sub.hx] + [L.sub.45]. (36)

Case 3: The Heat-Exchange Process Starts in the Two-Phase Flow Region ([L.sub.in] > [L.sub.sp])

Figure 12c shows heat-exchange process starts in the two-phase flow region. In this case, all regions are determined as described in the previous cases. The quality in the heat exchange or diabatic region of the capillary tube has been calculated from the assumption of linear quality model given by Equations 32 and 33.

The overall length of the capillary tube in this case is calculated from

L = [L.sub.12s] + [L.sub.2s3] + [L.sub.34] + [L.sub.45]. (37)

In Figure 14, a flowchart was drawn to demonstrate the computation of capillary tube length, mass flow rate, and the suction-line outlet temperature.

The proposed model differs from the Sinpiboon and Wongwises (2002) model in the following ways:

* Sinpiboon and Wongwises' (2002) numerical model uses the counter flow heat exchanger NTU-effectiveness method for calculating the temperature distribution in the single-phase liquid heat exchange region of the capillary tube; whereas, in the present case, the single-phase heat exchange region, as well as the two-phase region, has been discretized into infinitesimal elements. By discretizing the single-phase heat exchange region, the effect of change in refrigerant properties on the mass flow rate with change in temperature has been incorporated. The suction-line outlet temperature is assumed and the refrigerant temperature inside the capillary tube, as well as that of the inside suction line, has been progressively calculated. The calculated suction-line outlet temperature has been compared with that of the actual suction-line outlet temperature. Accordingly, a small temperature increment or decrement is applied to the initially assumed suction-line outlet temperature until the difference between the computed suction-line inlet temperature and the actual inlet temperature meets the convergence criterion.

* Sinpiboon and Wongwises' (2002) model assumes constant thermophysical properties of a refrigerant flowing inside the compressor suction-line, as well as that flowing inside the capillary tube of the single-phase flow region. In the proposed model, to increase the accuracy of prediction, the thermophysical properties equations have been generated by curve fitting the data obtained the from REFPROP 7 database (McLinden et al. 2002).

The proposed model differs from Valladares' (2007a) model and Xu and Bansal's (2002) model in the following manner:

* Valladares' (2007a) model was developed for transient as well as steady flow of refrigerant through diabatic capillary tube. On the other hand, the proposed model is quite simpler than Valladares' (2007a) model, as the proposed model has been developed for the steady flow of refrigerant through the diabatic capillary tube only. The transient flow through the capillary tube is not of interest in practical situations and, as such, neither Xu and Bansal (2002) nor Sinpiboon and Wongwises (2002) have considered transient aspects of the flow. Further, experimental data for transient flow of refrigerant through a diabatic capillary tube is not available in the literature.

* Valladares' (2007a) model takes into account metastability; whereas the proposed model, like Sinpiboon and Wongwises' (2002) model, does not take metastability into consideration, as it is a known fact that the effect of metastability diminishes as the heat transfer effect predominates the pressure-drop effect (Bansal and Xu 2003).

NUMERICAL RESULTS AND VALIDATION

The proposed numerical model for a diabatic capillary tube was validated with our own experimental data in addition to those of Pate and Tree (1984b), Mendoca et al. (1998), Peixoto (1995), and Liu and Bullard (2000). A comparison was also made between the proposed model and Sinpiboon and Wongwises' (2002), Xu and Bansal's (2002), and Valladares' (2007b) numerical models.

Figure 15 was drawn to compare the predictions of the proposed numerical model with the experimental data of Pate and Tree (1984b). The proposed model and the experimental data (Pate and Tree 1984b) are in good agreement. In the investigation of Pate and Tree (1984b) cold air was flowed inside the suction line, counter to the flow of R-12 in the capillary tube. The cold air received heat from the capillary tube, was heated, and left the heat exchanger at a higher temperature. The directions of the flow of R-12 in a capillary tube and air in the suction line are shown by the arrows in the Figure 15. As noted in the present case, the vaporization of refrigerant starts at the inlet of the heat exchange region. The refrigerant pressure falls inside the capillary tube's diabatic region, as well as the adiabatic region, due to friction and fluid acceleration as a result of increase in vapor quality. There is a fall in refrigerant temperature inside the capillary tube in the downstream direction because of the heat transfer from capillary tube to suction line. Further, as seen in Figure 15, there is a sharp fall in refrigerant temperature in the adiabatic region near the exit of the capillary tube. The pressure fall in the final adiabatic region is quite high, leading to a sharp decrease in temperature. It is a known fact that heat transfer in the diabatic region of the capillary tube causes the refrigerant inside the capillary tube to recondense; whereas, the pressure drop effect causes the refrigerant to vaporize. In the final adiabatic region, there is no heat transfer from capillary tube to suction line. Therefore, only pressure drop effect remains in the capillary tube, leading to an increase in vapor quality down the length of the capillary tube until the exit is reached. On the other hand, after receiving heat from the capillary tube, the air temperature in the suction line increases along the heat exchanger length.

[FIGURE 15 OMITTED]

Figures 16 has was drawn to compare the predictions of the proposed model with the experimental data of Mendoca et al. (1998). The difference in Figures 16a and 16b is the inlet adiabatic inlet capillary tube length. In Figure 16a it is taken as 1.07 m; whereas, in Figure 6b, it is 0.53 m (almost half of the first case). Apart from the difference in initial adiabatic lengths, another difference is that of the suction-line inlet temperatures. The direction of flow in the capillary tube and in the compressor suction line is shown by means of arrows. Figure 16a was drawn for the suction-line inlet temperature of 268.15 K, while Figure 16b was drawn for the suction-line temperature of 262.05 K. In fact, the temperature difference for the capillary tube and the suction line is higher in Figure 8. Because of this, the slope of the refrigerant temperature curve is higher in the case of Figure 16b. Therefore, the rate of heat transfer is higher for the case in Figure 16b as compared to that in Figure 16a. In the first adiabatic length of the capillary, [L.sub.in], the refrigerant temperature is constant, as the refrigerant enters the capillary tube with a sufficiently high subcooling. As a result of heat transfer, the refrigerant temperature along the capillary tube length decreases; whereas, that along the compressor suction line increases. In the final adiabatic region of the capillary tube, the refrigerant temperature is constant as long as the refrigerant is in liquid phase and there is a sudden drop in temperature with the onset of vaporization. This drop in the refrigerant temperature continues until the exit of the capillary tube is reached. The proposed model is in good agreement with the experimental data, as numerical mass flow rates are 5.65 and 5.82 kg/h as compared to experimental mass flow rates of 5.44 and 5.37 kg/h for the cases shown in Figure 16a and Figure 16b, respectively. Therefore, the deviations in the numerical and the experimental mass flow rates for Figures 16a and 16b are 3.9% and 8.3%, respectively.

[FIGURE 16 OMITTED]

As also seen in Figure 16b, there is disagreement in the predictions of the proposed model and the actual refrigerant temperature in the final adiabatic region of the capillary tube. However, the predicted temperature of the suction line is in very good agreement with the experimental data. The difference in the numerically obtained temperature is more than 3[degrees]C. The insufficient insulation of the capillary tube in the final adiabatic region may be one of the reasons for this deviation.

Table 7 was drawn to compare the results of the proposed Xu and Bansal (2002) and Valladares (2007) models with Mendoca et al.'s (1998) experimental results for the data shown in Figure 16. In the last column of Table 7, the percentage deviation from Mendoca et al. (1998) experimental mass flow rate is shown.

Table 7. Comparison of Different Models with Mendoca et al.'s (1998) Data Investigators Mass Flow Rate, kg/h Percentage Deviation, % Mendoca et al. (1998) 5.44 0.0 Xu and Bansal (2002) 5.33 -2.0 Valladares (2007b) 5.54 1.8 Proposed model 5.65 3.8

Figures 17 and 18 were drawn to compare the proposed model with the experimental data of Peixoto (1995) and Liu and Bullard (2000). Figure 17 was drawn taking inlet subcooling as the abscissa and refrigerant mass flow rate as the ordinate. The proposed model, as seen in the figure, is in good agreement with Peixoto (1995) experimental data. The accuracy of prediction improves as the inlet subcooling increases--i.e., at high inlet subcoolings, the predicted mass flow rate is closer to the experimental mass flow rates. The proposed model overpredicts the experimental refrigerant mass flow rate up to 5.3%. There is an increase in refrigerant mass flow rate with the rise in capillary inlet subcooling because high inlet subcooling gives a longer single-phase liquid length, and it is a known fact that liquid offers low resistance to flow as compared to that offered by a two-phase liquid and vapor mixture.

[FIGURE 17 OMITTED]

[FIGURE 18 OMITTED]

Figure 18 was drawn to compare the predictions of the proposed model with the experimental data of Liu and Bullard (2000), taking inlet subcooling as the abscissa and mass flow rate through the diabatic capillary tube as the ordinate. Similar trends were observed in this case as well--i.e., the refrigerant mass flow rate increases almost linearly with the inlet subcooling. As in Figure 17, the refrigerant mass flow rate predicted by the Sinpiboon and Wongwises (2002) model is slightly higher than that predicted by the proposed model. As seen in Figure 18, the proposed model is in good agreement with the experimental data of Liu and Bullard (2000). Further, at high inlet subcoolings, the predictions of the proposed model are closer to the experimental mass flow rates of Liu and Bullard (2000). The average percentage deviation of the mass flow rate from the Liu and Bullard (2000) experimental data (decreasing subcooling) predicted by the proposed model is less than 3%.

Further, the comparison between the proposed model and Sinpiboon and Wongwises' (2002) numerical model are displayed in Figures 17 and 18. Sinpiboon and Wongwises' model (2002) shows overpredicts the Peixoto (1995) model's experimental mass flow rate by up to 7.4%, compared to 5.3% overpredicted by the proposed model. The proposed model gives an under-prediction of nearly 2% as compared to the Sinpiboon and Wongwises (2002) model. The predictions of the proposed model are considered more accurate, as the proposed model takes into account the variation in thermophysical properties of the refrigerant with temperature, even in the single-phase region flowing inside the capillary tube and inside the compressor suction line.

Figure 19 was drawn to compare the predictions of the proposed, Sinpiboon and Wongwises (2002) and Valladares (2007b) numerical models with the experimental data of Peixoto (1995). Figure 19 was drawn taking Peixoto (1995) experimental mass flow rate as the abscissa and percentage deviation from Peixoto experimental data as the ordinate. The predictions from the proposed model are within the error band of [+ or -]5%. Also, the proposed model predicts the refrigerant mass flow rate closer than do the Valladares (2007b) and Sinpiboon and Wongwises (2002) models.

[FIGURE 19 OMITTED]

Figure 20 was plotted taking distance from capillary tube inlet as the abscissa and temperature as the ordinate for capillary tube lengths of 3.2 and 2.4 m. The inlet subcoolings in Figures 20a and 20b are also different. There is good agreement in the experimental data and the predictions of the proposed numerical model. The temperature in the inlet adiabatic region of the capillary tube is constant; whereas, in the diabatic region of the capillary tube, the temperature falls continuously. It is also noted that the vaporization takes place in the final adiabatic region of the capillary tube. Before vaporization, the refrigerant temperature is constant in the final adiabatic length of capillary tube. After vaporization, there is a large drop in temperature on account of an increase in the pressure drop due to onset acceleration pressure drop with the vaporization of the refrigerant. On the other hand, the refrigerant temperature along the compressor suction line increases after receiving heat from the capillary tube. The overprediction in the refrigerant mass flow rate by the proposed numerical model is only 3.8% for a 3.2 m capillary tube and 3.6% for a 2.4 m capillary tube.

[FIGURE 20 OMITTED]

CONCLUSIONS

The following conclusions can be drawn from the investigation:

1. It was found that the flow behavior of diabatic capillary tubes is entirely different from that of adiabatic capillary tubes. The trends of the effects of parameters like tube diameter, tube length, and inlet subcooling are similar for both diabatic and adiabatic capillary tubes. However, the effect of coiling seems to be suppressed by the effect of suction-line inlet superheat in the case of diabatic capillary tubes.

2. An empirical correlation for the refrigerant mass flow rate through a given diabatic capillary tube geometry--namely straight or helical--was developed. It was found that the proposed correlation predicts the refrigerant mass flow rate in the error band of [+ or -]5% of the measured experimental mass flow rate.

3. The proposed model was validated with the experimental data of Pate and Tree (1984b), Mendoca et al. (1998), Peixoto (1995), and Liu and Bullard (2000) with a good degree of agreement. There is very good agreement between the predictions of the proposed model and those of the Pate and Tree (1984a) model; whereas, the average percentage deviation between the predicted mass flow rate and Liu and Bullard's (2000) experimental mass flow rate is less than 3%. Further, the proposed model overpredicts the mass flow rate by up to 5.3% as compared with Peixoto's (1995) experimental data. The deviations from Mendoca et al. (1998) experimental data were found to be approximately 4%.

4. The proposed model was also compared with Sinpiboon and Wongwises' (2002) model and the two were found to be very close. The proposed model gives an underprediction of nearly 2% compared to that given by Sinpiboon and Wongwises' (2002) model.

5. The predictions from the proposed model are closer to Peixoto's (1995) experimental data than they are to the predictions from Valladares' (2007b) and Sinpiboon and Wongwises' (2007) numerical models.

6. The proposed model was compared with the present experimental data and found to be in good agreement.

NOMENCLATURE

A = cross sectional area of capillary tube, [m.sup.2]

[c.sub.p] = specific heat, J/kg*K

d = capillary tube internal diameter, m

[DELTA][T.sub.sub] = capillary inlet subcooling, [degrees]C

e = roughness height, m

f = friction factor

G = mass velocity, [rho]V, kg/[m.sup.2]*s

h = enthalpy, J/kg

k = entrance loss coefficient, 1.5

k = thermal conductivity, W/m*K

L = capillary tube length, m

[L.sub.hx] = heat exchanger length, m

[L.sub.f] = adiabatic length near capillary exit

m = mass flow rate, kg/s

N = number of elements in heat exchange region

n = number of element in adiabatic two-phase region

P = pressure, Pa

Pr = Prandtl number, [c.sub.p][mu]/k

Re = Reynolds number, GD/[mu]

s = entropy, J/kg*K

T = temperature, [degrees]C (K)

V = fluid velocity, m/s

v = specific volume, [m.sup.3]/kg

x = quality

Greek Letters

[alpha] = void fraction

[mu] = viscosity, kg/m*s

[rho] = density, kg/[m.sup.3]

[[tau].sub.w] = Wall shear stress, f[rho][V.sup.2]/8, N/[m.sup.2]

Subscripts

c = capillary tube

f = liquid phase

g = vapor phase

fg = liquid-vapor mixture

in = capillary tube inlet

k = condenser

o = evaporator

s = suction-line

sp = single-phase

tp = two-phase

w = wall

REFERENCES

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Mohd. Kaleem Khan, PhD

Ravi Kumar, PhD

Pradeep K. Sahoo, PhD

Associate Member ASHRAE

Received June 3, 2008; accepted June 4, 2008

Mohd. Kaleem Khan is a lecturer in the Department of Mechanical Engineering, Thapar University Patiala, India. Ravi Kumar and Pradeep K. Sahoo are associate professors in the Department of Mechanical and Industrial Engineering, Indian Institute of Technology, Roorkee, India.

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Author: | Khan, Mohd. Kaleem; Kumar, Ravi; Sahoo, Pradeep K. |
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Publication: | HVAC & R Research |

Article Type: | Report |

Geographic Code: | 1USA |

Date: | Nov 1, 2008 |

Words: | 10437 |

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