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Experimental investigation of the flow of R-134a through adiabatic and diabatic capillary tubes.

INTRODUCTION

The capillary tube is a commonly used expansion device in low-capacity vapor-compression refrigeration systems (e.g., household refrigerators, window-type air conditioners). Capillary tubes can be classified into two groups on the basis of flow conditions--adiabatic and diabatic capillary tubes. In an adiabatic arrangement, the refrigerant expands from the high-pressure side (condenser) to the low-pressure side (evaporator) with no heat transfer, with surroundings as shown in Figure 1a, A P-h diagram is also drawn in Figure 1a, in which the process of expansion is depicted by the process 3-4, with enthalpy remaining constant in the single-phase liquid region, whereas there is a fall in enthalpy in the two-phase liquid-vapor region. It is because of this fact that a part of total enthalpy gets converted into kinetic energy in the two-phase region. Conversely, in the diabatic arrangement, the expansion is accompanied by the heat exchange between the capillary tube and the compressor suction-line, as shown in Figure 1b. Similarly, also in this case, the P-h diagram shows that there is a continuous fall of enthalpy throughout the process of expansion on account of heat transfer from the capillary tube to the suction line. The refrigerant usually enters the capillary tube in a subcooled state, and the pressure drop causes the flow through the capillary tube divided into two distinct regions--the single-phase liquid region in the initial part, and the two-phase liquid-vapor region in the remaining part. In the case of the diabatic capillary tube, and the compressor-suction line being colder, the heat transfer from the capillary tube to the suction line causes the liquid length to increase, thereby causing the refrigerant mass flow rate through the capillary tube to increase. Consequently, the refrigerant enters the evaporator with low vapor quality, which ultimately results in an increased refrigerating effect. On the other hand, on receiving the heat from the capillary tube, the saturated vapor inside the suction line entering the heat exchanger gets superheated, thus diminishing the chances of liquid refrigerant entering the compressor.

[FIGURE 1 OMITTED]

Adiabatic capillary tubes have been investigated by a number of researchers (1-15). The studies of the flow of refrigerants through straight capillary tubes were pioneered by Bolstad and Jordan (1). Mikol (3) conducted an extensive study on the flow of refrigerants R-12 and R-22 through an adiabatic straight capillary tube. The glass capillary tube was 1.244 mm (0.049 in.) in diameter and 1.83 m (6 ft) in length, and a delay of vaporization was reported. After vaporization, homogeneous two-phase flow was also observed by Mikol (3). A number of correlations for the prediction of mass flow rate of various refrigerants through adiabatic capillary tubes have been proposed. Bansal and Rupasinghe (5) presented an empirical correlation for sizing both adiabatic and diabatic capillary tubes as well. The refrigerant mass flow rate predicted by the proposed model was found to be in the error band of [+ or -]8% for both types of capillary tubes. An experimental investigation for flow refrigerants such as R-12, R-134a, and R-600a was conducted by Melo et al. (6). They proposed separate correlations for each of the above-mentioned refrigerants. Also, a combined correlation for all of these refrigerants was also developed to predict the refrigerant mass flow rate. The proposed correlation was then compared with the Wolf et al. (7) correlation. Choi et al. (9) also developed a generalized empirical mass flow rate correlation for the adiabatic capillary tubes, pulling the experimental data of Melo et al. (6), Wolf et al. (7), and Fiorelli et al. (10) together. Further, Choi et al. (11) proposed another modified generalized mass flow rate correlation using R-22, R-407C, and R-290 experimental data of previous researchers. Jabaraj et al. (12) proposed a mass flow rate correlation for the flow of R-22 and M20 (R-407C/R-600a/R-290) through the adiabatic capillary tube. Most recently, Khan et al. (13) proposed a correlation for predicting the mass flow rate of R-134a through adiabatic spiral capillary tube. Apart from experimental research, numerical models are also available to predict the performance of adiabatic capillary tubes. Khan et al. (14-15) have also proposed mathematical models for adiabatic spiral and helical capillary tubes.

Compared to adiabatic capillary tubes, limited literature is available on diabatic capillary tubes (16-25). Pate and Tree (16) studied the diabatic flow of R-12 through the capillary tube with air flowing in the suction line in a counterflow direction, forming an open loop. They did not observe metastable flow in diabatic arrangement, whereas, the metastability was observed during adiabatic flow. Melo et al. (17) conducted the experiments on the concentric diabatic capillary tubes. They proposed separate empirical correlations using a factorial design of experiment technique for the determination of refrigerant mass flow and the suction line outlet temperature. Sinpiboon and Wongwises (18) developed a simple mathematical model for the refrigerant flow through a lateral diabatic capillary tube. The linear quality model of Pate and Tree (19) was used in the analysis of the heat exchange region of the diabatic capillary tube. Xu and Bansal (20) developed a numerical model by dividing the flow domain into numerous control volumes along the length of capillary tubes. Recently, Valladares (24-25) has developed a numerical model for diabatic capillary tubes based considering separated flow model and metastable regions. They validated their model with the existing experimental data.

Therefore, there is a need to conduct an experimental investigation to compare the performance of adiabatic and diabatic capillary tubes operating under similar inlet and exit conditions of capillary tube. The present experimental investigation is an attempt in this direction.

EXPERIMENTAL SETUP AND PROCEDURE

The schematic of experimental setup is shown in Figure 2. The test section (1) was a copper capillary tube, in which the refrigerant expands from high-pressure side to the low-pressure side. From the capillary tube, refrigerant entered the evaporator (2) consisting of a copper coil submerged in a water tank. A 5 kW (17,076 Btu/h) capacity electric heater (3) was fitted in the evaporator tank to provide heat load to the evaporator. The heating load was varied through a variac (4). An agitator (5) was also was fitted in the tank to maintain the uniform bulk temperature of water. The vapor emerging from the evaporator was sent to the liquid accumulator (6) in order to avoid liquid refrigerant to enter the compressor (7). The compressor (7) was run by means of a three-phase electric motor (8) using a belt-and-pulley-type arrangement. The high-pressure superheated vapor emerging from the compressor entered through the oil separator (9). The oil free vapor from the separator (9) were condensed in the water-cooled condenser (10). The tap water was circulated in the condenser by means of a centrifugal pump (11). The high-pressure saturated liquid from the condenser was collected in a receiver (12), to ensure a continuous supply of refrigerant to the capillary tube. The unwanted solid particles and moisture in the refrigerant were removed through a drier-cum-filter (13). The mass flow rate of high-pressure liquid refrigerant was measured by four rotameters (14) of different ranges. The bank of four rotameters facilitated in covering a wide range of refrigerant flow rate with accurate measurement. A refrigerant subcooler (15) was provided after the rotameters. The chilled water to the subcooler was supplied by means of a separate chiller unit based on the vapor-compression cycle with R-22 as a working fluid. The chiller consisted of a hermetically sealed compressor (16), an air-cooled condenser (17), and a tank for cooling water. A centrifugal pump (18) was used to circulate chilled water through the subcooler (15). To vary the degree of subcooling at the capillary tube inlet, a preheater (19) followed the subcooler (15). In the preheater, resistance heating of tube carrying the refrigerant was done, and the heat input was controlled by a variac (20). A sight glass (21) was provided after the preheater to visualize the state of refrigerant flow. A hand-operated expansion valve (22) was also provided after the condenser (10) to control the refrigerant flow rate in the capillary tube by bypassing the excess refrigerant. A number of hand shut-off valves (23) were provided in between the major components of the experimental setup. Therefore, in case of leak or any repair, the damaged component was retrieved with ease. The temperature at different locations of the setup and the test-section was measured by means of copper-constantan (T-type) thermocouples (24), while the pressure of the refrigerant was measured with pressure gauges (26) as well as pressure transducers (27) using pressure headers (25). Furthermore, the pressure at the suction and discharge of the compressor was measured with separate bourdon tube pressure gauges.

[FIGURE 2 OMITTED]

The test section, as shown in Figure 3, was a 6.4 m (21.0 ft) capillary tube out of which 5.6 m (18.37 ft)of the tube was brazed with a compressor suction line of 6.35 mm (0.25 in.) diameter to form a counterflow heat exchanger. Thus, the initial and final adiabatic lengths are taken as 0.4 m (1.31 ft) each. Furthermore, a copper tape was wrapped on the two brazed tubes to promote the heat exchange between the capillary tube and the compressor suction line. The test section was completely insulated by a layer of ceramic wool. Figure 3 also shows the cross-section of the capillary tube/suction line heat exchanger with copper tape wrapped around the two tubes.

[FIGURE 3 OMITTED]

The experiments were conducted on capillary tubes under adiabatic and diabatic conditions. Therefore, the experimental setup was designed in such a way that the same test section behaved as adiabatic capillary tube or diabatic capillary tube by operating a set of hand shut-off valves fixed across the test section on the compressor suction line. The test section was fitted in the experimental setup by means of hand shut-off valves placed across the capillary tube and in the compressor suction line as well. The test section acted as an adiabatic capillary tube when there was no flow of refrigerant in the suction line of the test section, i.e., valves V1 and V2 were closed. The refrigerant was bypassed by opening valve V3, shown in Figure 4. The same capillary tube acted as the diabatic capillary tube when valves V1 and V2 were open and V3 was closed.

[FIGURE 4 OMITTED]

Table 1 shows the range of input parameters of the present experimental investigation. A total of three test sections for instrumented (with pressure taps) capillary tubes and one test section for non-instrumented (without pressure taps) capillary tube were fabricated. For each test section, the inlet pressure was maintained at 740 kPa (107.3 psia), and inlet subcooling was varied at four to five levels in the range of 0[degrees]C to 25[degrees]C (32[degrees] to 77[degrees]F). Furthermore, for each test section, the studies were carried out for six different capillary tube lengths obtained by cutting 0.8 m (2.62 ft) length of capillary tube after each run. Therefore, for every test section, 24 to 30 test runs were conducted for adiabatic arrangement, and the same number of test runs were conducted for diabatic flow arrangement. Hence, a total of 205 test runs were conducted during the entire experimental investigation. The uncertainties in the measurement of various quantities are shown in Table 2.
Table 1. Range of Input Parameters

                                   Selected Range

Parameters           Adiabatic                     Diabatic

              Instrumented        Non-      Instrumented   Non-
                             Instrumented                  Instrumented

d, mm         1.12, 1.40,    1.40 (0.055    1.12, 1.40,    1.40 (0.055
              1.63 (0.044,   in.)           1.63 (0.044,   in.)
              0.055, 0.064                  0.055, 0.064
              in.)                          in.)

* L, m        6.4 to 2.4     6.4 to 2.4     6.4 to 2.4     6.4 to (21.0
              (21.0 to 7.87  (21.0 to 7.87  (21.0 to 7.87  to 7.87 ft)
              ft)            ft)            ft)

[delta]       0 to 25 (32    0 to 25 (32    0 to 25 (32    0 to 25 (32
[T.sub.sub],  [degrees]F to  [degrees]F to  [degrees]F to  [degrees]F
[degrees]C    77 [degrees]   77 [degrees]   77 [degrees]   to 77
              F)             F)             F)             [degrees] F)

[P.sub.in],   740 (107.3     740 (107.3     740 (107.3     740 (107.3
kPa           psia)          psia)          psia)          psia)

Table 2. Uncertainties in the Measured Parameters

Parameters                 Instruments             Uncertainty

Temperature             Thermocouple (T-Type)   0.1[degree]C
                                                (32.18[degree]F

Pressure                Pressure gauge (4       6.87 kPa (1.0 psia)
                        Nos.)

                        pressure transducer (4  0.25% FS (2 MPa [290
                        Nos.)                   psi])

Mass flow rate          Analog rotameters (3    0.5 LPH
                        Nos.)                   (0.0176f[t.sup.3]/h

                        digital rotameter (1    1% FS (50 LPH [1.76
                        No.)                    f[t.sup.3] /h])

Capillary tube length   Steel rule              1.0 mm (0.0394 in.)

Capillary tube          Toolmaker's microscope  0.01 mm ([3.94.sup.-4]
diameter                                        in.)

Internal surface        Surface profilometer    0.01 [mu]m
roughness of capillary                          ([3.94.sup.-7] in.)


RESULTS AND DISCUSSION

The experiments have been mainly conducted on instrumented (with pressure taps) capillary tubes. However, for the sake of comparison, the experiments are also carried out on non-instrumented (without pressure taps) capillary tubes. It has already been shown that the effect of pressure taps on the refrigerant mass flow rate is so small that it can be neglected (13), as the deviations in the mass flow rate is of the order of uncertainty in the measurement of mass flow rate. However, the data of non-instrumented capillary tube have been used in the development of empirical correlations.

The effect of capillary tube length, capillary tube diameter, and inlet subcooling on the mass flow rate of R-134a through adiabatic and diabatic capillary tube has been shown in Figures 5 and 6, respectively.

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

Figure 5 was drawn to study the effect of capillary tube length, diameter, and inlet subcooling on the mass flow rate of R-134a through adiabatic capillary tube. A number of observations have been made from Figure 5, and they are as follows:

* For all of the capillary tube diameters and lengths, an increase in inlet subcooling increases the refrigerant mass flow rate. At the capillary tube inlet, refrigerant is in a liquid state and, at the exit of the capillary tube, the refrigerant is in the two-phase liquid vapor mixture of quality. Therefore, the entire length of the capillary tube can be divided into two parts. The first part is the single-phase liquid region, and the remaining part is a two-phase liquid-vapor mixture. It is obvious that high capillary inlet subcooling leads to more length of liquid region inside the capillary tube. It is a known fact that liquid offers a lower resistance to the flow in comparison to a two-phase liquid vapor mixture. The longer the liquid length of the capillary tube, the higher will be the refrigerant mass flow rate.

* Further, it has been observed that the rate of change in refrigerant mass flow rate with inlet subcooling is nearly constant for all capillary tube lengths and for a given capillary tube diameter. However, the variation in refrigerant mass flow rate is steeper for large diameter tubes. For the change of subcooling from approximately 0.5[degrees]C to 25[degrees]C (32.9[degrees]F to 77[degrees]F) for the capillary tube diameters 1.12, 1.40, and 1.63 mm (0.044, 0.055, 0.064 in.), the average rise in refrigerant mass flow rate is 67%, 70%, and 75%, respectively.

* For a given length of capillary tube, the increase in tube diameter results in the rise of refrigerant mass flow rate in a significant manner. For 10[degrees]C (50[degrees]F) inlet subcooling, as the tube diameter is increased from 1.12 to 1.63 mm, the refrigerant mass flow rate has increased by 191% and 182% for the capillary tube length of 6.4 m (21.0 ft) and 2.4 m (7.87 ft).

* For a given capillary tube diameter with a decrease in capillary tube length, refrigerant mass flow rate increases considerably. For 10[degrees]C (50[degrees]F) inlet subcooling, when the capillary tube length is reduced from 6.4 m (21.0 ft) to 2.4 m (7.87 ft), the refrigerant mass flow rate for capillary tube diameters 1.12, 1.40, and 1.63 mm (0.044, 0.055, 0.064 in.) has increased by 65%, 63%, and 60%, respectively. So, in short, the flow capacity of capillary tube reduces significantly when either the capillary length is increased or the capillary bore is reduced.

The flow of R-134a inside the capillary tube becomes non-adiabatic or diabatic when the capillary tube is in thermal contact with the compressor suction line, forming a counter-flow heat exchanger. For this reason, diabatic capillary tubes are often termed as capillary-tube/suction-line heat exchangers. In the present case, for each capillary tube length, the initial 0.4 m (1.31 ft) and last 0.4 m (1.31 ft) capillary tube lengths are adiabatic. The remaining length of the capillary tube has been bonded with the compressor suction line. Therefore, the difference between the total capillary length, L, and the bonded capillary length, [L.sub.hx], is always 0.8 m (2.62 ft). The effect of capillary tube geometry, i.e., tube diameter, tube length, and inlet subcooling on the refrigerant mass flow rate through diabatic capillary tube have been investigated. The pattern of experimental investigation was the same as it was for the adiabatic capillary tubes. For diabatic capillary tubes, the parameters also influencing the refrigerant mass flow rate are (a) the length of heat exchange between the capillary tube and the compressor suction line, [L.sub.hx], and (b) the compressor suction-line inlet superheat, [AT.sub.sup]. However, the suction-line inlet superheat is not a controlled parameter in the present investigation. This compressor suction-line inlet superheat has an interfering effect on the refrigerant mass flow rate through the diabatic capillary tubes. The capillary inlet subcooling has been varied in the range 0[degrees]C to 25[degrees]C (32.9[degrees]F to 77[degrees]F), whereas, the variation in the suction line inlet superheat has been noted to be in the range of 0[degrees]C to 19[degrees]C (32[degrees]F to 66.2[degrees]F).

Figure 6 was drawn to show the effect of various parameters on the refrigerant mass flow rate through a diabatic capillary tube. It is clear from the figure that the trend of characteristic curves is nearly similar to that observed for adiabatic capillary tubes. The following observations were made in Figure 6:

* The mass flow rate of R-134a through capillary tubes increases with the rise in capillary inlet subcooling. For all capillary tube lengths of 4.0 m, as the inlet subcooling increases from 1[degrees]C to 20[degrees]C (33.8[degrees]F to 68[degrees]F), the refrigerant mass flow rate increases by 56%, 57%, and 45% for capillary tubes of diameter 1.12, 1.40, and 1.63 mm (0.044, 0.055, 0.064 in.), respectively. The increase in mass flow rate is attributed to the increased liquid length for high inlet subcooling. It is a known fact that the resistance to the flow of liquids is less than that for two-phase liquid-vapor mixture or pure vapor. Hence, the refrigerant mass flow rate is more due to the longer length of single-phase liquid region inside the capillary tube as in the case of the high capillary inlet subcooling condition.

* The mass flow rate of R-134a increases with the increase in tube diameter for all the lengths and inlet subcoolings. In fact, for 10[degrees]C (50[degrees]F) inlet subcooling, as the capillary tube diameter increases from 1.12 to 1.63 mm (0.044 to 0.064 in.), the refrigerant mass flow rate increases in a range of 160% to 190% for all capillary tube lengths. The reason for the increase in mass flow rate with the increase in tube diameter is attributed to the increased flow capacity of the capillary tube.

* The mass flow rate of R-134a increases with a reduction in capillary tube length for all of the capillary tube diameters. At 10[degrees]C (50[degrees]F) inlet subcooling, as the capillary tube length is reduced from 6.4 to 2.4 m (21.0 to 7.87 ft), the refrigerant mass flow rate is increased by about 22% for tube diameter 1.12 mm (0.044 in.), and 34% for the tube diameters 1.40 and 1.63 mm (0.055 to 0.064 in.). The increase in the mass flow rate with the decrease in capillary tube length is due to the rise in flow capacity of the capillary tube. It has also been observed the effect of tube length is significant at high capillary inlet subcooling. Also, for 1.63 mm (0.064 in.) diameter tube, the effect of tube length is quite significant.

* Unlike adiabatic capillary tubes where the mass flow rate varies almost linearly with the inlet subcooling, as is the case of diabatic capillary tubes, this behavior seems somewhat nonlinear. The reason is because most evaporators do not have good mixing of refrigerant at the exit of the evaporator. Flow measurements at superheat conditions below 7[degrees]C (44.6[degrees]F) are likely to be in error. At low superheat conditions, refrigerant droplets can be carried along with superheated vapors. The results above 7[degrees]C (44.6[degrees]F) appear to be linear.

* It can also be observed that the mass flow rate increases with the fall in suction-line inlet superheat and vice versa. The reason is when the suction-line inlet superheat is low, the heat transfer from the capillary tube to the suction line is more, which causes the liquid length of the capillary tube to increase. Consequently, the refrigerant mass flow rate will increase.

DEVELOPMENT OF CORRELATION

The empirical correlations for diabatic capillary tubes have been developed to predict the mass flow rate of R-134a through adiabatic as well as diabatic capillary tubes.

The refrigerant mass flow rate through the adiabatic capillary tube depends upon the capillary tube diameter, length, roughness, and degree of subcooling at capillary inlet. Other parameters such as fluid density, viscosity, and specific heat of the refrigerant all have an influence on the mass flow rate. The capillary tubes are only available in a limited band of roughness. Therefore, the roughness is not considered in the development of the correlations.

For adiabatic capillary tube, the mass flow rate can be represented by Equation 1.

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

The total number of variables in the above equation are eight (n = 8), with four repeating variables, d, [[rho].sub.f], [[mu].sub.f], and [c.sub.pf]], i.e., (m = 4). Therefore, the nondimensional [pi]-terms are (n -m = 4) for adiabatic capillary tube.

The number of parameters involved has increased from eight for adiabatic capillary tubes to eleven for diabatic capillary tubes. Three additional parameters are [P.sub.s,in], [DELTA][T.sub.sup], and [L.sub.hx]. Therefore, the refrigerant mass flow rate through diabatic capillary tubes can be defined as a function of the following parameters:

m = f(L, [L.sub.hx] d, [P.sub.in], [P.sub.sin], [DELTA][T.sub.sub], [DELTA][T.sub.sup], [[rho].sub.f], [[mu].sub.f], [c.sub.pf]) (2)

The total number of variables in the above equation are eleven (n = 11), with four repeating variables, d, [p.sub.f], [[mu].sub.f], and [c.sub.pf], i.e., (m = 4). Therefore, the nondimensional 7i-terms are (n - m = 7) for diabatic capillary tube.

The nondimensional 7i-terms have evolved from the above-mentioned parameters using the Buckingham-7i theorem shown in Table 3. The REFPROP 7.0 database (26) has been used to determine the thermodynamic and transport properties of R-134a appearing in Equations 1 and 2.
Table 3. Nondimensinoal Parameters

[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 inlet
               [mue sup 2]f                       pressure

[[pi].sub.3]   [d sup 2] [p.sub.f][p.sub.s, in]/  Suction line
               [mu].sub.f.sup.2]f                 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]      Capilary inlet
               [c.sub.pf][[delta]T.sub.sub]/      subcooling
               [[mu].sub.f.sup.2]f

[[pi].sub.7]  [d.sup.2] [[rho].sub.f.sup.2]       Suction line inlet
              [c.sub.pf][[delta]T.sub.sup]/       superheating
              [[mu].sub.f.sup.2]f


The multiple-variable regression technique was applied to fit the nonlinear power law on 205 test runs having 103 data sets for adiabatic capillary tube and 102 data sets for diabatic capillary tube. Equations 3 and 4 represent the correlations for mass flow rate through adiabatic capillary tube and diabatic capillary tube, respectively.

For adiabatic capillary tube,

[[pi].sub.1] = 0.1126[([[pi].sub.2]]).sup.0.436][([[pi].sub.4]).sup.-0.507] [([[pi].sub.6]).sup.0.186]] (3)

For diabatic capillary tube,

[[pi].sub.1] = 0.0093[([[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] (4)

The proposed correlations represented by Equations 3 and 4 have been compared with the Melo et al. (6) correlation for adiabatic capillary tube and the Wolf and Pate (27) correlation for diabatic capillary tube, respectively.

The Melo et al. (6) correlation for adiabatic capillary tube is given by

[[pi].sub.1] = 0.125[([[pi].sub.2]).sup.0.46][([[pi].sub.4]).sup.-0.552][([[pi].sub.6]).sup.0.178] (5)

The Wolf and Pate (27) correlation for diabatic capillary tube is as follows:

[[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 7 shows the comparison of the mass flow rate predicted by Equation 3 and that by the Melo et al. (6) correlation with the measured experimental mass flow rate for adiabatic capillary tube. The mass flow rate predicted by the proposed correlation lies within the error band of [+ or -]10%. However, the predicted mass flow rate by the Melo et al. (6) correlation overpredicts the mass flow rate in the error band of 0% to 20%. Melo et al. (6) have reported a [+ or -]15% deviation of the predicted mass flow rate from their own experimental mass flow rate. Therefore, it can be concluded that the proposed correlation is in good agreement with Melo et al. (6) study. Thereason for the slight discrepancy may be due to the fact that two correlations have been developed for different ranges of operating conditions, as shown in Table 4.

[FIGURE 7 OMITTED]
Table 4. Range of Operating Parameters

Parameters         Proposed         Melo et al. [6]   Wolf and Pate
                 Correlations         Correlation    [27] Correlation

d, mm         1.12 TO 1Q.63        0.66 to 1.05      0.5 to 1.25
              (0.044 to 0.064 in)                    (0.0197 to 0.0492
                                                     in.)

L,m           2.4 to 6.4 (7.87 to  1.99 to 3.02      Up to 3.3 (10.8
              21.0 ft)             (6.53 to 9.91     ft)
                                   ft

[L.sub.hx],   1.6 to 5.6 (5.25 to  -                 0.5 to 2.5 (1.64
m             18.37 ft)                              to 8.2 ft)

[DELTA]       0.5 to               0 to 16           1 to 17
[L.sub.sub],  25(32.9[degrees]F)   (32[degrees]F to  (33.8[degrees]F.
K                                  60.8[degrees]F)   to 62.6[degrees]F)

[DELTA]       1 to 19              -                 3 to 22
[L.sub.sub],  (33.8[degrees]F to                     (37.4[degrees]F
K             66.2[degrees]F)                        to 71.6[degrees]F)


Figure 8 has been drawn to compare the predictions of the proposed correlation and those of the Wolf and Pate (27) correlation with the measured experimental mass flow rate. The mass flow rate predicted by the proposed correlation (Equation 4) lies within the error band of [+ or -]10%. However, the predictions by the Wolf and Pate (27) correlation have a higher degree of disagreement with the measured experimental mass flow rate. The mass flow rate predicted by the Wolf and Pate correlation (27) lies in the error band of -25% to 15%. In fact, for lower mass flow rates up to 15 kg/h (33 [lb.sub.m]/h), the mass flow rate data predicted by the Wolf and Pate (27) correlation is equally dispersed around the zero error line, while, for higher mass flow rates, the data predicted by the Wolf and Pate correlation (27) lie below the zero error line. The range of operating parameters used by Wolf and Pate (27) is shown in Table 4. In other words, the prediction by the Wolf and Pate (27) correlation has some degree of agreement with that of the proposed correlation for the lower range of capillary tube diameters. For a higher range of capillary tube diameters, the deviations are more. Furthermore, Wolf and Pate (27) reported an error band of [+ or -]10% from their own experimental data.

[FIGURE 8 OMITTED]

CONCLUSIONS

The following conclusions have been drawn:

1. The tube diameter, tube length, and degree of subcooling at capillary inlet on the mass flow rate of R-134a through adiabatic and diabatic capillary tubes have been investigated. For both adiabatic and adiabatic capillary tubes, it has been observed that the refrigerant mass flow rate increases with the increase in tube diameter and inlet subcooling and decrease in tube length.

2. The characteristic curves for diabatic capillary tubes differ from those of adiabatic capillary tubes. In case of adiabatic capillary tubes, the variation of mass flow rate with inlet subcooling is almost linear. Mass flow rate, however, does not vary linearly with inlet subcooling because of the interfering effect of suction-line superheat, which is not a controlled parameter in the present investigation.

3. Separate empirical correlations for the prediction of mass flow rate through adiabatic and diabatic capillary tube have been proposed, compared with the existing correlations of Melo et al. (6) and Wolf and Pate (27) for adiabatic and diabatic capillary tubes, respectively.

NOMENCLATURE

[c.sub.p] = specific heat at constant pressure, J/ kg.K

d = capillary tube diameter, m

[DELTA][T.sub.sub] = capillary inlet subcooling, K

[DELTA][T.sub.sup] = suction-line inlet superheat, K

e = roughness height, m

h = enthalpy, J/kg

L = capillary tube length, m

m = mass flow rate, kg/s

P = pressure, Pa

T = temperature, [degrees]C

Greek Letters

[mu] = dynamic viscosity, kg/ms

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

Subscripts

f = final, liquid phase

hx = heat exchanger

in = inlet, initial

s = suction-line

REFERENCES

(1.) Bolstad, M.M., and R.C. Jordan. 1948. Theory and use of the capillary tube expansion device. Refrigerating Engineering 56:577-83.

(2.) Cooper, L., C.K. Chu, and W.R Brisken. 1957. Simple selection method for capillaries derived from physical flow conditions. Refrigerating Engineering, pp. 37-41.

(3.) Mikol, E.P. 1963. Adiabatic single and two-phase flow in small bore tubes. ASHRAE Journal 5:75-86.

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Mohd. Kaleem Khan, PhD

Ravi Kumar, PhD

Associate Member ASHRAE

Pradeep K. Sahoo, PhD

Member ASHRAE

Mohd. Kaleem Khan is an assistant professor in the Department of Mechanical Engineering, Indian Institute of Technology Patna, Patna, India. Ravi Kumar is an associate professor and Pradeep K. Sahoo is an associate professor in the Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, India.

DISCUSSION

Robert Bittle, Texas Christian University, Fort Worth, TX: You stated that the inlet subcool level was always approached from a lower temperature condition. This is fine for minimizing experimental error. However, did you try approaching the inlet temperature level from a higher temperature? At low [DELTA][T.sub.sc], this can make a difference.

Mohd. Kaleem Khan: Sir, the hysteresis effect has not been studied as far as subcooling at inlet of the capillary tube is concerned. The inlet subcooling is varied in the decreasing mode. The hysteresis effect was studied by Zhou and Zhang (2006) for the flow of R-22 through an adiabatic helically coiled capillary tube.

Zhou, G., and Y. Zhang. 2006. Experimental investigation on hysteresis effect of refrigerant flowing through a coiled adiabatic capillary tube. Energy Conversion and Management 47(18-19):3084-93.
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Author:Khan, Mohd. Kaleem; Kumar, Ravi; Sahoo, Pradeep K
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Date:Jan 1, 2009
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