Non-adiabatic capillary tube flow with isobutane

Non-adiabatic capillary tube flow with isobutane

Cl�aaudio Melo a,*, Luis Antoonio Torquato Vieira a, Roberto Horn Pereira b,1

a NVRA Department of Mechanical Engineering, Federal University of Santa Catarina,

880400-900 Florian�oopolis, SC, Brazilb Embraco S.A. 1020, Rui Barbosa Street, 89219-901 Joinville, SC, Brazil

Received 22 August 2001; accepted 7 March 2002

Abstract

This work reports the results of an experimental study on concentric capillary tube–suction line heatexchangers commonly used as expansion devices in household refrigerators and freezers. Heat exchangerperformance (mass flow rate and suction line outlet temperature) with the hydrocarbon HC-600a wasexperimentally evaluated for a range of heat exchanger geometries and operating conditions. The tests wereplanned and performed following a statistically based methodology. Based on the resulting database em-pirical correlations were developed to predict the refrigerant mass flow rate and the suction line outlettemperature.� 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Capillary tube; Isobutane; Expansion device; Heat exchanger

1. Introduction

Nowadays every household refrigerating system employs a capillary tube for metering the flowof liquid refrigerant. The capillary tube is simply a small bore tube connecting the condenser tothe evaporator. Liquid refrigerant flows into one end and expands down to the evaporator pres-sure. In doing so it meters refrigerant at the desired mass flow rate.Such tubes are usually placed in contact with the suction line forming a counterflow capillary

tube–suction line heat exchanger. This heat exchanger provides heat exchange to the low-pressurevapor passing through the suction line from the high-pressure refrigerant passing through the

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*Corresponding author. Tel.: +55-48-234-5691; fax: +55-48-234-5166.

E-mail addresses: [email protected] (C. Melo), [email protected] (R.H. Pereira).1 Tel.: +55-47-441-2671; fax: +55-47-441-2775.

1359-4311/02/$ - see front matter � 2002 Elsevier Science Ltd. All rights reserved.

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capillary tube, increasing evaporator capacity and preventing slugging of the compressor andsweating of the suction line.Two types of heat exchanger are usually found: lateral and concentric. The capillary tube is

soldered to the suction line in the lateral arrangement, while it passes inside the suction line in theconcentric arrangement. The contact between the capillary tube and the suction line does notoccur along the entire length of the capillary tube. This creates one region upstream and otherdownstream of the heat exchanger region, where the capillary tube may be considered as adiabatic(see Fig. 1).With the phaseout of CFC-12 several research works were performed with such heat ex-

changers, mostly with HFC-134a [1–7]. However there has been much resistance in adoptingHFC-134a for household refrigerating systems in some parts of the globe, specially in Europewhere HC-600a has become the dominant fluid. For this refrigerant capillary tube performancewith heat transfer to the suction line has been largely ignored.The study presented herein focuses on an experimental evaluation of concentric capillary tube–

suction line heat exchanger performance with HC-600a. Several capillary tube length and dia-meter combinations were tested with various suction line lengths, diameters and positions using atest loop that provided full control of the boundary operating conditions. The analysis of thecollected database provided significant insight into the behavior of a concentric capillary tube–suction line heat exchanger and also provided enough data to explore the relationship between theindependent (geometry and operating conditions) and dependent (mass flow rate and suction lineoutlet temperature) variables.

2. Experimental apparatus

A schematic diagram of the experimental apparatus is shown in Fig. 2 and has been describedin detail by Gonc�alves [8] and Mendonc�a [4].

Fig. 1. Concentric and lateral heat exchangers.

1662 C. Melo et al. / Applied Thermal Engineering 22 (2002) 1661–1672

This is a conventional refrigeration cycle consisting primarily of two hermetic reciprocatingcompressors (COMP1, COMP2), a water cooled condenser (COND), one evaporator (EVAP2),and four expansion devices (TCI, TCNI, VP1, VP2). The first of the expansion devices, TCI is thecapillary tube being tested, whereas TCNI is an uninstrumented capillary tube that is used onlywhen the test section is under maintenance. The other two valves (VP1 and VP2), bypass thedesired amount of refrigerant to control the evaporating pressure. The pressure in the condenser isestablished by a water flow, controlled by a pressure regulating valve (VPC). The subcooling ischanged by using a subcooler (SUB) and a PID controlled electric heater (AETC). Two oilseparators (SO1, SO2) and an oil filter (FO) are placed between the compressor and the con-denser. The refrigerant/water–glycol heat exchanger (EVAP1), the needle valve (VG) and themixer (MS) are used to establish the refrigerant temperature at the inlet of the suction line. Thetemperature of the water–glycol supplied to the heat exchanger is controlled by a constant tem-perature circulating bath (BT). Leaving the subcooler, a Coriolis type mass flow meter (FLUX)is installed to measure the refrigerant mass flow rate, with an uncertainty of �0.03 kg/h.The heat exchanger geometry (length, L, and diameter, D, of the capillary tube, heat exchanger

length, Ltc, adiabatic inlet length, Le, diameter of the suction line, Ds) is indicated in Fig. 3. Themeasurement stations for the boundary operating conditions (inlet (2) and evaporating (9) pres-sures, refrigerant temperature at the inlet (11) and outlet (19) of the suction line) are also indicatedin Fig. 3. The subcooling is calculated from the temperature (1) and pressure (2) measurements atthe inlet of the capillary tube. Additional measurement stations for the refrigerant temperature (6)and pressure (5) at the outlet of the capillary tube and for the refrigerant pressure at the outlet of

Fig. 2. Experimental apparatus.

C. Melo et al. / Applied Thermal Engineering 22 (2002) 1661–1672 1663

the suction line (21) are also shown in Fig. 3. The refrigerant temperature at the inlet and outlet ofthe suction line is measured by T-type immersion thermocouples in order to avoid heat con-duction errors as pointed out by Mendonc�a [4]. Thermocouples are also placed along the length ofthe capillary tube and suction line to determine the wall temperature distribution. A specialmeasuring station (14) for the suction line fluid temperature (16) and capillary tube wall tem-perature (15) in the diabatic region of the heat exchanger is also shown in Fig. 3.Strain gauge pressure transducers are used to measure the absolute pressures, with an uncer-

tainty of �0.02 bar. The temperatures are measured by T-type thermocouples, 0.13 mm in dia-meter, with an uncertainty of �0.2 �C. The output signals from the transducers, thermocouplesand flow meter are recorded through a computerized data acquisition system. Further details ofthe instrumentation can be found in [6].A special care [9] was given to the capillary tube internal diameter measurements, since the

manufacturer’s nominal tube diameter was found to be quite different, in practice, from the actualdiameter. The uncertainty associated with these measurements was found to be less than �0.02mm.The test section is made of copper and was placed inside a 0:3� 0:3 m2 cross-sectional area

wood box, filled with glass wool [9]. The surrounding air temperature was maintained at 20� 2�C. The capillary tube wall roughness was not measured, but as the tube manufacturer was thesame of a previous work [9] it is believed that it ranges from 0.6 to 1.0 lm.

3. Experimental test plan

In order to reduce the experimental effort the test matrix was constructed based on a statisticaltechnique, known as two-level fractional factorial design [10], used with success by several re-

Fig. 3. Test section.


searchers [3,6,11,12]. The main advantage of this approach was to obtain the maximum infor-mation from a minimum amount of experimental data.

3.1. Factorial design

The factorial design is a statistical method that evaluates the combined effects of two or moreindependent variables (factors) on the dependent (response) variables. The information given bythe factorial design is therefore more complete than the one obtained from a one-factor-at-a-timeapproach.Eight factors were chosen for the present study because of their potential to affect refrigerant

mass flow rate and heat transfer: inlet pressure (Pin), subcooling (Sub), suction line inlet temper-ature (Tin), internal diameter of the capillary tube (D), internal diameter of the suction line (Ds),length of the capillary tube (L), length of the heat exchanger (Ltc), adiabatic inlet length (Le). Thewall roughness of the capillary tube was not taken as an independent variable because the com-mercial tubes are available only in a limited band of roughness, usually from 0.6 to 1.0 lm [9].As mentioned previously the test matrix was constructed based on a two-level fractional fac-

torial design that requires only a fraction (1/16) of the experimental runs of the complete two-levelfactorial design (28); specifically 16 of the possible 256 heat exchanger geometry and boundaryoperating conditions combinations. The disadvantage of this approach was the impossibility todifferentiate between some of the confounded two-factor interaction effects [10].

3.2. Test matrix

The low and high levels of each variable are indicated in Table 1 by the ‘‘)’’ and ‘‘þ’’ signs,respectively. The signs of the first four columns were supplied by the fractional factorial design,

Table 1

Test matrix

Test Variable

1 2 3 4 5 6 7 8

1 ) ) ) þ þ þ ) þ2 þ ) ) ) ) þ þ þ3 ) þ ) ) þ ) þ þ4 þ þ ) þ ) ) ) þ5 ) ) þ þ ) ) þ þ6 þ ) þ ) þ ) ) þ7 ) þ þ ) ) þ ) þ8 þ þ þ þ þ þ þ þ9 þ þ þ ) ) ) þ )10 ) þ þ þ þ ) ) )11 þ ) þ þ ) þ ) )12 ) ) þ ) þ þ þ )13 þ þ ) ) þ þ ) )14 ) þ ) þ ) þ þ )15 þ ) ) þ þ ) þ )16 ) ) ) ) ) ) ) )


whereas the signs of the last four columns were derived by multiplication of the individual signs ofthe first four columns, respecting the following combinations: 234 ¼ 5; 134 ¼ 6; 123 ¼ 7; 124 ¼ 8[10].Each of the 16 heat exchangers was prepared in the same manner. The tests were performed in a

random order and using identical procedures [6]. Besides the 16 matrix tests, 14 additional testswere also performed in order to check the assumption of linear variation of the dependentvariables.The complete set of experimental data is given in Table 2, where the variables Pout; Texp and _mmexp

represent the refrigerant pressure at the outlet of the capillary tube, the fluid temperature at theoutlet of the suction line and the refrigerant mass flow rate, respectively. The wall thickness of the0.553 and 0.766 mm I.D. capillary tube is 0.624 and 0.592 mm, respectively. The wall thicknessof the 6.30 and 7.86 mm I.D. suction line is 0.82 mm and 0.99 mm, respectively.

4. Analysis of the experimental data

The main and two-factor interaction effects on the refrigerant mass flow rate and suction lineoutlet temperature were calculated using Yate’s algorithm [10] and are shown in Figs. 4–7.The main effects were confounded with three and higher order insignificant interactions. Be-

cause of that the significant main effects are easily recognized in Figs. 4 and 5. The dependency ofrefrigerant mass flow rate on the main effects (Pin, D, Ltc, L and Sub) was significant, as well as thedependency of the temperature at the outlet of the suction line on the main effects (Pin, D, Ltc, Ds

and Sub).On the other hand the two-factor interactions were confounded with other two-factor inter-

actions. This complicated the task of identifying the significant two-factor interaction effects. Ifthe two-factor interactions became really important, additional experiments may be required.The experience from previous work on heat exchanger performance [2,4,6] provided guidance

in electing the variables given in Table 3, as the significant variables for the present study.

5. Empirical correlations

Empirical correlations for the refrigerant mass flow rate and suction line outlet temperature,including all the statistically significant effects, were determined from the 16 matrix test points andare given below in Eq. (1) and (2), respectively. The units are the ones indicated in Table 2.

_mmemp ¼ �7:1650þ 0:1755Pin þ 0:8454Lþ 12:7375Dþ 0:0276Sub þ 0:0960Ltc

� 0:0005PinTin � 0:0150SubLe � 1:6512DLþ 0:0024LtcDs ð1Þ

Temp ¼ 10:0861þ 2:3625Pin þ 2:4964Sub þ 5:3390Dþ 11:4987Ltc � 3:1265Ds

þ 0:1446PinDs � 4:4467SubDþ 0:2263TinLtc � 0:0728LLe ð2Þ


Table 2

Experimental data

Test Pin(bar)

Pout(bar)

Sub(�C)

D

(mm)

Tin(�C)

Ltc(m)

L

(m)

Ds

(mm)

Le(m)

Texp(�C)

Temp(�C)

Error

(�C)_mmexp

(kg/h)

_mmemp

(kg/h)

Error

(kg/h)

Matrix tests

1 5.01 0.58 5.7 0.553 )16.0 2.2 4.0 6.30 0.6 26.9 27.1 0.2 0.74 0.88 0.14

2 6.49 0.59 6.6 0.553 )20.7 1.0 4.0 7.86 0.6 17.6 18.0 0.4 1.13 1.05 )0.083 5.03 0.60 10.2 0.553 )19.7 2.2 3.0 7.86 0.6 21.7 21.8 0.1 1.05 1.05 0.00

4 6.51 0.60 10.0 0.553 )15.1 1.0 3.0 6.30 0.6 23.3 22.9 )0.4 1.13 1.16 0.03

5 5.03 0.64 5.0 0.766 )15.2 1.0 3.0 7.86 0.6 10.1 10.5 0.4 2.38 2.46 0.08

6 6.53 0.86 5.0 0.766 )15.2 2.2 4.0 6.30 0.6 29.6 28.9 )0.7 3.02 2.87 )0.157 5.01 0.63 10.0 0.766 )19.1 1.0 4.0 6.30 0.6 9.1 8.8 )0.3 2.09 2.14 0.05

8 6.49 0.79 10.0 0.766 )12.7 2.2 4.0 7.86 0.6 22.4 22.0 )0.4 2.62 2.53 )0.099 6.50 0.90 10.0 0.766 )14.9 1.0 3.0 7.86 0.2 11.6 11.3 )0.3 2.81 2.89 0.08

10 5.01 0.66 9.8 0.766 )14.7 2.2 3.0 6.30 0.2 19.3 19.9 0.6 2.75 2.74 )0.0111 6.53 0.67 5.0 0.766 )13.0 1.0 4.0 6.30 0.2 19.3 19.8 0.5 2.27 2.34 0.07

12 5.03 0.62 5.0 0.766 )20.4 2.2 4.0 7.86 0.2 18.3 17.7 )0.6 2.25 2.22 )0.0313 6.52 0.70 10.0 0.553 )20.4 2.2 4.0 6.30 0.2 29.9 30.1 0.2 1.27 1.31 0.04

14 5.01 0.59 10.0 0.553 )14.9 1.0 4.0 7.86 0.2 14.9 14.4 )0.5 1.00 0.89 )0.1115 6.50 0.60 6.2 0.553 )15.1 2.2 3.0 7.86 0.2 29.3 29.2 )0.1 1.17 1.27 0.10

16 5.02 0.60 5.5 0.553 )19.5 1.0 3.0 6.30 0.2 17.7 17.0 )0.7 0.98 0.85 )0.13

Additional tests

1 5.76 0.78 10.0 0.766 )11.9 2.2 3.0 6.30 0.6 23.8 23.4 )0.4 2.80 2.81 0.01

2 5.78 0.79 9.9 0.766 )14.9 2.2 3.0 6.30 0.6 23.4 22.1 )1.3 2.86 2.82 )0.063 5.02 0.66 6.9 0.766 )18.9 2.2 3.0 6.30 0.2 20.7 20.5 )0.2 2.75 2.68 )0.074 5.39 0.74 7.6 0.766 )14.7 1.0 4.0 6.30 0.6 11.7 13.2 1.5 2.29 2.15 )0.145 5.65 0.67 9.9 0.766 )17.8 1.0 3.0 7.86 0.6 8.3 7.7 )0.6 2.62 2.68 0.06

6 6.11 0.86 8.9 0.766 )14.6 1.0 3.0 7.86 0.2 11.4 11.0 )0.4 2.69 2.79 0.10

7 5.84 0.72 6.9 0.766 )16.0 2.2 4.0 7.86 0.6 21.9 20.9 )1.0 2.43 2.37 )0.068 5.01 0.59 6.1 0.553 )15.5 2.2 4.0 6.30 0.6 25.8 27.4 1.6 0.93 0.88 )0.059 6.51 0.72 7.0 0.553 )15.6 2.2 3.0 7.86 0.2 29.9 29.1 )0.8 1.11 1.20 0.09

10 5.71 0.60 8.2 0.553 )18.6 2.2 3.0 7.86 0.2 29.0 29.0 0.0 1.17 1.29 0.12

11 6.11 0.60 8.1 0.553 )19.7 2.2 3.0 7.86 0.6 27.9 25.5 )2.4 1.14 1.21 0.07

12 6.52 0.60 10.0 0.553 )14.8 1.0 3.0 6.30 0.6 23.3 23.1 )0.2 1.13 1.16 0.03

13 5.93 0.59 8.2 0.553 )16.8 1.0 3.0 6.30 0.6 22.3 20.6 )1.7 1.08 1.03 )0.0514 5.00 0.60 5.8 0.553 )16.6 1.0 3.0 6.30 0.2 18.4 17.6 )0.8 0.98 0.85 )0.13

C.Melo

etal./Applied

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Fig. 4. Main effects on the mass flow rate.

Fig. 5. Main effects on the suction line outlet temperature.

Fig. 6. Two-factor interaction effects on the mass flow rate.


The predicted values ( _mmemp and Temp) given by Eqs. (1) and (2) are compared with the 16 ma-trix test points and with the 14 additional measured data in Table 2. As one can see the abso-lute difference between the mass flow rate calculated and measured values is less than 0.15 kg/hfor the whole set of experimental data. On the other hand the calculations of Eq. (2) are muchcloser to the matrix than to the additional measured data. This may means that the assumptionof linear variation of the suction line outlet temperature is not entirely valid within the rangestested.

6. Comparison with the CAPHEAT program

A comparison between the experimental dataset with the mass flow rate predictions of theCAPHEAT program [1,2] is illustrated in Fig. 8. It is shown that the program and the measureddata are in most of the cases within 10%. This level of agreement is in line with similar com-parisons performed by Mendonc�a et al. [5] and Melo et al. [7].The extrapolation limits of Eq. (1), both in relation to the degree of subcooling at the inlet of

the capillary tube as well as to the degree of superheating at the inlet of the suction line, were alsoinvestigated, by comparing the predicted results with the tendency shown by the CAPHEATprogram.Test point #11, from the test matrix, was used as the baseline. Both the subcooling and the

superheating were varied from 0 to 10 �C, keeping all other variables constant. The results arepresented in Figs. 9 and 10 for the subcooling and superheating, respectively.

Fig. 7. Two-factor interaction effects on the suction line outlet temperature.

Table 3

Significant effects

Response variable Main effect Second order effect

_mmexp Pin, D, Ltc, L, Sub PinTin, SubLe, DL, LtcDs

Texp Pin, D, Ltc, Ds, Sub PinDs, SubD, TinLtc, LLe


It can be observed that the behavior of Eq. (1) is quite similar to the behavior of the CAPHEATprogram, except for very small values of subcooling. In this area, however, the tendency deviationgenerates insignificant errors. Similar comparisons were also performed with all other indepen-dent variables of the present study. In all cases Eq. (1) and the CAPHEAT program have shownthe same tendency. This led to the conclusion that Eq. (1) may also be applied to situationsoutside the ranges covered by the factorial design.

Fig. 8. Eq. (1) vs. CAPHEAT program.

Fig. 9. Extrapolation limits of Eq. (1)––Subcooling.


7. Concluding remarks

A very comprehensive experimental research program dealing with concentric capillary tube–heat exchangers has been performed. Heat exchanger performance with HC-600a was exper-imentally evaluated over a wide range of boundary operating conditions and heat exchangergeometries typical of household refrigerators and freezers.Empirical correlations to estimate the refrigerant mass flow rate through the capillary tube and

the suction line outlet temperature were derived from the experimental data. The experimentaldata were quite well reproduced by the derived correlations. In fact the absolute mean deviationerror for the refrigerant mass flow rate and suction line outlet temperature was 0.07 kg/h (5.1%)and 0.6 �C, respectively.It has been shown that the empirical correlation to estimate the refrigerant mass flow rate

through the capillary tube may also be applied to situations outside the ranges covered by thefactorial design. It is anticipated that the proposed correlations will become a powerful tool fordesigners modeling HC-600a refrigeration systems.

Acknowledgements

The authors are grateful to Empresa Brasileira de Compressores (EMBRACO S.A.) for spon-soring this research program. The continued support for this research program from ConselhoNacional de Desenvolvimento Cientifico (CNPq) is also duly acknowledged.

Fig. 10. Extrapolation limits of Eq. (1)––Superheating.


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Non-adiabatic capillary tube flow with isobutane

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