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Experimental investigation on diabatic flow of R-134a through spiral capillary tube
international journal of refrigeration 32 (2009) 261–271
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Experimental investigation on diabatic flow of R-134a through spiral capillary tube Mohd. Kaleem Khana, Ravi Kumarb,*, Pradeep K. Sahoob a
Department of Mechanical Engineering, Thapar University, Patiala 147 004, India Department of Mechanical and Industrial Engineering, Indian Institute of Technology, Roorkee 247 667, Uttarakhand, India
b
article info
abstract
Article history:
The present experimental investigation has been carried out to investigate the effects of
Received 6 March 2008
various geometric parameters on the mass flow rate of R-134a through diabatic spiral
Received in revised form 3 May 2008
capillary tube. In diabatic flow, the capillary tube is bonded with the compressor suc-
Accepted 24 May 2008
tion-line to form a counter-flow exchanger. The lateral type of diabatic capillary tube
Published online 3 June 2008
has been investigated in the present experimental study. The major geometric parameters investigated are capillary tube diameter, capillary tube length and coil pitch. In addition,
Keywords:
effect of inlet subcooling on the mass flow rate through diabatic spiral capillary tube is
Refrigeration system
also done. A comparison of the performance of diabatic spiral capillary tube has been
Compression
made with adiabatic spiral capillary tube. Generalized empirical correlation for diabatic
R134a
spiral capillary tube has also been proposed. It has been found that the predictions of
Experiment
the proposed correlation lie in the error band of 7%. ª 2009 Elsevier Ltd and IIR. All rights reserved.
Flow Capillary Spiral tube Geometry
Etude expe´rimentale sur l’e´coulement diabatique du R-134a dans un capillaire en spirale Mots cle´s : Syste`me frigorifique ; Syste`me a` compression ; R134a ; Expe´rimentation ; E´coulement ; Capillaire ; Tube he´licoı¨dal ; Ge´ome´trie
1.
Introduction
Capillary tube is a hollow drawn copper tube and is commonly used in refrigeration industry as an expansion device in low capacity refrigeration systems, where the load is fairly constant. Capillary tubes, in vapour compression systems, are used in two configurations – adiabatic and diabatic. In
the present investigation, the idea is to club the advantages of coiling with those of diabatic configuration together. Fig. 1 shows the schematic diagram of vapour compression system using diabatic capillary tube as expansion device. In diabatic configuration, the capillary tube is bonded with the compressor suction-line by means of brazing or soldering to form counter-flow capillary tube/suction-line heat exchanger,
* Corresponding author. Tel.: þ91 1332 285740; fax: þ91 1332 285665. E-mail address: [email protected] (R. Kumar). 0140-7007/$ – see front matter ª 2009 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2008.05.010
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Nomenclature cp d DTsub DTsup e L P p T v
specific heat at constant pressure, J kg capillary tube internal diameter, m capillary tube inlet subcooling, C suction-line inlet superheating, C roughness height, m capillary tube length, m pressure, Pa coil pitch, m temperature, C specific volume, m3 kg1
1
1
K
Greek letters m viscosity, kg m1 s1 r density, kg m3 Subscripts in capillary tube inlet f liquid hx heat exchange
whereas, in adiabatic configuration, there is no heat transfer from the capillary tube to the surroundings. The performance of the system enhances considerably if the capillary tube is used in diabatic mode, as heat transfer from the capillary to the cold suction-line causes a delay in vapourization, i.e., refrigerant leaves the capillary tube with lower vapour quality. This ultimately results in an increase in the refrigerating effect. On the other hand, heat transfer to the suction-line causes superheating of the vapours, thus diminishes the chances of liquid refrigerant entering the compressor and, thus, saving the compressor from being damaged. An exhaustive review of the literature has revealed that diabatic capillary tubes have been scarcely investigated in comparison to adiabatic capillary tubes. Similarly, literature on coiled capillary tubes compared to straight capillary tubes is also scarce. Flow through diabatic capillary tubes was pioneered by Staeblar (1948). They presented capacity balance characteristics to determine the length of diabatic capillary tube for R-12 and R-22. Pate and Tree (1984) studied the
Fig. 1 – Schematic diagram of vapour compression system using diabatic capillary tube for expansion.
diabatic flow of R-12 through the capillary tube with air flowing in the suction-line in counter-flow direction forming an open loop. Melo et al. (2002) conducted the experiments on the concentric diabatic capillary tubes using R-600a as working fluid. Based on their experimental results, they proposed separate empirical correlations for the determination of refrigerant mass flow and the suction-line outlet temperature using factorial design of experimental technique. A number of numerical investigations have been made for the flow through diabatic capillary tubes. Further, the contributions of Mendoca et al. (1998) and Zangari et al. (2000) cannot be ignored as far the flow of R-134a through diabatic capillary tube is concerned. Bansal and Yang (2005) proposed a model for the flow of refrigerant through a diabatic capillary tube. The control volume formulation for the flow through diabatic capillary tube has been adopted by a number of researchers. Escanes et al. (1995) developed a numerical simulation model based on the control volume formulation on the 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 non-critical flow was made iteratively by means of Newton–Raphson algorithm. Mezavila and Melo (1996) presented a numerical model based on the homogeneous two-phase flow model to simulate the flow of refrigerant flow through a non-adiabatic capillary tube. Valladares et al. (2002a) developed a numerical simulation similar to simulation model by Escanes et al. (1995). This simulation model was based on the finite volume formulation of the governing equations. As a sequel of 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 the review of his own numerical work (Valladares et al., 2002a,b). Most recently, Valladares (2007a) has extended his own work (Valladares et al., 2002a,b) on diabatic capillary tubes considering separated flow model and metastable regions. Further, Valladares (2007b) validated their renewed model with the existing experimental data. The effect of coiling on the refrigerant mass flow rate has been discussed by numerous investigators. Kuehl and Goldschmidt (1990) have conducted experiments on the flow of R-22 through adiabatic capillary tubes of straight and coiled geometries. They have concluded that because of the coiling of capillary tube, the refrigerant mass flow rate was reduced by up to 5%. Kim et al. (2002) have studied the flow of R-22 and its alternatives viz., R-407C and R-410A through the straight and helically coiled adiabatic capillary tubes. About 9% reduction in refrigerant mass flow rate through a coiled tube as compared to straight capillary tube was observed. Zhou and Zhang (2006) also found that the mass flow rate through helical capillary tube is reduced by 10% when compared with straight capillary tube. A numerical model was also developed by Zhou and Zhang (2006) for adiabatic helical capillary tube and was validated by their own experimental data. Park et al. (2007) studied the flow of R-22 and its alternatives, R-407C and R-410A. They reported slightly higher reduction in mass flow rates of the coiled capillary
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263
Fig. 2 – Schematic diagram of experimental set-up.
tubes compared, i.e., 5–16% compared to straight capillary tube. They also proposed a generalized mass flow rate correlation for helically coiled capillary tubes. Recently, Khan et al. (2008a) have also presented a mathematical model to evaluate the length of adiabatic helical capillary tube considering the effect of coil pitch as well as that of coil diameter. Studies on the spiral capillary tube were not figured in the literature until Khan et al. (2007) proposed a mathematical model for the computation of length of adiabatic spiral capillary tube. It has been found that because of coiling the length of the capillary tube is reduced considerably for a given set of
input conditions. Most recently, an experimental investigation on the flow of R-134a through an adiabatic spiral capillary tube has been presented by Khan et al. (2008b). They proposed an empirical correlation for the prediction of refrigerant mass flow rate through adiabatic spiral capillary tube. The effect of parameters like capillary tube diameter, capillary tube length, coil pitch and inlet subcooling on the refrigerant mass flow rate through adiabatic spiral capillary tube has been also presented. Considering the scarcity of literature on diabatic coiled capillary tube, the present investigation has been conducted
Fig. 3 – Spiral test-section and its cross-section.
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Table 1 – Range of input parameters Parameters
Selected range Straight
d, mm La, m Lhx, m p, mm DTsub, C Pin, kPa
Spiral
Instrumented (with pressure taps)
Non-instrumented (without pressure taps)
Instrumented (with pressure taps)
Non-instrumented (without pressure taps)
1.12, 1.40, 1.63 6.4–2.4 5.6–1.6 – 0–25 740
1.40 6.4–2.4 5.6–1.6 – 0–25 740
1.12, 1.40, 1.63 6.4–2.4 5.6–1.6 20, 40, 60 0–25 740
1.40 6.4–2.4 5.6–1.6 20, 40, 60 0–25 740
a A total of six capillary lengths viz., 6.4, 5.6, 4.8, 4.0, 3.2, 2.4 m, have been taken for each test-section.
to study the effect of geometric parameters especially that of coiling on the mass flow rate of R-134a through diabatic spiral capillary tubes. Further, the present work may be perceived as an extension of our own experimental work (Khan et al., 2008b). As it is already known that helically coiled capillary tube suction-line heat exchangers are extensively used in applications like domestic refrigerators. The proposed spiral capillary tube/suction-line heat exchanger design may be used as an alternative to the helical capillary tube suctionline heat exchanger. However, the proposed design seems to take more space if used in horizontal position but if the same is used in vertical orientation, the space requirement will be reduced. In vertical position, the proposed capillary design will be a better option because at the back of refrigerator the space is sufficiently large to accommodate even large pitch spiral heat exchanger.
2.
Experimental set-up and procedure
The schematic diagram of experimental set-up has been shown in Fig. 2. The test-section (1) was a copper capillary tube bonded with suction from middle. From capillary tube, the refrigerant entered the evaporator (2) consisting of a copper coil submerged in a water tank. A 5 kW capacity electric heater (3) was fitted in the evaporator tank to provide heat load to evaporator. The heating load was varied by means of a variac (4). An agitator (5) was also fitted in the tank to maintain the uniform bulk temperature of water. The vapours emerging from the evaporator were sent to liquid accumulator (6) in to separate out liquid refrigerant so that only vapour could enter the compressor (7). The compressor (7) was run by means of three phase electric motor (8) using belt and pulley type arrangement. The compressor activated the refrigerant to high pressure and high temperature. These superheated vapours are passed through oil separator (9). The oil-free vapours from 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 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 refrigerant were removed through 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 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 vapour 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 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 set-up 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). Further, the pressure at the suction and discharge of the compressor was measured with separate bourdon tube pressure gauges.
Table 2 – Uncertainties in the measured parameters Parameters Temperature Pressure
Instruments
Thermocouple (T-type) Pressure gauge (4 nos.) Pressure transducer (4 nos.) Mass flow rate Analog rotameters (3 nos.) Digital rotameter (1 no.) Capillary tube length Steel rule Capillary tube diameter Tool maker’s microscope Internal surface Surface profilometer roughness of capillary Coil pitch Vernier calipers
Uncertainty 0.1 C 6.87 kPa 0.25% FS (2 MPa) 0.5 LPH 1% FS (50 LPH) 1.0 mm 0.01 mm 0.01 mm 0.1 mm
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265
Fig. 4 – Variation of the mass flow rate of R-134a with inlet subcooling for the tube diameter 1.12 mm.
The experimental set-up has been designed in such a way that the same capillary tube test-section behaves as diabatic capillary tube when the refrigerant is allowed to flow through the suction-line of the heat exchanger. The same test-section acts like an adiabatic capillary tube when the flow is bypassed through valve V3 and by closing the valves V1 and V2. The spiral capillary tube test-section and its cross-section are shown in Fig. 3. The spiral is formed by marking a groove of required pitch on a wooden disc. The procedure has already been described by Khan et al. (2008b). The test-section was a 6.4 m capillary tube out of which 5.6 m length of the tube was brazed with compressor suction-line of 6.35 mm diameter to form counter-flow heat exchanger. Thus, the initial and final adiabatic lengths are taken as 0.4 m each. Further, 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. Fig. 3 also shows the cross-section of the capillary tube/suction-line heat exchanger with copper tape wrapped around the two tubes. After wrapping copper tape on the two tubes, they were embedded in the spiral groove carved on the wooden disc. The present experimental investigation was mainly focused on the flow of R-134a through instrumented (with pressure taps) capillary tubes. However, for the sake of comparison data have been collected for non-instrumented (without pressure taps) capillary tube of 1.40 mm diameter as well. It has already been established in our previous work that the effect of pressure taps on the refrigerant mass flow rate is negligibly small. Therefore, the results of the instrumented capillary tubes can be applicable to the noninstrumented capillary tubes also. Table 1 shows the range of input parameters of the present experimental investigation. The spiral capillary tubes of three different diameters,
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Fig. 5 – Variation of the mass flow rate of R-134a with inlet subcooling for the tube diameter 1.40 mm.
i.e., 1.12, 1.40 and 1.63 mm, six different lengths, i.e., 2.4–6.4 m with steps of 0.8 m and three different pitches were used to carry out the present experimental investigation. Further, for each length, diameter and coil pitch of capillary tube the inlet subcooling was varied at four to five levels in the range of 0–25 C. The capillary tube inlet pressure was maintained at 740 kPa. Hence, a total of 1304 test-runs were conducted during the entire experimental investigation. The internal surface roughness of capillary tubes having diameters 1.12, 1.40 and 1.63 mm were 7.05, 6.22 and 3.58 mm, respectively. The uncertainties in the measurement of various parameters are shown in Table 2.
3.
Results and discussion
The flow of R-134a inside the capillary tube becomes nonadiabatic or diabatic when capillary tube is in thermal
contact with compressor suction-line forming a counterflow 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 and last 0.4 m 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, Lhx, is always 0.8 m. However, the suction-line inlet superheat is not a controlled parameter in the present investigation. The variation in the suctionline inlet superheat has been noted to be in the range of 0–19 C. This compressor suction-line inlet superheat has an interfering effect on the refrigerant mass flow rate through the diabatic capillary tubes. The effect of capillary tube geometry, i.e., tube diameter, tube length, coil pitch and inlet subcooling on the refrigerant mass flow rate through diabatic capillary tube have been
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Fig. 6 – Variation of the mass flow rate of R-134a with inlet subcooling for the tube diameter 1.63 mm.
investigated. For diabatic capillary tubes, the parameters also influencing the refrigerant mass flow rate are the length of heat exchange between the capillary tube and the compressor suction-line, Lhx and the compressor suctionline inlet superheat, DTsup, as well. Figs. 4–6 have been drawn for spiral capillary tubes of diameter 1.12, 1.40 and 1.63 mm, respectively. These figures show the effect of tube diameter, tube length, spiral coil pitch and the capillary inlet subcooling on the mass flow rate of R-134a through these tubes. The best-fit lines have been drawn to depict the trend. The following observations have been made from Figs. 4–6: – The diabatic spiral capillary tubes show an increase in mass flow rate of R-134a with the rise in inlet subcooling. 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–vapour mixture or pure vapour. Hence, the refrigerant mass flow rate is more for higher length of single phase liquid region inside the capillary tube as in the case of high capillary inlet subcooling condition. – For spiral capillary tubes also, the mass flow rate of R134a increases with the increase in tube diameter and with the reduction in the tube length. 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 with the increase in capillary tube diameter. The increase in the mass flow rate with the decrease in capillary tube length is due to rise in flow capacity of the capillary tube with the reduction in capillary tube length. It has also been observed that the effect of tube length is significant at high capillary
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Fig. 7 – Effect of suction-line inlet superheat on the mass flow rate of R-134a through a diabatic spiral capillary tube of 6.4 m length.
inlet subcooling. Also, for 1.63 mm diameter tube, the effect of tube length is quite significant. – The effect of coil pitch on the mass flow rate of R-134a is difficult to ascertain due to interfering effect of suctionline inlet superheat. It is because of this, the refrigerant mass flow rate through spiral capillary tubes has gone beyond the mass flow rate through straight capillary tube in some of the curves in Figs. 4–6. In fact an inverse relationship seems to exist between the suction-line superheat and the mass flow rate of R-134a. – The behaviour of diabatic spiral tubes is entirely different from that of adiabatic spiral capillary tubes. In adiabatic spiral capillary tubes, the mass flow rates of R-134a through coiled capillary tubes are always lesser in comparison to those through straight capillary tubes. Further, the refrigerant mass flow rate increases with the increase in coil pitch. Fig. 7 has been drawn to show the effect of suction-line inlet superheat for capillary tube length of 6.4 m and diameter 1.63 mm. The test run data have also been provided at the right hand side of the figure to explain the flow behaviour of R-134a inside the capillary tube due to suction-line inlet superheat. In adjoining table of Fig. 7, corresponding to each test run, the suction-line inlet superheat has also been mentioned. It is a known fact that the refrigerant mass flow rate should increase with the increase in coil pitch and for straight capillary tube the mass flow rate of R-134a should be the highest. In the present investigation, as shown in Fig. 7, the effect of suction-line inlet superheat is so strong that the mass flow rate of R-134a through the spiral capillary tubes of 20 and 40 mm coil pitches exceeds the mass flow rate of R-134a through the straight capillary tube. The relevant test-runs have been marked by A, B and C, respectively, in Fig. 7. The refrigerant mass flow rate through 60 mm coil pitch capillary tube falls below that of 20 mm coil pitch capillary tube has been marked by D in the figure. A thorough study of the data adjoining the Fig. 7 shows that for low suction-line inlet superheat, there is a sharp increase in the refrigerant mass flow rate irrespective of coil pitch and vice-versa. Low inlet suction-line inlet
superheat indicates that the refrigerant vapours from the evaporator enter the suction-line of the test-section at a lower temperature. The heat transfer from the capillary tube to the suction-line will cause the point of vapourization to shift further in the downstream direction inside the capillary tube causing the liquid length to increase. The increase in liquid length would ultimately lead to increase in refrigerant mass flow rate through the capillary tube. Therefore, the refrigerant mass increases to even higher value than that of the straight capillary tube. The mass flow rate of R-134a through diabatic capillary tubes have been compared with those through adiabatic capillary tubes to work out the difference in the flow behaviour of refrigerant in the two cases. Fig. 8 has been drawn to study the behaviour in flow characteristics as the mode of operation of the capillary tube is changed from adiabatic to diabatic. The following conclusions can be drawn regarding the mass flow rate of R-134a through these capillary tubes: – The mass flow rate of R-134a increases with the rise in capillary inlet subcooling in for diabatic and adiabatic capillary tubes as well. However, the rate of rise in the refrigerant mass flow rate is more in case of adiabatic capillary tubes of both geometries. In other words, the effect of capillary inlet subcooling is not as strong in diabatic capillary tubes as in the case of adiabatic capillary tubes. The increase in refrigerant mass flow rate in diabatic capillary tube is restricted by the effect of suction-line inlet superheat. – 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 in length. – In adiabatic coiled capillary tubes, it can be clearly observed that the refrigerant mass flow rate increases with the increase in the coil pitch of the spiral capillary tubes. However, the effect of coil pitch from the mass flow characteristics of spiral capillary tubes is difficult to ascertain from the Fig. 8. The effect of coil pitch seems
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269
Fig. 8 – Comparison of the mass flow rate characteristics of diabatic spiral capillary tube with those of adiabatic spiral capillary tube.
to be suppressed by the effect of suction-line inlet superheat. – The effect of coil pitch on refrigerant mass flow rate in 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 suctionline inlet superheat on the refrigerant mass flow rate. In some test-runs, low suction-line inlet superheat has resulted in the refrigerant mass flow rate higher than that for the straight capillary tube. Further for certain test-runs having the high suction-line inlet superheat, the mass low rate of R-134a is lower through the tubes having higher coil pitch in comparison to that through the capillary tubes of low pitch.
4.
Development of correlation
Like adiabatic capillary tubes, a generalized correlation for diabatic capillary tubes has also been developed to predict the mass flow rate of R-134a through straight and spiral capillary tube geometries. The number of parameters involved has increased from 9 for adiabatic capillary tubes to 12 for diabatic capillary tubes. Three additional parameters are Ps,in, DTsup and Lhx. Therefore, the refrigerant mass flow rate through diabatic capillary tubes can be defined as a function of the following parameters: (1) m ¼ f L; Lhx ; d; p; Pin ; Psin ; DTsub ; DTsup ; rf ; mf ; cpf The thermophysical properties appearing in Eq. (1) have been evaluated by REFPROP 7 refrigerant database (McLinden et al.,
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Table 3 – Non-dimensional p-groups p-group Original parameter
Description
p1
m dmf
Mass flow rate
p2
d2 rf Pin m2f
Capillary inlet pressure
p4
d2 rf Ps; m2f L d
p5
Lhx d
Heat exchange length
p6
d2 r2f cpf DTsub m2f
Capillary inlet subcooling
p3
in
Suction-line inlet pressure Total length
d2 r2f cpf DTsup m2f p d
p7 p8
Suction-line inlet superheating Coil pitch
2002). The total number of variables in Eq. (1) including dependent variable m is 12 for diabatic spiral capillary tube and 11 for diabatic straight capillary tube. The number of repeating variables is 4, viz., d, rf, mf and cpf. Therefore, the non-dimensional p-terms are 8 (12 4) in case of coiled capillary tubes and 7 (11 4) for the straight capillary tube. All the non-dimensional terms have been summarized in Table 3. Hence, Eq. (1) can be rewritten as taking p1 as dependent variable is developed in the following form: p1 ¼ f1 ðp1 ; p2 ; p3 ; p4 ; p5 ; p6 ; p7 ; p8 Þ
(2)
In non-linear power law form, Eq. (2) can be written as p1 ¼ c1 ðp2 Þc2 ðp3 Þc3 ðp4 Þc4 ðp5 Þc5 ðp6 Þc6 ðp7 Þc7 ðp8 Þc8
(3)
Eq. (3) can further be generalized as follows: p1 ¼ Cðp2 Þc2 ðp3 Þc3 ðp4 Þc4 ðp5 Þc5 ðp6 Þc6 ðp7 Þc7 F
(4)
The multiple variable regression technique has been applied on the 381 data sets spiral and straight capillary tube to obtain the constants appearing in Eq. (4). Equation of the following form has been evolved as a result of data analysis: 0:6547
p1 ¼ Cðp2 Þ
0:0018
ðp3 Þ
0:3985
ðp4 Þ
0:1004
ðp5 Þ
0:1013
ðp6 Þ
0:0762
ðp7 Þ
F
Fig. 10 – Comparison of the proposed correlation with Wolf and Pate (2002) correlation.
For spiral tube: C ¼ 0.0079; F ¼ (p8)0.0271 for 279 data sets. Fig. 9 shows the comparison between the mass flow rate predicted by Eq. (5) and the measured experimental mass flow rate for diabatic spiral and straight capillary tubes. For both straight and spiral geometries of capillary tube, the experimental data are predicted by the developed correlation within the error band of 7%. Therefore, it can be concluded that the generalized correlation is in good agreement with the measured experimental data. The proposed generalized correlation has also been compared with the following mass flow rate correlation by ASHRAE Refrigeration Handbook (2006), proposed by Wolf and Pate (2002): p1 ¼ 0:07602ðp2 Þ0:7342 ðp3 Þ0:1204 ðp4 Þ0:4583 ðp5 Þ0:07751 ðp6 Þ0:03774 ðp7 Þ0:04085
ð6Þ
(5)
For straight tube: C ¼ 0.0093; F ¼ 1 for 102 data sets.
Fig. 10 has been drawn to compare the proposed correlation with Wolf and Pate correlation (2002). The refrigerant mass flow rate predicted by Wolf and Pate correlation (2002) lies in the error band of 30 to þ15%. In fact, for lower mass flow rates up to 15 kg h1, the mass flow rate data predicted by Wolf and Pate (2002) correlation is equally dispersed about the zero error line while for higher mass flow rates the data predicted by Wolf and Pate correlation (2002) lies below the zero error line. Therefore, it can be concluded that for lower refrigerant mass flow rates Wolf and Pate (2002) correlation predicts
Table 4 – Difference in range of operating parameters
Fig. 9 – Comparison of the mass flow rate predicted by the proposed correlation with the measured experimental mass flow rate.
Parameters
Wolf and Pate (2002) correlation
d, mm L, m Lhx, m DTsub, K DTsup, K
0.5–1.25 Up to 3.3 0.5–2.5 1–17 3–22
Proposed correlation 1.12–1.63 2.4–6.4 1.6–5.6 0.5–25 1–19
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the refrigerant mass flow rate in the error band of 25% and for higher refrigerant mass flow rates this correlation underpredict the data in the error band of 0–30%. However, the proposed correlation predicts the experimental data in an error band of 7%. The predictions of the developed correlation and those from the correlation of Wolf and Pate (2002) do not agree in the same error band. Table 4 shows the difference in the range of operating parameters used in the development of proposed correlation and that by Wolf and Pate (2002). Since, the upper limit of tube diameter, in case of Wolf and Pate (2002) study lies in the operating range of present experimental study, there is an agreement between the two correlations to a certain extent for low refrigerant mass flow rate.
5.
Conclusions
The following conclusions have been drawn from the experimental results of the flow of R-134a through diabatic capillary tubes: – The effect tube diameter, tube length and degree of subcooling at capillary inlet on the refrigerant mass flow rate of diabatic straight and spiral capillary tubes have been investigated. – The refrigerant mass flow rate characteristic curves of the diabatic capillary tubes have been compared with those of the adiabatic capillary tubes. It has been found that the flow behaviour of the diabatic capillary tubes is entirely different from those of adiabatic capillary tubes. In case of diabatic capillary tube, the refrigerant mass flow has been found to be the function of suction-line inlet superheat and heat exchange length in addition to capillary tube diameter, capillary tube length, coil pitch and capillary inlet subcooling. – An empirical correlation for the refrigerant mass flow rate through diabatic spiral capillary tube geometry has been developed. It has been found the proposed correlation predicts the refrigerant mass flow rate in the error band of 7% of the measured experimental mass flow rate.
references
ASHRAE Handbook – Refrigeration, 2006. American Society of Heating, Refrigerating and Air-Conditioning Engineer Inc., p 26 (Chapter 44). Bansal, P.K., Yang, C., 2005. Numerical investigation of capillary tube-suction line exchanger performance. Applied Thermal Engineering 25, 2014–2028. Escanes, F., Perez-Segarra, C.D., Oliva, A., 1995. Numerical simulation of capillary tube expansion devices. International Journal of Refrigeration 18, 113–122. Khan, M.K., Kumar, R., Sahoo, P.K., 2007. Flow characteristics of refrigerants flowing inside an adiabatic spiral capillary tube. HVAC&R Research ASHRAE 13, 731–748.
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Khan, M.K., Kumar, R., Sahoo, P.K., 2008a. A homogeneous flow model for adiabatic helical capillary tube. ASHRAE Transactions 114 (Part I). Khan, M.K., Kumar, R., Sahoo, P.K., 2008b. An experimental study of the flow of R-134a inside an adiabatic spirally coiled capillary tube. International Journal of Refrigeration, doi:10. 1016/j.ijrefrig.2008.01.008. Kim, S.G., Ro, S.T., Kim, M.S., 2002. Experimental investigation of the performance of R22, R407C and R410A in several capillary tubes for air-conditioners. International Journal of Refrigeration 25, 521–531. Kuehl, S.J., Goldschmidt, V.W., 1990. Steady flows of R-22 through capillary tubes: test data. ASHRAE Transactions 96, 719–728. McLinden, M.O., Klein, S.A., Lemmon, E.W., 2002. REFPROP – Version 7 – thermodynamic and transport properties of refrigerants and refrigerant mixtures, NIST Standard Reference Database. Melo, C., Vieira, L.A.T., Pereira, R.H., 2002. Non-adiabatic capillary tube flow with isobutene. Applied Thermal Engineering 22, 661–672. Mendoca, K.C., Melo, C., Ferreira, R.T.S., Pereira, R.H., 1998. Experimental study on lateral capillary tube-suction line heat exchangers. International Refrigeration Conference at Purdue, West Lafayette, USA, pp. 437–442. Mezavila, M.M., Melo, C., 1996. CAPHEAT: An homogeneous model to simulate refrigerant flow through non-adiabatic capillary tubes. International Refrigeration Conference at Purdue, West Lafayette, USA, pp. 95–100. Park, C., Lee, S., Kang, H., Kim, Y., 2007. Experimentation and modeling of refrigerant flow through coiled capillary tube. International Journal of Refrigeration 30, 1168–1175. Pate, M.B., Tree, D.R., 1984. An analysis of pressure and temperature measurements along a capillary tube – suction line heat exchanger. ASHRAE Transactions 90, 291–301. Staeblar, L.A., 1948. Theory and use of a capillary tube for liquid refrigerant control. Refrigerating Engineering, 55–59. Valladares, G., Perez-Sagarra, C.D., Oliva, A., 2002a. Numerical simulation of capillary expansion devices behaviour with pure and mixed refrigerants considering metastable region. Part I: Mathematical formulation and numerical model. Applied Thermal Engineering 22, 173–182. Valladares, G., Perez-Sagarra, C.D., Oliva, A., 2002b. Numerical simulation of capillary expansion devices behaviour with pure and mixed refrigerants considering metastable region. Part II: Experimental validation and parametric studies. Applied Thermal Engineering 22, 379–391. Valladares, G., 2004. Review of numerical simulation of capillary tube using refrigerant mixtures. Applied Thermal Engineering 24, 949–966. Valladares, G., 2007a. Numerical simulation of non-adiabatic capillary tubes considering metastable region. Part I: Mathematical formulation and numerical model. International Journal of Refrigeration 30, 642–653. Valladares, G., 2007b. Numerical simulation of capillary expansion devices behaviour with pure and mixed refrigerants considering metastable region. Part II: Experimental validation. International Journal Refrigeration 30, 654–663. Wolf, D.A., Pate, M.B., 2002. Performance of a capillary tube/ suction line heat exchanger with alternative refrigerants. ASHRAE Research Project RP-948. Zangari, J.M., Melo, C., Ferreira, R.T.S., Pereira, R.H., 2000. Experimental studies of non-adiabatic flow of HFC-134a through capillary tubes. International Refrigeration Conference at Purdue, West Lafayette, USA, pp. 305–312. Zhou, G., Zhang, Y., 2006. Numerical and experimental investigations on the performance of coiled adiabatic capillary tube. Applied Thermal Engineering 26, 1106–1114.
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Experimental investigation on diabatic flow of R-134a through spiral capillary tube Mohd. Kaleem Khana, Ravi Kumarb,*, Pradeep K. Sahoob a
Department of Mechanical Engineering, Thapar University, Patiala 147 004, India Department of Mechanical and Industrial Engineering, Indian Institute of Technology, Roorkee 247 667, Uttarakhand, India
b
article info
abstract
Article history:
The present experimental investigation has been carried out to investigate the effects of
Received 6 March 2008
various geometric parameters on the mass flow rate of R-134a through diabatic spiral
Received in revised form 3 May 2008
capillary tube. In diabatic flow, the capillary tube is bonded with the compressor suc-
Accepted 24 May 2008
tion-line to form a counter-flow exchanger. The lateral type of diabatic capillary tube
Published online 3 June 2008
has been investigated in the present experimental study. The major geometric parameters investigated are capillary tube diameter, capillary tube length and coil pitch. In addition,
Keywords:
effect of inlet subcooling on the mass flow rate through diabatic spiral capillary tube is
Refrigeration system
also done. A comparison of the performance of diabatic spiral capillary tube has been
Compression
made with adiabatic spiral capillary tube. Generalized empirical correlation for diabatic
R134a
spiral capillary tube has also been proposed. It has been found that the predictions of
Experiment
the proposed correlation lie in the error band of 7%. ª 2009 Elsevier Ltd and IIR. All rights reserved.
Flow Capillary Spiral tube Geometry
Etude expe´rimentale sur l’e´coulement diabatique du R-134a dans un capillaire en spirale Mots cle´s : Syste`me frigorifique ; Syste`me a` compression ; R134a ; Expe´rimentation ; E´coulement ; Capillaire ; Tube he´licoı¨dal ; Ge´ome´trie
1.
Introduction
Capillary tube is a hollow drawn copper tube and is commonly used in refrigeration industry as an expansion device in low capacity refrigeration systems, where the load is fairly constant. Capillary tubes, in vapour compression systems, are used in two configurations – adiabatic and diabatic. In
the present investigation, the idea is to club the advantages of coiling with those of diabatic configuration together. Fig. 1 shows the schematic diagram of vapour compression system using diabatic capillary tube as expansion device. In diabatic configuration, the capillary tube is bonded with the compressor suction-line by means of brazing or soldering to form counter-flow capillary tube/suction-line heat exchanger,
* Corresponding author. Tel.: þ91 1332 285740; fax: þ91 1332 285665. E-mail address: [email protected] (R. Kumar). 0140-7007/$ – see front matter ª 2009 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2008.05.010
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Nomenclature cp d DTsub DTsup e L P p T v
specific heat at constant pressure, J kg capillary tube internal diameter, m capillary tube inlet subcooling, C suction-line inlet superheating, C roughness height, m capillary tube length, m pressure, Pa coil pitch, m temperature, C specific volume, m3 kg1
1
1
K
Greek letters m viscosity, kg m1 s1 r density, kg m3 Subscripts in capillary tube inlet f liquid hx heat exchange
whereas, in adiabatic configuration, there is no heat transfer from the capillary tube to the surroundings. The performance of the system enhances considerably if the capillary tube is used in diabatic mode, as heat transfer from the capillary to the cold suction-line causes a delay in vapourization, i.e., refrigerant leaves the capillary tube with lower vapour quality. This ultimately results in an increase in the refrigerating effect. On the other hand, heat transfer to the suction-line causes superheating of the vapours, thus diminishes the chances of liquid refrigerant entering the compressor and, thus, saving the compressor from being damaged. An exhaustive review of the literature has revealed that diabatic capillary tubes have been scarcely investigated in comparison to adiabatic capillary tubes. Similarly, literature on coiled capillary tubes compared to straight capillary tubes is also scarce. Flow through diabatic capillary tubes was pioneered by Staeblar (1948). They presented capacity balance characteristics to determine the length of diabatic capillary tube for R-12 and R-22. Pate and Tree (1984) studied the
Fig. 1 – Schematic diagram of vapour compression system using diabatic capillary tube for expansion.
diabatic flow of R-12 through the capillary tube with air flowing in the suction-line in counter-flow direction forming an open loop. Melo et al. (2002) conducted the experiments on the concentric diabatic capillary tubes using R-600a as working fluid. Based on their experimental results, they proposed separate empirical correlations for the determination of refrigerant mass flow and the suction-line outlet temperature using factorial design of experimental technique. A number of numerical investigations have been made for the flow through diabatic capillary tubes. Further, the contributions of Mendoca et al. (1998) and Zangari et al. (2000) cannot be ignored as far the flow of R-134a through diabatic capillary tube is concerned. Bansal and Yang (2005) proposed a model for the flow of refrigerant through a diabatic capillary tube. The control volume formulation for the flow through diabatic capillary tube has been adopted by a number of researchers. Escanes et al. (1995) developed a numerical simulation model based on the control volume formulation on the 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 non-critical flow was made iteratively by means of Newton–Raphson algorithm. Mezavila and Melo (1996) presented a numerical model based on the homogeneous two-phase flow model to simulate the flow of refrigerant flow through a non-adiabatic capillary tube. Valladares et al. (2002a) developed a numerical simulation similar to simulation model by Escanes et al. (1995). This simulation model was based on the finite volume formulation of the governing equations. As a sequel of 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 the review of his own numerical work (Valladares et al., 2002a,b). Most recently, Valladares (2007a) has extended his own work (Valladares et al., 2002a,b) on diabatic capillary tubes considering separated flow model and metastable regions. Further, Valladares (2007b) validated their renewed model with the existing experimental data. The effect of coiling on the refrigerant mass flow rate has been discussed by numerous investigators. Kuehl and Goldschmidt (1990) have conducted experiments on the flow of R-22 through adiabatic capillary tubes of straight and coiled geometries. They have concluded that because of the coiling of capillary tube, the refrigerant mass flow rate was reduced by up to 5%. Kim et al. (2002) have studied the flow of R-22 and its alternatives viz., R-407C and R-410A through the straight and helically coiled adiabatic capillary tubes. About 9% reduction in refrigerant mass flow rate through a coiled tube as compared to straight capillary tube was observed. Zhou and Zhang (2006) also found that the mass flow rate through helical capillary tube is reduced by 10% when compared with straight capillary tube. A numerical model was also developed by Zhou and Zhang (2006) for adiabatic helical capillary tube and was validated by their own experimental data. Park et al. (2007) studied the flow of R-22 and its alternatives, R-407C and R-410A. They reported slightly higher reduction in mass flow rates of the coiled capillary
international journal of refrigeration 32 (2009) 261–271
263
Fig. 2 – Schematic diagram of experimental set-up.
tubes compared, i.e., 5–16% compared to straight capillary tube. They also proposed a generalized mass flow rate correlation for helically coiled capillary tubes. Recently, Khan et al. (2008a) have also presented a mathematical model to evaluate the length of adiabatic helical capillary tube considering the effect of coil pitch as well as that of coil diameter. Studies on the spiral capillary tube were not figured in the literature until Khan et al. (2007) proposed a mathematical model for the computation of length of adiabatic spiral capillary tube. It has been found that because of coiling the length of the capillary tube is reduced considerably for a given set of
input conditions. Most recently, an experimental investigation on the flow of R-134a through an adiabatic spiral capillary tube has been presented by Khan et al. (2008b). They proposed an empirical correlation for the prediction of refrigerant mass flow rate through adiabatic spiral capillary tube. The effect of parameters like capillary tube diameter, capillary tube length, coil pitch and inlet subcooling on the refrigerant mass flow rate through adiabatic spiral capillary tube has been also presented. Considering the scarcity of literature on diabatic coiled capillary tube, the present investigation has been conducted
Fig. 3 – Spiral test-section and its cross-section.
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Table 1 – Range of input parameters Parameters
Selected range Straight
d, mm La, m Lhx, m p, mm DTsub, C Pin, kPa
Spiral
Instrumented (with pressure taps)
Non-instrumented (without pressure taps)
Instrumented (with pressure taps)
Non-instrumented (without pressure taps)
1.12, 1.40, 1.63 6.4–2.4 5.6–1.6 – 0–25 740
1.40 6.4–2.4 5.6–1.6 – 0–25 740
1.12, 1.40, 1.63 6.4–2.4 5.6–1.6 20, 40, 60 0–25 740
1.40 6.4–2.4 5.6–1.6 20, 40, 60 0–25 740
a A total of six capillary lengths viz., 6.4, 5.6, 4.8, 4.0, 3.2, 2.4 m, have been taken for each test-section.
to study the effect of geometric parameters especially that of coiling on the mass flow rate of R-134a through diabatic spiral capillary tubes. Further, the present work may be perceived as an extension of our own experimental work (Khan et al., 2008b). As it is already known that helically coiled capillary tube suction-line heat exchangers are extensively used in applications like domestic refrigerators. The proposed spiral capillary tube/suction-line heat exchanger design may be used as an alternative to the helical capillary tube suctionline heat exchanger. However, the proposed design seems to take more space if used in horizontal position but if the same is used in vertical orientation, the space requirement will be reduced. In vertical position, the proposed capillary design will be a better option because at the back of refrigerator the space is sufficiently large to accommodate even large pitch spiral heat exchanger.
2.
Experimental set-up and procedure
The schematic diagram of experimental set-up has been shown in Fig. 2. The test-section (1) was a copper capillary tube bonded with suction from middle. From capillary tube, the refrigerant entered the evaporator (2) consisting of a copper coil submerged in a water tank. A 5 kW capacity electric heater (3) was fitted in the evaporator tank to provide heat load to evaporator. The heating load was varied by means of a variac (4). An agitator (5) was also fitted in the tank to maintain the uniform bulk temperature of water. The vapours emerging from the evaporator were sent to liquid accumulator (6) in to separate out liquid refrigerant so that only vapour could enter the compressor (7). The compressor (7) was run by means of three phase electric motor (8) using belt and pulley type arrangement. The compressor activated the refrigerant to high pressure and high temperature. These superheated vapours are passed through oil separator (9). The oil-free vapours from 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 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 refrigerant were removed through 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 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 vapour 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 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 set-up 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). Further, the pressure at the suction and discharge of the compressor was measured with separate bourdon tube pressure gauges.
Table 2 – Uncertainties in the measured parameters Parameters Temperature Pressure
Instruments
Thermocouple (T-type) Pressure gauge (4 nos.) Pressure transducer (4 nos.) Mass flow rate Analog rotameters (3 nos.) Digital rotameter (1 no.) Capillary tube length Steel rule Capillary tube diameter Tool maker’s microscope Internal surface Surface profilometer roughness of capillary Coil pitch Vernier calipers
Uncertainty 0.1 C 6.87 kPa 0.25% FS (2 MPa) 0.5 LPH 1% FS (50 LPH) 1.0 mm 0.01 mm 0.01 mm 0.1 mm
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265
Fig. 4 – Variation of the mass flow rate of R-134a with inlet subcooling for the tube diameter 1.12 mm.
The experimental set-up has been designed in such a way that the same capillary tube test-section behaves as diabatic capillary tube when the refrigerant is allowed to flow through the suction-line of the heat exchanger. The same test-section acts like an adiabatic capillary tube when the flow is bypassed through valve V3 and by closing the valves V1 and V2. The spiral capillary tube test-section and its cross-section are shown in Fig. 3. The spiral is formed by marking a groove of required pitch on a wooden disc. The procedure has already been described by Khan et al. (2008b). The test-section was a 6.4 m capillary tube out of which 5.6 m length of the tube was brazed with compressor suction-line of 6.35 mm diameter to form counter-flow heat exchanger. Thus, the initial and final adiabatic lengths are taken as 0.4 m each. Further, 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. Fig. 3 also shows the cross-section of the capillary tube/suction-line heat exchanger with copper tape wrapped around the two tubes. After wrapping copper tape on the two tubes, they were embedded in the spiral groove carved on the wooden disc. The present experimental investigation was mainly focused on the flow of R-134a through instrumented (with pressure taps) capillary tubes. However, for the sake of comparison data have been collected for non-instrumented (without pressure taps) capillary tube of 1.40 mm diameter as well. It has already been established in our previous work that the effect of pressure taps on the refrigerant mass flow rate is negligibly small. Therefore, the results of the instrumented capillary tubes can be applicable to the noninstrumented capillary tubes also. Table 1 shows the range of input parameters of the present experimental investigation. The spiral capillary tubes of three different diameters,
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Fig. 5 – Variation of the mass flow rate of R-134a with inlet subcooling for the tube diameter 1.40 mm.
i.e., 1.12, 1.40 and 1.63 mm, six different lengths, i.e., 2.4–6.4 m with steps of 0.8 m and three different pitches were used to carry out the present experimental investigation. Further, for each length, diameter and coil pitch of capillary tube the inlet subcooling was varied at four to five levels in the range of 0–25 C. The capillary tube inlet pressure was maintained at 740 kPa. Hence, a total of 1304 test-runs were conducted during the entire experimental investigation. The internal surface roughness of capillary tubes having diameters 1.12, 1.40 and 1.63 mm were 7.05, 6.22 and 3.58 mm, respectively. The uncertainties in the measurement of various parameters are shown in Table 2.
3.
Results and discussion
The flow of R-134a inside the capillary tube becomes nonadiabatic or diabatic when capillary tube is in thermal
contact with compressor suction-line forming a counterflow 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 and last 0.4 m 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, Lhx, is always 0.8 m. However, the suction-line inlet superheat is not a controlled parameter in the present investigation. The variation in the suctionline inlet superheat has been noted to be in the range of 0–19 C. This compressor suction-line inlet superheat has an interfering effect on the refrigerant mass flow rate through the diabatic capillary tubes. The effect of capillary tube geometry, i.e., tube diameter, tube length, coil pitch and inlet subcooling on the refrigerant mass flow rate through diabatic capillary tube have been
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267
Fig. 6 – Variation of the mass flow rate of R-134a with inlet subcooling for the tube diameter 1.63 mm.
investigated. For diabatic capillary tubes, the parameters also influencing the refrigerant mass flow rate are the length of heat exchange between the capillary tube and the compressor suction-line, Lhx and the compressor suctionline inlet superheat, DTsup, as well. Figs. 4–6 have been drawn for spiral capillary tubes of diameter 1.12, 1.40 and 1.63 mm, respectively. These figures show the effect of tube diameter, tube length, spiral coil pitch and the capillary inlet subcooling on the mass flow rate of R-134a through these tubes. The best-fit lines have been drawn to depict the trend. The following observations have been made from Figs. 4–6: – The diabatic spiral capillary tubes show an increase in mass flow rate of R-134a with the rise in inlet subcooling. 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–vapour mixture or pure vapour. Hence, the refrigerant mass flow rate is more for higher length of single phase liquid region inside the capillary tube as in the case of high capillary inlet subcooling condition. – For spiral capillary tubes also, the mass flow rate of R134a increases with the increase in tube diameter and with the reduction in the tube length. 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 with the increase in capillary tube diameter. The increase in the mass flow rate with the decrease in capillary tube length is due to rise in flow capacity of the capillary tube with the reduction in capillary tube length. It has also been observed that the effect of tube length is significant at high capillary
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Fig. 7 – Effect of suction-line inlet superheat on the mass flow rate of R-134a through a diabatic spiral capillary tube of 6.4 m length.
inlet subcooling. Also, for 1.63 mm diameter tube, the effect of tube length is quite significant. – The effect of coil pitch on the mass flow rate of R-134a is difficult to ascertain due to interfering effect of suctionline inlet superheat. It is because of this, the refrigerant mass flow rate through spiral capillary tubes has gone beyond the mass flow rate through straight capillary tube in some of the curves in Figs. 4–6. In fact an inverse relationship seems to exist between the suction-line superheat and the mass flow rate of R-134a. – The behaviour of diabatic spiral tubes is entirely different from that of adiabatic spiral capillary tubes. In adiabatic spiral capillary tubes, the mass flow rates of R-134a through coiled capillary tubes are always lesser in comparison to those through straight capillary tubes. Further, the refrigerant mass flow rate increases with the increase in coil pitch. Fig. 7 has been drawn to show the effect of suction-line inlet superheat for capillary tube length of 6.4 m and diameter 1.63 mm. The test run data have also been provided at the right hand side of the figure to explain the flow behaviour of R-134a inside the capillary tube due to suction-line inlet superheat. In adjoining table of Fig. 7, corresponding to each test run, the suction-line inlet superheat has also been mentioned. It is a known fact that the refrigerant mass flow rate should increase with the increase in coil pitch and for straight capillary tube the mass flow rate of R-134a should be the highest. In the present investigation, as shown in Fig. 7, the effect of suction-line inlet superheat is so strong that the mass flow rate of R-134a through the spiral capillary tubes of 20 and 40 mm coil pitches exceeds the mass flow rate of R-134a through the straight capillary tube. The relevant test-runs have been marked by A, B and C, respectively, in Fig. 7. The refrigerant mass flow rate through 60 mm coil pitch capillary tube falls below that of 20 mm coil pitch capillary tube has been marked by D in the figure. A thorough study of the data adjoining the Fig. 7 shows that for low suction-line inlet superheat, there is a sharp increase in the refrigerant mass flow rate irrespective of coil pitch and vice-versa. Low inlet suction-line inlet
superheat indicates that the refrigerant vapours from the evaporator enter the suction-line of the test-section at a lower temperature. The heat transfer from the capillary tube to the suction-line will cause the point of vapourization to shift further in the downstream direction inside the capillary tube causing the liquid length to increase. The increase in liquid length would ultimately lead to increase in refrigerant mass flow rate through the capillary tube. Therefore, the refrigerant mass increases to even higher value than that of the straight capillary tube. The mass flow rate of R-134a through diabatic capillary tubes have been compared with those through adiabatic capillary tubes to work out the difference in the flow behaviour of refrigerant in the two cases. Fig. 8 has been drawn to study the behaviour in flow characteristics as the mode of operation of the capillary tube is changed from adiabatic to diabatic. The following conclusions can be drawn regarding the mass flow rate of R-134a through these capillary tubes: – The mass flow rate of R-134a increases with the rise in capillary inlet subcooling in for diabatic and adiabatic capillary tubes as well. However, the rate of rise in the refrigerant mass flow rate is more in case of adiabatic capillary tubes of both geometries. In other words, the effect of capillary inlet subcooling is not as strong in diabatic capillary tubes as in the case of adiabatic capillary tubes. The increase in refrigerant mass flow rate in diabatic capillary tube is restricted by the effect of suction-line inlet superheat. – 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 in length. – In adiabatic coiled capillary tubes, it can be clearly observed that the refrigerant mass flow rate increases with the increase in the coil pitch of the spiral capillary tubes. However, the effect of coil pitch from the mass flow characteristics of spiral capillary tubes is difficult to ascertain from the Fig. 8. The effect of coil pitch seems
international journal of refrigeration 32 (2009) 261–271
269
Fig. 8 – Comparison of the mass flow rate characteristics of diabatic spiral capillary tube with those of adiabatic spiral capillary tube.
to be suppressed by the effect of suction-line inlet superheat. – The effect of coil pitch on refrigerant mass flow rate in 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 suctionline inlet superheat on the refrigerant mass flow rate. In some test-runs, low suction-line inlet superheat has resulted in the refrigerant mass flow rate higher than that for the straight capillary tube. Further for certain test-runs having the high suction-line inlet superheat, the mass low rate of R-134a is lower through the tubes having higher coil pitch in comparison to that through the capillary tubes of low pitch.
4.
Development of correlation
Like adiabatic capillary tubes, a generalized correlation for diabatic capillary tubes has also been developed to predict the mass flow rate of R-134a through straight and spiral capillary tube geometries. The number of parameters involved has increased from 9 for adiabatic capillary tubes to 12 for diabatic capillary tubes. Three additional parameters are Ps,in, DTsup and Lhx. Therefore, the refrigerant mass flow rate through diabatic capillary tubes can be defined as a function of the following parameters: (1) m ¼ f L; Lhx ; d; p; Pin ; Psin ; DTsub ; DTsup ; rf ; mf ; cpf The thermophysical properties appearing in Eq. (1) have been evaluated by REFPROP 7 refrigerant database (McLinden et al.,
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Table 3 – Non-dimensional p-groups p-group Original parameter
Description
p1
m dmf
Mass flow rate
p2
d2 rf Pin m2f
Capillary inlet pressure
p4
d2 rf Ps; m2f L d
p5
Lhx d
Heat exchange length
p6
d2 r2f cpf DTsub m2f
Capillary inlet subcooling
p3
in
Suction-line inlet pressure Total length
d2 r2f cpf DTsup m2f p d
p7 p8
Suction-line inlet superheating Coil pitch
2002). The total number of variables in Eq. (1) including dependent variable m is 12 for diabatic spiral capillary tube and 11 for diabatic straight capillary tube. The number of repeating variables is 4, viz., d, rf, mf and cpf. Therefore, the non-dimensional p-terms are 8 (12 4) in case of coiled capillary tubes and 7 (11 4) for the straight capillary tube. All the non-dimensional terms have been summarized in Table 3. Hence, Eq. (1) can be rewritten as taking p1 as dependent variable is developed in the following form: p1 ¼ f1 ðp1 ; p2 ; p3 ; p4 ; p5 ; p6 ; p7 ; p8 Þ
(2)
In non-linear power law form, Eq. (2) can be written as p1 ¼ c1 ðp2 Þc2 ðp3 Þc3 ðp4 Þc4 ðp5 Þc5 ðp6 Þc6 ðp7 Þc7 ðp8 Þc8
(3)
Eq. (3) can further be generalized as follows: p1 ¼ Cðp2 Þc2 ðp3 Þc3 ðp4 Þc4 ðp5 Þc5 ðp6 Þc6 ðp7 Þc7 F
(4)
The multiple variable regression technique has been applied on the 381 data sets spiral and straight capillary tube to obtain the constants appearing in Eq. (4). Equation of the following form has been evolved as a result of data analysis: 0:6547
p1 ¼ Cðp2 Þ
0:0018
ðp3 Þ
0:3985
ðp4 Þ
0:1004
ðp5 Þ
0:1013
ðp6 Þ
0:0762
ðp7 Þ
F
Fig. 10 – Comparison of the proposed correlation with Wolf and Pate (2002) correlation.
For spiral tube: C ¼ 0.0079; F ¼ (p8)0.0271 for 279 data sets. Fig. 9 shows the comparison between the mass flow rate predicted by Eq. (5) and the measured experimental mass flow rate for diabatic spiral and straight capillary tubes. For both straight and spiral geometries of capillary tube, the experimental data are predicted by the developed correlation within the error band of 7%. Therefore, it can be concluded that the generalized correlation is in good agreement with the measured experimental data. The proposed generalized correlation has also been compared with the following mass flow rate correlation by ASHRAE Refrigeration Handbook (2006), proposed by Wolf and Pate (2002): p1 ¼ 0:07602ðp2 Þ0:7342 ðp3 Þ0:1204 ðp4 Þ0:4583 ðp5 Þ0:07751 ðp6 Þ0:03774 ðp7 Þ0:04085
ð6Þ
(5)
For straight tube: C ¼ 0.0093; F ¼ 1 for 102 data sets.
Fig. 10 has been drawn to compare the proposed correlation with Wolf and Pate correlation (2002). The refrigerant mass flow rate predicted by Wolf and Pate correlation (2002) lies in the error band of 30 to þ15%. In fact, for lower mass flow rates up to 15 kg h1, the mass flow rate data predicted by Wolf and Pate (2002) correlation is equally dispersed about the zero error line while for higher mass flow rates the data predicted by Wolf and Pate correlation (2002) lies below the zero error line. Therefore, it can be concluded that for lower refrigerant mass flow rates Wolf and Pate (2002) correlation predicts
Table 4 – Difference in range of operating parameters
Fig. 9 – Comparison of the mass flow rate predicted by the proposed correlation with the measured experimental mass flow rate.
Parameters
Wolf and Pate (2002) correlation
d, mm L, m Lhx, m DTsub, K DTsup, K
0.5–1.25 Up to 3.3 0.5–2.5 1–17 3–22
Proposed correlation 1.12–1.63 2.4–6.4 1.6–5.6 0.5–25 1–19
international journal of refrigeration 32 (2009) 261–271
the refrigerant mass flow rate in the error band of 25% and for higher refrigerant mass flow rates this correlation underpredict the data in the error band of 0–30%. However, the proposed correlation predicts the experimental data in an error band of 7%. The predictions of the developed correlation and those from the correlation of Wolf and Pate (2002) do not agree in the same error band. Table 4 shows the difference in the range of operating parameters used in the development of proposed correlation and that by Wolf and Pate (2002). Since, the upper limit of tube diameter, in case of Wolf and Pate (2002) study lies in the operating range of present experimental study, there is an agreement between the two correlations to a certain extent for low refrigerant mass flow rate.
5.
Conclusions
The following conclusions have been drawn from the experimental results of the flow of R-134a through diabatic capillary tubes: – The effect tube diameter, tube length and degree of subcooling at capillary inlet on the refrigerant mass flow rate of diabatic straight and spiral capillary tubes have been investigated. – The refrigerant mass flow rate characteristic curves of the diabatic capillary tubes have been compared with those of the adiabatic capillary tubes. It has been found that the flow behaviour of the diabatic capillary tubes is entirely different from those of adiabatic capillary tubes. In case of diabatic capillary tube, the refrigerant mass flow has been found to be the function of suction-line inlet superheat and heat exchange length in addition to capillary tube diameter, capillary tube length, coil pitch and capillary inlet subcooling. – An empirical correlation for the refrigerant mass flow rate through diabatic spiral capillary tube geometry has been developed. It has been found the proposed correlation predicts the refrigerant mass flow rate in the error band of 7% of the measured experimental mass flow rate.
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