olic

hnolDep

Alternative refrigerant

ctsingnergomhedhadhat the traditional refrigerants consistently gave lower pressure drops for both

e capillst, lowrefrig

between 0.52.0 mm in diameter and 25 m in length. Several respectively. In addition, the mass ow rates of straight capillary

International Communications in Heat and Mass Transfer 37 (2010) 13051311

Contents lists available at ScienceDirect

International Communications

.e ldecades ago, the ow characteristics owing through the straightcapillary tube of various refrigerants were both experimentally andtheoretically studied. In practical applications, however, capillarytubes are generally coiled to save space. The most productive studieshave been continuously carried out by the following researchers.

Zhou and Zhang [1] theoretically and experimentally studied theperformance of coiled adiabatic capillary tubes and compared theresults with straight capillary data. These results showed that themass ow rate of a refrigerant substantially increases by increasingthe coil diameter. However, little change was observed for coil

tubes are higher than those of coiled capillary tubes, especially atsmaller coiled diameters. For instance, mass ow rates for 40 mmcoiled diameter tubes are smaller than the straight capillary tubes byapproximately 9%.

Park et al. [4] studied the ow characteristics of coiled capillarytubes for R-22 and developed a mass ow rate correlation for coiledcapillary tubes. At the same operating condition, they found that themass ow rates of the coiled capillary tubes decreased by 516% morethan those of the straight capillary tubes. The Buckingham theoremwas used to form a generalised correlation to calculate the refrigerantdiameters larger than 300 mm.Ali [2] proposed the pressure drop correla

of uid properties ( and ), ow rate (V) andand L). In most previous works, the rele

Communicated by W.J. Minkowycz. Corresponding author.

E-mail address: somchai.won@kmutt.ac.th (S. Wong

0735-1933/$ see front matter 2010 Elsevier Ltd. Aldoi:10.1016/j.icheatmasstransfer.2010.07.005eration systems with asehold refrigerators andcapillary tube ranges

Buckingham theorem for R-22 and its alternatives, R-407C and R-410A. Their results indicated that themass ow rates of R-407C and R-410A were higher than those of R-22 by about 4% and 23%,cooling capacity less than 10 kW such as houair conditioners. The nominal size of theexpansion device because of its low comaintenance. Normally, it is used in1. Introduction

In small refrigeration systems, thtubes. However, pitch variation (more than 300 mm) had no signicant effect on the length of helicalcapillary tubes. This adiabatic helical capillary tube model can be used to integrate system models workingwith alternative refrigerants for design and optimisation.

2010 Elsevier Ltd. All rights reserved.

ary tube is used as thestarting torque and low

developed in terms of Dean number (De), Helical number (He),curvature ratio (DC/di) and Euler number (Eu), Reynolds number (Re)and the obtained geometrical group.

Kim et al. [3] presented a mass ow rate correlation based on thetions developed in termstube geometry (di, DC, pvant correlations were

mass ow rate foof inlet conditionconsidered. Forshowed that thewith the experimand standard de

Garca-Valladnite volume fowises).

l rights reserved.y tube geometries affected the length of helical capillaryCoil diameterPitch single-phase and two-phase ows, which resulted in longer tube lengths. The results show that coil diameter

variation (less than 300 mm) for helical capillarHomogeneous owconventional refrigerantsnumerical results showed tEffects of coil diameter and pitch on therefrigerants owing through adiabatic he

Sukkarin Chingulpitak a,b, Somchai Wongwises b,a The joint Graduate School of Energy and Environment, King Mongkut's University of Tecb Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Lab. (FUTURE),Bangmod, Bangkok 10140, Thailand

a b s t r a c ta r t i c l e i n f o

Available online 3 August 2010

Keywords:Capillary tubeCoiled tubeAdiabatic

This paper presents the effealternative refrigerants owthe conservation of mass, edeveloped was based on a hexperimental data of publis

j ourna l homepage: wwww characteristics of alternativeal capillary tubes

ogy Thonburi, Bangmod, Bangkok 10140, Thailandartment of Mechanical Engineering, King Mongkut's University of Technology Thonburi,

of various geometries of helical capillary tubes on the ow characteristics ofthrough adiabatic helical capillary tubes. The theoretical model is based ony and momentum of uids in the capillary tube. The two-phase ow modelogenous ow assumption. The model was validated by comparing it with thein literature for R-22, particularly various pairs of refrigerants. It was foundlower capillary lengths than alternative refrigerants. For all pairs, the

in Heat and Mass Transfer

sev ie r.com/ locate / ichmtr both straight and coiled capillary tubes. The effects, refrigerant property and coiled tube geometry wereboth straight and coiled capillary tubes, the resultsproposed correlation gave a satisfactory agreementental data for R-22, R-407C and R-410A. The averageviations were around 0.24% and 4.4%, respectively.ares [5] presented a numerical simulation based onrmulation for describing the ow characteristics of

1306 S. Chingulpitak, S. Wongwises / International Communications in Heat and Mass Transfer 37 (2010) 13051311Nomenclature

A cross sectional area of capillary tube (m2)di capillary tube internal diameter (m)DC coil diameter (m)De Dean number De = Re

di =DC

pe/di relative roughnessTsub degree of subcooling (C)f friction factorg gravitational acceleration (m/s2)G mass ow rate per unit area (kg/s m2)h specic enthalpy (J/kg)Hloss total head loss (m)He Helical number He = Re di =DC = 1 + p=DC 2

n oh i1=2p pitch of coil (m)k entrance loss coefcientL length (m)m mass ow rate (kg/s)P pressure (Pa)Re Reynolds numbercoiled adiabatic capillary tubes. The numerical model was consideredfor various aspects such as geometry, type of uid (pure substancesand mixtures), critical or non-critical ow conditions, metastableregion and transient behaviour.

Mittal et al. [6] presented an experimental investigation of coilingeffect on the ow characteristics of R-407C in an adiabatic helicalcapillary tube. It was observed that the coiling of capillary tubes (coildiameters 60 mm, 100 mm and 140 mm) signicantly inuenced themass ow rate of R-407C. From the experimental results, the massow rates of coiled capillary tubes were about 510% less than thoseof straight capillary tubes. In addition, they also proposed correlationsto predict the mass ow rate of R-407C owing through straight andhelical capillary tubes. Compared with the experimental data, it couldclearly be seen that the majority of the data fell within 10% of theirproposed correlation.

Although some information is available on the ow characteristicsin helical capillary tubes, there remains room for further research, forexample the effect of the relevant parameters on ow characteristics.In this study, the aim is to analyse the effect of coil diameters and pitchon ow characteristics of refrigerants owing through the adiabatichelical capillary tubes. Moreover, this investigation will aim to

s specic entropy (J/kg K)T temperature (C)V velocity (m/s)x quality

Greek lettersw shear stress at wall (N/m2) specic volume (m3/kg) dynamic viscosity (kg/m s) density (kg/m3)

Subscriptscond, evap condenser and evaporator, respectivelyf, g liquid phase and gas phase, respectivelyh homogeneous owi capillary inlet conditionsp, tp single-phase and two-phase, respectivelycompare various alternative mixtures of refrigerants, particularlybetween the following pairs of HCFCs with HFCs:

R-502 (R-22/R-115; 48.8.51.2) and R-404A (R-125/R-143a/R-134a;44%/52%/4%);

R-502 (R-22/R-115; 48.8.51.2) and R-507A (R-125/R-143a; 50%/50%);

R-22 and R-407B (R-32/R-125/R-134a; 10%/70%/20%); R-22 and R-407C (R-32/R-125/R-134a; 23%/25%/52%); R-22 and R-410A (R-32/R-125; 50%/50%); and R-22 and R-410B (R-32/R-125; 45%/55%).

2. Mathematical modelling

As shown in Fig. 1, the ow of refrigerants through a capillary tubecan be divided into two distinct regions: the single-phase subcooledliquid and two-phase regions. In modelling, the physical method,which is used to describe ow characteristics, is developed from theconservations of mass, energy and momentum. Moreover, the modelincludes the effect of the condenser and evaporator temperatures,inner diameter, degree of subcooling and mass ow rate ofrefrigerant.

The position between points 1 and 2 indicated in Fig. 1 is thecapillary tube inlet associated with a pressure drop because of suddencontraction. Similarly, the position between points 2 and 3 is thesingle-phase subcooled liquid region and the position between points3 and 4 corresponds to the two-phase region consisting of the liquidvapour two-phase region. The developed model is based on thefollowing assumptions:

The horizontal helical coiled tube has a constant diameter; The inner diameter and roughness of the capillary tube are constant; Adiabatic and homogeneous two-phase ow; Non-metastable liquid region; One-dimensional and steady ow; Oil-free refrigerant; and The thermodynamic equilibrium through the capillary tube.

The governing equations for describing ow characteristics for thesingle-phase and two-phase ow regions are presented below.

2.1. Single-phase ow region

A pressure loss because of an inlet sudden contraction betweenpoints 1 and 2 is determined from:

P1P2 = kV2

2g; 1

where k is the entrance loss coefcient (for square edged, k=0.5). Thesteady ow energy equation between points 2 and 3 can be expressedas:

P22g

+V222g

+ z2 =P33g

+V232g

+ z3 + fspLspdi

V2

2g: 2

For an incompressible uid, 2

3=, the continuity equation is

presented as:

m = 2V2 A = 3V3 A = VA: 3

Rearranging Eqs. (2)(3) yield:

P2 = P3 + g z3z2 +fspLspdi

V2

2

!: 4

n ad

1307S. Chingulpitak, S. Wongwises / International Communications in Heat and Mass Transfer 37 (2010) 13051311For z2=z3, substituting Eq. (4) into Eq. (1) gives:

Lsp =difsp

2G2

P1P3 k1

5

where

G = V 6

The important parameter is the single-phase friction factor (fsp),which can be calculated from three different friction factor models.These equations are expressed as follows (where fc is the frictionfactor for coiled capillary tubes and fs is the friction factor for straightcapillary tubes):Schmidt [7]

fc = fs = 1 + 0:14Rex; 7

where x=[10.0644/(DC /di)0.312] /(DC /di)0.97. Mori and Nakayama[8]

fc =C1 di =DC 0:5

Re di =DC 2:5 1=6 1 + C2Re di =DC 2:5 1=6

( )8

C1=1.88411177101+85.2472168( /di)4.63030629104( /di)2+1.31570014107( /di)3C2=6.79778633102+25.3880380( /di)1.06133140104( /di)2+2.54555343106( /di)3 Manla-paz and Churchill [9]

Fig. 1. Schematic diagram of afc = fs = 10:18=f1 + 35=He2g0:5m+ 1 + di =f3DCg 2He=88:330:5

9

where m=0 for DeN40

He = Re di =DC =f1 + p=DC 2gh i1=2

:

2.2. Two-phase ow region

In this region, the capillary tube is divided into a number ofelements as shown in Fig. 1. The following equations are based on thecontrol volume considerations in the two-phase region. The conser-vation of mass can be calculated using the following equation:

m =AVivi

=AVi + 1vi + 1

: 10The conservation of energy for the steady-state adiabatic conditionwithout external work can be expressed as follows:

h3 + gz3 +V232

!= hi + gzi +

V2i2

!11

If the elevation difference is neglected, we get:

h +V2

2= constant 12

where h and V are the enthalpy and velocity of uid at any point,respectively.

Because the refrigerant ows along the capillary tube, the pressuregradually drops and the liquid ashes into vapour arising purely fromthe reduced pressure at any point. Hence:

hi = hfi 1xi + hgixi;vi = vfi 1xi + vgixi 13

Also, m=VA=constant

V =mA

=G= Gv 14

iabatic helical capillary tube.The energy balance between point 3 and at any point along thecapillary tube in the two-phase ow region can be calculated bysubstituting Eqs. (13) and (14) into Eq. (12):

h3 +V232

= hf + x hghf

+G2

2vf 1x + vgx 2 15

Expanding the right-hand side of Eq. (15) and rearranging yields:

vgvf 2G2

2

" #x2 + G2vf vgvf

+ hghf h i

x

+G2v2f2h3

V232

+ hf

" #= 0

16

Fig. 2. Comparison of the present numerical results with themeasuredmass ow rate atdifferent coil diameters and degrees of subcooling.

Fig. 3. Comparison of pressure distributions along the capillary tube for R-502, R-404A

1308 S. Chingulpitak, S. Wongwises / International Communications in Heat and Mass Transfer 37 (2010) 13051311The quality (x) can be expressed in the form of a quadraticequation as shown in Eq. (17):

x =

hfgG2vf vfg +G2vf vfg + hfg 2 2G2v2fg G2v2f2 h3 V232 + hf

s

G2v2fg17

where hfg=hghf and vfg=vgvf.Again, the conservation of momentum can be expressed by

reconsidering the element of uid as shown in Fig. 1.

Pd2i4

! P + dP d

2i

4wdi dL = mdV 18

where w is the wall shear stress which is dened as follows:

w =fV2

819

substituting Eq. (19) into Eq. (18), we get:

d2i

4dP

ftp8V2didL = mdV 20

or

dL =diftp

2dPV2

+2mdiVAV2

: 21

For the constant mass ow rate, dm=0, Eq. (22) is obtained:

dVV

=d

: 22

Substituting Eq. (22) into Eq. (21) gives:

dL =2diftp

dPV2

+d

: 23

3. Solution method

As shown in Fig. 1, the capillary tube between points 3 and 4 can bedivided into numerous sections. Because P3 is known (saturatedliquid), the pressure at any section i can be calculated from thefollowing equation:

Pi = P3iP: 24

The pressure (Pi) and quality (xi) can be calculated from Eq. (16).So, the entropy of each section can be calculated from:

si = sif 1x + sigx: 25

The Reynolds number in the two-phase region is determined by:

Retp =Vditpvtp

26

where

V = Gtp = G xvg + 1 x vf

: 27The two-phase dynamic viscosity correlation proposed by McA-dams et al. [10] is presented as follows:

1tp

=xg

+1xf

: 28

The gradual increase of the entropy is obtained along the capillarytube. When the entropy reaches its maximum value, the uid velocityis equal to the local speed of sound and the ow is choked. As aconsequence, the calculation is ended at this point. The pressure of theelement, where the entropy has the maximum value (Pi)s max, is thencompared with the evaporator pressure (Pevap) given by:

if Pi;smax = Pevap then P4 = Pevap

if Pi;smax Pevap then P4 = Pi;smax:

Thus, from Eq. (23) the two-phase length can be expressed asfollows:

Ltp = di2G2

Psmax

P3

ftp

dp + 2 Psmax

P3

dftp

24

35: 29and R-507A.

Fig. 4. Comparison of pressure distributions along the capillary tube for R-22, R-407B,R-407C, R-410A and R-410B.

Fig. 6. Comparison of pressure distributions along the capillary tube for R-22 atdifferent coil diameters.

1309S. Chingulpitak, S. Wongwises / International Communications in Heat and Mass Transfer 37 (2010) 13051311The capillary length of each section is calculated by:

Li =2diftp;i

iPG2

+i

: 30

The total length of the two-phase region is determined from:

Ltp = n

i=1Li : 31

Finally, the total length of the capillary tube is a summation of thesingle-phase and two-phase lengths, which is dened as follows:

Ltotal = Lsp + Ltp : 32

4. Results and discussion

With the suitable friction factor equations, the straight capillarytube model can also be applied to the coiled capillary tubes. Theviscosity model is calculated with the McAdams et al. [10] model(recommended by Wongwises and Pirompak [11]).Fig. 5. Comparison of quality distributions along the capillary tube for R-22, R-407B, R-407C, R-410A and R-410B.4.1. Mathematical model verication

To validate the present model, comparisons are made with theavailable experimental data of Zhou and Zhang [1] for R-22. Fig. 2 showsthe comparisons between the present results and experimental data ofZhou and Zhang [1] for R-22 at different coil diameters and degrees ofsubcooling. The results show that the calculated mass ow rate of R-22deviates from the experimental results. Moreover, the results alsoindicate that the mass ow rate obtained from the present model tsvery well with the data. In particular, the friction factor of Mori andNakayama [8] gives the best result, which is in agreement with theresults of Zhou and Zhang [1] for R-22. Moreover, the friction factor ofMori and Nakayama [8] gives a mean absolute error of 1.58%.

4.2. Alternative refrigerants

As shown in Figs. 3 and 4, comparing the pressure dropcharacteristics for the rest of the pairs of refrigerant types showsthat for all cases in the single-phase region the conventionalrefrigerant owing through capillary tubes gives a slightly lowerpressure drop than the newer alternative refrigerants because ofthe higher viscosity of the alternative refrigerant. In the two-phaseFig. 7. Comparison of quality distributions along the capillary tube for R-22.

Fig. 8. Comparison of pressure distributions along the capillary tube for R-22. Fig. 10. Comparison of pressure distributions along the capillary tube for R-22.

1310 S. Chingulpitak, S. Wongwises / International Communications in Heat and Mass Transfer 37 (2010) 13051311ow region, however, the conventional refrigerant gives a signif-icantly lower pressure drop than the alternative refrigerant,resulting in a longer total tube length. This result indicates thatalthough both refrigerants have differences in composition, thepressure distributions along the capillary tube are almost the same.

Fig. 5 shows the change in quality with position along the capillarytube length. For all refrigerants, as expected, the quality is zero up tothe ash point and then increases in a non-linear fashion, rising morerapidly as the critical length is approached. It also shows that allalternative refrigerants vaporise earlier than their correspondingconventional refrigerants.

4.3. Effects of coil diameter on helical capillary tube

As shown in Figs. 2 and 6, in the case of coil diameters less than300 mm, the experimental data showed that the mass ow rate ofrefrigerants rapidly increases by about 67%. On the contrary, themass ow rate increase of refrigerants is small (around 12%) for coildiameters between 300 mm and 600 mm.

Fig. 7 illustrates the change in quality with position along thecapillary tube length. The observed trend for geometry considerationis similar to that corresponding to the refrigerant considerationpreviously mentioned. The quality is zero up to the ash point andthen increases in a non-linear fashion, rising more rapidly as theFig. 9. Comparison of pressure distributions along the capillary tube for R-22.critical length is approached. In addition, the total tube length of thehelical capillary tube is shorter than the straight capillary tube byabout 20% (at a coil diameter of 40 mm).

4.4. Effects of pitch on helical capillary tube

Figs. 812 present the pressure distributions at different pitchesalong the helical capillary tube. The friction factor can be calculatedfrom Manlapaz and Churchill [9] because their correlation includespitch parameter (p) in the calculation. In the case of pitches less than300 mm, the numerical results show that the total tube length rapidlyincreases by about 260290%. On the contrary, the total tube lengthslightly decreases by around 915% for pitches from 300 mm to morethan 900 mm (to innity).

5. Conclusion

This paper presents the effects of coil diameter and pitch on theow characteristics of alternative refrigerants owing through theadiabatic helical capillary tubes. From the results, it is evident that themost suitable equations for calculating the friction factor are Schmidt[7] and Mori and Nakayama [8]. These equations provided a deviationof 14%. This model was validated by comparing it with theexperimental data of Zhou and Zhang [1] R-22 and was found toFig. 11. Comparison of pressure distributions along the capillary tube for R-22.

give an average discrepancy of around 4%. The obtained results showthat coil diameter variation (less than 300 mm) affects the length ofthe helical capillary tube. Nevertheless, pitch variation (more than300 mm) has no signicant effect on the length of the helical capillarytube because the geometries of helical capillary tubes have similarshapes to straight capillary tubes. By varying the model inputparameters for all pairs, it was found that new alternative refrigerantsconsistently gave lower pressure drops for both single-phase andtwo-phase regions, resulting in longer capillary tube lengths.

Acknowledgements

The authors are indebted to King Mongkuts University ofTechnology Thonburi (KMUTT), the Ofce of Higher EducationCommission, the Thailand Research Fund (TRF) and National ResearchUniversity Project for supporting this study.

References

[1] G. Zhou, Y. Zhang, Numerical and experimental investigations on the performanceof coiled adiabatic capillary tubes, Applied Thermal Engineering 26 (1112)(2006) 11061114.

[2] S. Ali, Pressure drop correlations for ow through regular helical coil tubes, FluidDynamics Research 28 (5) (2001) 295310.

[3] S.G. Kim, S.T. Ro, M.S. Kim, Experimental investigation of the performance of R-22,R-407C and R-410A in several capillary tubes for air-conditioners, InternationalJournal of Refrigeration 25 (5) (2002) 521531.

[4] C. Park, S. Lee, H. Kang, Y. Kim, Experimentation and modelling of refrigerant owthrough coiled capillary tubes, International Journal of Refrigeration 30 (7) (2007)11681175.

[5] G. Valladares, Numerical simulation and experimental validation of coiled adiabaticcapillary tubes, Applied Thermal Engineering 27 (56) (2007) 10621071.

[6] M.K. Mittal, R. Kumar, A. Gupta, An experimental study of the ow of R-407C inan adiabatic helical capillary tube, International Journal of Refrigeration 33 (4)(2010) 840847.

[7] E.F. Schmidt, Warmeubergang and Druckverlust in Rohrschlangen, The ChemicalEngineering and Technology 39 (13) (1967) 781789.

[8] Y. Mori, W. Nakayama, Study on forced convective heat transfer in curve pipes II,International Journal of Heat and Mass Transfer 10 (1) (1967) 3759.

[9] R.L. Manlapaz, S.E.W. Churchill, Fully developed laminar ow in a helicallycoiled tube of nite pitch, Chemical Engineering Communications 7 (13)(1980) 5778.

[10] W.H. McAdams, W.K. Wood, R.L. Bryan, Vaporization inside horizontal tubes. II.Benzeneoil mixture, Transaction ASME 64 (1942) 193200.

[11] S. Wongwises, W. Pirompak, Flow characteristics of pure refrigerants andrefrigerant mixtures in adiabatic capillary tubes, Applied Thermal Engineering21 (8) (2001) 845861.

Fig. 12. Comparison of pressure distributions along the capillary tube for R-22.

1311S. Chingulpitak, S. Wongwises / International Communications in Heat and Mass Transfer 37 (2010) 13051311

Effects of coil diameter and pitch on the flow characteristics of alternative refrigerants flowing through adiabatic helica...IntroductionMathematical modellingSingle-phase flow regionTwo-phase flow region

Solution methodResults and discussionMathematical model verificationAlternative refrigerantsEffects of coil diameter on helical capillary tubeEffects of pitch on helical capillary tube

ConclusionAcknowledgementsReferences