Purdue University
Purdue e-Pubs
International Refrigeration and Air Conditioning
Conference
School of Mechanical Engineering
1994
A Study on Capillary Tube Flow
T. N. Wong
Nanyang Technological University
K. T. Ooi
Nanyang Technological University
C. T. Khoo
Matsushita Refrigeration Industries
Follow this and additional works at: http://docs.lib.purdue.edu/iracc
Wong, T. N.; Ooi, K. T.; and Khoo, C. T., "A Study on Capillary Tube Flow" (1994). International Refrigeration and Air Conditioning
Conference. Paper 275.
http://docs.lib.purdue.edu/iracc/275
This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu for
additional information.
Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/
Herrick/Events/orderlit.html
A STUDY ON CAPILLARY TUBE FLOW
C.T. KHOO
Matsushita Refrigeration Industries (S) Pte Ltd
1, Bedok South Road
Singapore 1646
Republic of Singapore
T.N. Wong and K.T. 001
School of Mechanical and Production Engineering
Nanyang Technological University
Nan yang Avenue, Singapore 2263
Republic of Singapore
ABSTRACT
This paper studies the effects of various design parameters on the perfonnance of the capillary tube. A homogeneous
two phao;;e How model was used to illustrate various etlects of the design parameters such as: tube diameter, tube roughness,
tube length, degrees of sub-cooling and the refrigerant t1ow rates on capillary tube perfonnance. The validation of the prediction
is confinned by comparing predicted pressure distribution and critical mass flow with available mea<;ured values.
Symbol
A
c
d
e
f
G
h
M
p
u,
X
z
( :~ )F
(~)r
Greek
J.l.
v
p
NOMENCLATURE
Description
Area
sonic velocity
nominal pipeline diameter
relative surface roughness
friction factor
mass velocity
specific enthalpy
mass now rate
pressure
mixture velocity
mass dryness fraction (quality)
axial direction or length
pressure gradient due to wall friction
Dimension
m
kglm 2s
kJ/kg
kgls
Nlm 2
mls
total pressure gradient
Nslm 2
m 3/kg
viscosity
specific volume
density
kg 1m
3
Subscript
f
g
tp
liquid
gas or gas plug or saturated vapour
twopha<>e
INTRODUCTION
The capillary tube is one of the most important component in a vapour compression refrigeration system. It is specially
used in small system with capacity below 10 kW. Although it is the simplest device in the refrigeration cycle, the tlow phenomena
involved is not simple. Two phase refrigerant vapour and liquid usually exist in the tube and make the study more complicated.
In the design of refrigeration systems, an incorrect matching of the capillary tube with the compressor and evaporator may
penalise the perfonnance of the whole system. Various adiabatic capillary tube models are available in the open literature. The
now parameters such as pressure drop, mass tlow rate, critical mass tlow rate and the delay of vaporisation were studied by
numerous researchers.
In studies of such systems, the refrigerant tlow in the capillary tube is generally divided into a single pha..o.;e sub-cooled
liquid region and a two phase liquid-vapour tlow region. Visual and photographic studies on the two phase tlow patterns on
the capillary tube by Mikol [1], Mikol and Dudley [2] and Koizumi and Yokoyama [3] show that the t1ow condition can be
assumed as homogeneous. To model the capillary tube now, homogeneous now assumption were made by Goldstein [4],
Koizumi and Yokoyama (3] and Melo [5].
371
Recent studies on the etiects of metastable now on the capillary tube perfonnance was carried out by Li et all6,7] and
Chen (8]. The model includes the etlects of the thennodynamic non-equilibrium vaporization and-relative velocity between the
liquid and vapour phase.
To study on the effects of new refrigerant, Wijaya [9] presented experimental test data of an adiabatic capillary tlow
as the working fluid.
HFC-134a
using
Previous study on the two phase tlow by the author [ 10] showed that the homogeneous t1ow model worked reasonable well for
pipe flow of a refrigerant R 113 liquid-vapour system. This paper attempts to use a simple homogeneous two pha.<;e tlow model
of
[10] to study the effects of the design parameters such as, the tube diameter, the tube roughness, the tube length, the degrees
sub-cooling on the perfonnance of the capillary tube.
THEORETI CAL MODELLIN G
In present analysis, the flow in the capillary tube is divided into a sub-cooled single phase liquid and saturated two pha.<>e
flow regions. In the two phase flow region the flow is modelled by assuming one dimensional, adiabatic and thermodynamic
equilibrium homogeneous tlow. Liquid tlashing arising purely from the reducing pressure. The unknown tlow parameters in
the model are quality, velocity, pressure and void fraction. It is important to mention that metastable tlow phenomena are
neglected in the modeL The governing equations used in describing the flow are presented below:
Single phase now region
For a horizontal, sub-cooled single phase flow in tube, from the conservation of momentum, the pressure drop along the
tube may be expressed as:
2
-u
jG
dP)
rvtJ
( dZ F =
(I)
the friction factor jean be obtained from Colebrook single pha..'>e friction factor curve,
J (eld)
1
9.3 ]
(2)
ff= 1.14-2lol 3.7 + Reff
As the sub-cooled liquid refrigerant flows along the tube, the fluid pressure drops along the line, hence the saturated
temperature of the liquid decrea.;;es. The length of the single phase flow region can be determined when the saturated temperature
of the liquid approaches the initial sub-cooled liquid temperature.
Two phase tlow region
As the saturated temperature reaches the initial sub-cooled temperature of the liquid, two phase llow situation occurred. The
two phase flow is assumed a homogeneous mixture in this case. The mixture velocity of the vapour-liquid refrigerant may be
.
obtained from the consideration of mass conservation. It can be expressed as:
M
M
um "'j\vm "'"A[xv~ +(1-x)v/]
(3)
The change of quality of the t1uid along the Lube may be derived from the conservation of energy, see eqn (4). The two-phase
pressure drop along the tube can be expressed as U1e sum of the pressure drop due to tube wall friction as well as the tluid
acceleration effects as shown in eqn (5).
dx
dZ
--( ~)
dZ
-
and
-
B
(~~l
F
D =
A
A
-e;)F +
372
D
c
c
(4)
d>
dZ
(5)
D
l
dv]
1
dv
1-x)=I+G x-~+(
dP
dP
1
fG
dP)
( dZ F=--u tv,J
factor expressed by Colebro ok's equation as shown
Notice that in the two phase flow region, the single phase Moody 's friction
.
as:
defined
being
number
ds
Reynol
in eqn (2) is employed, with the
U.,.d
!l,pv,.,
Re=-~
and Duklcr [ 111 mixture viscosity is defined a.~:
!!,,, = 11/ I-~)+!!~~
Where
~=
XV
<
xv,+(l -x)v1
Sonic velocity in homogeneous two phase now region
A situation will reach such that the tluid velocity reaches
The t1uill velocity increases in the now direction due to pressure drop.
now condition or choked.
the local sonic velocity, and the t1ow is said to have reached the critical
a.-; the denominator or eqn (5) approaching zero, i.e
The sonic velocity may be obtained from eqn (5). Choking occurs
(dP!dZ)T -7 0, hence
[(l-x)v1 +xv,l
C=
_/
~'.J
dv,
(6)
dv 1
-XdP- (l-x)d P
led liquid region. Once the saturated condition is
In the above analysis, equation (1) is applied to the single phase sub-coo are solved using a standard 4th order Runge- Kulla
tlow
reached, the governing equations (4) and (5) for homogeneous two pha.-;e ns (3) and (6) are computed to determine if the critical
technique with a small length increment. During the computation, equatio
is choked. The tube length corresponds to the choked
now condition is reached. The computation terminates when the flow
Moody 's single phase rriction factor with Dukler [Ill
the
,
analysis
condition is tenned the critical tube length. In the above
region.
mixture viscosity expression has been applied in the two phase now
RESUL TS AND lliSCU SSION S
Comparison with existing experimental data
available experimental results by Wijaya 191 and Li et al
To validate the simulation model, comparisons have been made with
(7].
length. The predicted results compare reasonable well
Fig 1 shows variation of critical mass now rate against the critical tube
tube for both predicted and mea:mred result-; [7]. Good
the
along
with measured data (9]. Fig 2 shows that pressure distribution
agreement is shown.
t1uid. The inlet pressure at the capillary tube entrance
In the following analysis, refrigerant HFC-134a was used as the working
the critical now condition and the computation
reaches
now
the
until
is fixed at 13.27 bar, while the exit pressure is computed
is terminated.
Effect of tuhe diameters.
various tuhe diameters. It shows a constant temperature
Fig 3 shows the temperature distribution along the capillary tube with
drop in temperature indicating that t11e point which
sudden
a
by
d
followe
distribution in the single phase liquid region and
t11e occurrence of t11e vaporisation.
vaporization hegins. The results show that bigger tube diameters delay
As the diameter increases, lhe critical mass tlow rate
Fie: 4 shows the critical ma.-;s tlow rates with various tube dimneters. mass now rate, increases in the tube diameter increase
given
a
for
t11at,
increases for a given tube length. The results also show
the necessary restriction for the desired now condition.
the tube length. In practice, an optimum dil;lmeter is required to provide
length of t11e tube available and the mass now rate.
However, as depicted in Fig 4 the optimum dimneter is affected hy t11c
373
Effects of degree of sun-cooling
Fig 5 shows the variation of the critical mass !low rate wiU1 various degrees of sub-cooling. The results show Utat for a given
tube lengU1, a higher degree of inlet sub-cooling produces a higher mass How rate. This is because as U1e inlet suh-cooling
increases, it allows the refrigerant to remain in Ule single phase liquid over a longer portion of U1e tube, Ums the two phase flow
region is shorten. Thi~ illustrates U1at the restriction to the critical mass flow rate depends very much on U1e lengU1 of the two
phase tlow region which is affected by U1C degree of suh-cooling. Whereas, at a given critical mass now rate an incre<t<.;e of
inlet sub-cooling increases U1e critical tube lengUl.
Fig 6 shows the temperature distribution along the capillary tube wiU1 various degrees of sub-cooling. The resull shows U1at
Ule higher the degree of suh-cooling the later the onset of vaporisation. Clearly, the single phase liquid region is extended at a
higher degree of suh-cooling. Fig 6 can be used to detennine Ule location for Ule onset of vaporization.
Effects of tube roughness
As shown in Fig 7, the results demonstrate Ulat for a given mass rlow rate, a decrease in tuhe roughness resulted in a longer
tuhe before the chocked condition is reached.
Fig 8 shows the variation of quality at the tube exit wiU1 various tuhe roughness. As indicated in U1e figure, higher tuhe roughnesses
increase Ule refrigerant quality at the tube exit for a given critical tube lengUl.
CONCLUSIONS
The results reconfirmed Ulat a simple homogeneous flow model may be adequately used to predict U1e performance of Ule two
phase capillary tube tlow. The effects on various parameters are shown. The results also show that, U1e single ph<t'ie Moody's
friction factor espressed by Colebrook equation wiU1 U1e Duklcr mixture viscosity expression can he used to predict U1e tlow
of two phase refrigerant Utrough capillary tuhe. It is believed that, the model, at it<-; ctuTent state, may be used to assist ilie
selection of U1c capillary tube in refrigeration systems.
ACKNOWLEDGEMENTS
The auU1ors wish to iliank Mat'iushita Refrigeration Industries (S) for tJ1e support of tl1is project. Special Umnks to Mr Noriaki
Okubo and Mr Khoo Chew Thong for U1eir support and suggestion.
REFERENCES
1.
Mikol E.P., Adiahatic single and two phase llow in small bore tubes. ASHRAE Journal (1963) Vol 5, Nov.
pp.75-88
2.
Mikol, E.P. and Dudley, J.C., A visual and photographic study ofthe inception of vaporization in adiabatic tlow.
ASME Transactions, June (1964) pp.257-264
3.
Koi:wmi H. and Yokoyama K., Characteristics of refrigerant flow in a capillary tube. ASHRAE Transactions
(1980) Vol 86, Part 2. p.19-27
4.
Goldstein S.D., A computer simulation method for dcscrihing two- ph<L'ic llashing tlow in small diameter tubes.
ASHRAE Transactions (1981) Vol87, Part2. pp.51-60
5.
Melo, C., Ferreira, R.T.S.R., Pereira,H., Modelling adiahatic capillary tubes: A critical analysis. Int. Refrigeration
Conference (1992) Vol. 1 pp.113-I22
6.
Li R.Y. Lin S., Chen Z.Y. and Chen Z.H., Metastable now of R12 through capillary tubes. Int. Journal of
refrigeration (1990), pp.181-186
7.
Li R. Y., Lin S. and Chen Z.H., N umericalmodeling of t11ermod ynamic non-eq uili hri um How or refrigerant tltrough
capillary tubes. ASH RAE Transactions (1990) Vol YO, Part 1. pp.542-549
X.
Chen Z.H, Li R.Y., Lin S. and Chen Z.Y., A correlation for metastable now of refrigerant 12 Utrough capillary
tubes. ASHRAE Transactions
(1990) Vol%, Part 1. pp.550-554
9.
10
Wijaya, H., Adiabatic capillary tube. Te~t data for HFC-134a.lnt. refrigeration conference (1992) Vol. I pp.63-71
Gilchrist, A., Callander, T.M.S. and Wong T.N .. Investigation of fluid property in horizontal two phm;c llow !low of refrigerant R113. European Two Phase Flow Group Meeting, Brussels, (19XX)
11
Dukler, A.E., cut!, Pressure drop and holdup in two phase now, AICHE Joumal (1964) 10(1), pp38-51
374
(Predicte d results ote/d~0.002)
(dm0.838 2mm)
Cose 1-
1<ood~37.78
0.005
p
.
0.003
•
"'
,· .]5€:
0
Meosured
9
'2:
8
16.7 OC subLoolc d
...
-
6
5
~
0.002
Predicted
10
T<ond;48 .9 °C
Theory
Theory
"
O.OQ-4
11
5.55 OC svbcoole d
Measured data: Case 1
Me(lsured doto: Cose 2
:i
DC
0
L~1.5rn.
J
------
0=0.66m rn. G=3306 kg/(sm~)
P;=9.67bo r. T;=-41.4
oc
2
0001
~~--~
~~~~-0~~~~~
1 _6
1 .-4
1 .2
1 .0
0.8
0.6
OA
-'------'--'--------L-~-'--___._____;
0.000 ":-':----:-'::--:-':::~:":----:-'
2.4 2.6 2.8 3.0 3 2
1.6 1 .8 :2.0 2.2
1A
0.0
0.2
Tube length (rn)
Tube le<>g!h (m)
Compar ison of predicte d and me:Lwred pressure
Fig. 2
Compnr ison of predicte d :md measured critical m:L\s flow rate
Fig. I
along
th~
1uhc
with tube length
Variatio n of mass flowrot e
Variat ion of tempe rature along the tube
50
,.--....
1\\~-,-- ............
40
u
'
0
'-'
30
(l)
::>
..._..
I
\
I
-"-~---
()__
0
\
~
\
I
I
0
f-
0.003
~
10
E
(!)
o>
.::::.,
'
'---
(!)
0.004
..-..
........
"'
\
20
0
0.002
0
-..._
2
(fJ
0.001
0
::::;;:
0.000
4
3
2
0
Tube length (m)
Fig. 3
---
<Il
--~~--~
-10~~0----~--~--~--~
1
mm
mm
mm
mm
do=1_0 mm
do=0.6
d=0.7
doo0.8
d=0.9
ds0.6 mm
d;Q.7mm
d;0.8mm
d;0_9mm
d;::=l_Omm
Fig.4
Temperature distribution along the tube
5
4
3
(m)
length
Tube
8
7
6
Mass flow rate at choked condition
Variat ion of tempe rature along the tube
0 OC subcoole d
Variation of moss flowrat e ot choked conditi on
with various degrees of subcoo ling (d=0.6 mm)
5 DC subcoole d
1 0 OC subcQol~d
0.00~0
oc subcool~d
oc subcoole d
oc subcoole d
15 oc -:subcoolt! d
20 oc gubcool• d
0
5
0.0035
.------.,
u
10
0.0030
0
0.0025
-----· 40
0
(l)
()__
0.0020
E
Q
f-
0.0015
...___,___
'"::'"~:'":-----:"':---'"::'-:~-'----'-~-'--"'"--'--'--
~0
nt
~2
QJ ~4 Q5 Q6 0~
OB
0~
1~
::"""~;_---
----- -_......_ ~--
.... ~'-...----.L-~___:_' ,_ __
'
-
30
----...
'\
\
I
20
\
.
'\
\
\
~~~~~~~~~--~~'~
10~
0.0 0.2 0.4 0.6 0.8 1.0 1 .2 1 .4 1 .6
Tube length (m)
Tube length (m)
Fig. S
:w DC subeoole d
50
(l)
::>
0.001 0
1 5 OC subcoole d
60
Fig.6
Mass flow rate at choked condition
375
Temperature distribution along the tube
Variation of moss flowrote ot choked condition
0.0035
........ 0.0033
"' 0.0031
.........
a>
0.0029
-"'
0.0027
.2 0.0025
0
~ 0.0023
0.0021
2i 0.0019
"'0"' 0.0017
2
0.0015
0.0013
o.oo1
b.o
-
\ .\l
I
'
\
'
'
'
\
'
\
'
'" "
''
\
'
e/d=5x1 0-6
e/d=5x1 0- 4
e/d=5x1 0-3
e/d=5x1 o- 2
0.34
0.32
c
.9
"
\
u
"'
' ' "'
0.5
Variation of quality ot choked condition
1 .0
Jg
"'
<f)
' "
OJ
' '
'
c
i':'
0
'
1.5
2.0
ejde=5x1 0-6
e/d=5x1 O-<
e/d=5x1 O-J
e/d=5x1 0-2
0.22
0.20'
0.1 ~
3.0
Tube length (m)
Fig. 7
0.26'
0.24
0.18
'
-2.5
0.30
0.28
.0
0.5
1.0
1.5
2.0
lube length (m)
Mass now rate at choked condition
Fig. X
376
Quality at choked condition
3.0