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Two-phase pressure drop in return bends: Experimentalresults for R-410A
Miguel Padilla a,b, Remi Revellin a,b,*, Philippe Haberschill a,b, Jocelyn Bonjour a,b
aUniversite de Lyon, CNRS, Lyon, Franceb INSA-Lyon, CETHIL, UMR5008, F-69621, Villeurbanne, France
a r t i c l e i n f o
Article history:
Received 4 November 2010
Received in revised form
9 March 2011
Accepted 17 March 2011
Available online 24 March 2011
Keywords:
Two-phase flow
Pressure drop
Refrigerant
Experimentation
* Corresponding author. Tel.: þ33 4 72 43 72E-mail address: remi.revellin@insa-lyon.f
0140-7007/$ e see front matter ª 2011 Elsevdoi:10.1016/j.ijrefrig.2011.03.009
a b s t r a c t
This study presents 238 pressure drop data pointsmeasured for two-phase flow of R-410A in
horizontal return bends. The tube diameter (D) varies from 7.90 to 10.85 mm and the
curvature ratio (2R/D) from 3.68 to 4.05. Themass velocity ranges from 179 to 1695 kgm�2 s�1
and the saturation temperatures from 4.6 �C to 20.7 �C. Preliminary tests show that the
recovery length necessary for a correct pressure drop measurement downstream of the
return bend is less than 20D, for the experimental conditions covered in this study. The
singular pressure drop is determined by subtracting the regular pressure drop in straight
tube from the total pressure drop. The experimental data are compared against four
available correlations found in the literature. The present experimental database for the
return bend pressure drop is presented in the Appendix A.
ª 2011 Elsevier Ltd and IIR. All rights reserved.
Chute de pression diphasique dans les coudes de retour :resultats experimentaux obtenus avec le R-410A
Mots cles : Ecoulement diphasique ; Chute de pression ; Frigorigene ; Experimentation
1. Introduction
Due to environmental issues, there is a growing interest in
refrigerant charge reduction in HVAC& R systems. Oneway to
achieve this refrigerant charge reduction is related to the
change in the design of evaporator and condenser coils, which
become more and more compact. In this sense, the effect of
singularities (e.g. return bends) on the hydrodynamic perfor-
mance becomes more important. It is necessary to be able to
predict not only the pressure drop in straight tubes, but also
that in singularities such as return bends.
31; fax: þ33 4 72 43 88 10r (R. Revellin).ier Ltd and IIR. All rights
Return bends are extensively used in compact refrigeration
systems such as air conditioners or heat pumps. Either single-
phase or two-phase flow can occur in these applications. For
single-phase flow, extensive studies were carried out
numerically and experimentally by various investigators. In
return bends, the centrifugal force makes the fluid accelerate
in the concave part of the curved channelwhile the fluid in the
convex part is slowing down (Dean (1927)).
Two-phase pressure drops in return bends in refrigeration
systems have also been experimentally investigated by several
authors in the open literature. Pierre (1964) studied thepressure
.
reserved.
Nomenclature
a empirical constant (s2/3 m�1/3)
b empirical constant
D tube diameter (m)
f friction factor
G mass velocity (kg m�2 s�1)
h enthalpy (J kg�1)
J superficial velocity (m s�1)
K pressure drop coefficient of Chisholm (1983)
L length (m)
MAE Mean absolute error
ðMAEÞ ¼ 1N
XN1
����predicted value� experimental valueexperimental value
�����100 ð%Þ
MRE Mean relative error
ðMREÞ ¼ 1N
XN1
�predicted value� experimental value
experimental value
�
�100 ð%Þ
p pressure (Pa)_Q heat rate (W)
q heat flux (W m�2)
R curvature radius (m)
T temperature (�C)
Re Reynolds number
v specific volume m3 kg�1
x vapor quality
Greeks
b coefficient of volume expansion K�1
L curvature multiplier of Domanski and Hermes
(2008)
m dynamic viscosity (Pa s)
F two-phase multiplier
r density (kg m�3)
s surface tension (N m�1)
Sub and superscripts
eq equivalent
f frictional
heater from the heater
in inlet
l liquid
o turning of the flow
p constant pressure
rb return bend
sat saturation
sing singular
sp single-phase
st straight tube
tp two-phase
tot total
v vapor
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 8 5 4e1 8 6 5 1855
drop for R-12 in return bends with two-phase flow for the oil-
free medium and for oil-refrigerant mixtures. Traviss and
Rohsenow (1973) measured two-phase pressure drops of R-12
in a 8.00 mm tube in order to determine whether the distur-
bance caused by a return bend was only a localized effect or
extended over a significant length of the condenser tube. Geary
(1975) investigated the two-phase adiabatic flow pressure drop
inreturnbendsbasedonhisR-22datawith tubediameters from
11.05mm to 11.63mmwith curvature ratios (2R/D) from 2.32 to
6.54. Later, Chen et al. (2004) presented single-phase and two-
phase frictional pressure drop data for R-410A in four types of
return bendswith tube diameters ranging from3.30 to 5.07mm
and curvature ratios varying from 3.91 to 8.15. Then, Chen et al.
(2007) presented a study with single-phase and two-phase
pressure drop data for R-134a/oil mixture with several oil
concentrations, flowing in a meandering tube with an inner
diameterof 5.07mmandacurvature ratio of 5.18.Very recently,
Chenetal. (2008)presentedmeasurementsofR-134a two-phase
frictional pressure gradients for vertical and horizontal
arrangements of a U-type copper meandering tube which
contained nine consecutive return bends with an inner diam-
eter of 5.07 mm and a curvature ratio of 5.18.
In the open literature, among the articles related to two-
phase pressure drop correlations in return bends, only few
provided specific information (fluid, saturation temperature,
mass velocity, diameter, etc.) for refrigerants as a working
fluid. In Tables 1 and 2 are summarized those correlations
with their experimental conditions.
1.1. Effect of the singularities on the downstreampressure drop
One of the most important parameter when designing an
experimental bench for measuring two-phase pressure drop
in singularities is the flow recovery length. Indeed, the loca-
tion of the pressure taps before and after the singularity is
important. In the study of Traviss and Rohsenow (1973) on R-
12 two-phase flow in straight tubes with inner diameters of
12.70 mm and 25.40 mm, the pressure drop was measured
incrementally along the test sectionwith the first pressure tap
located approximately 10D downstream of the return bend.
They found that the amount of pressure recovery in the test
section downstream of the return bend was negligible. The
pressure gradient in the first downstream increment did not
deviate significantly (�10%) from the fully developed pressure
gradient. Hoang andDavis (1984) suggested that a length equal
to 9D is required to complete the remixing process of the
phases after leaving a return bend. However, the relatively
well-mixed flow condition does not mean that the two-phase
structure (or flow pattern) is fully recovered, and hence the
pressure gradient at 9D upstream is totally different with the
pressure gradient at 9D downstream of the return for each
operating case. In addition, Chen et al. (2003) referred to
a former study (Cheng and Yuen, 1987) on two-phase flow in
which the flow recovery length was 70D. However, this
reference is not correct since Cheng and Yuen (1987) used only
air as a working fluid (laminar single-phase flow experiments
Table 1 e Two-phase pressure drop correlations in return bends.
Chisholm (1983)
and Idelshik (1986)
Dprb ¼ FDpsp Dpsp ¼ KspG2
2rl
Ksp ¼ flLDþ 0:294
�RD
�0:5
F ¼ 1þ�rl
rv� 1
�x
�bð1� xÞ þ x
�
b ¼ 1þ 2:2
Ksp
�2þ R
D
�
Chen et al. (2004)
�dpdz
�rb
¼ frvJ
2v
2Df ¼ 10�2Re0:35m
We0:12v exp�0:194
�2RD
��x1:26
Domanski
and Hermes (2008)
�dpdz
�rb
¼ L
�dpdz
�st
L ¼ 6:5�10�3
GxDmv
!0:54�1x� 1
�0:21�rl
rv
�0:34�2RD
��0:67
Padilla et al. (2009)
�dp
dz
�rb
¼�dp
dz
�st
þ�dp
dz
�sing
where
�dp
dz
�st
is calculated with the (Muller-Steinhagen and Heck (1986)
correlation and
�dpdz
�sing
¼ a
�rvJ
2v
R
��J2lR
�bwhere a ¼ 0.047 s2/3 m�1/3
and b ¼ 1/3 Jv ¼ Gxrv
Jl ¼Gð1� xÞ
rlNote that Dpsing ¼ pR
�dpdz
�sing
Validity range of the above methods given in Table 2.
All the methods are applied over the return bend only (over the length pR).
Table 2 e Experimental conditions of the prediction methods from the literature.
Correlation Refrigerant D 2R/D G Tsat x
Chen et al. (2004) R-410A 3.25e3.30 3.91e8.15 300e900 25.0 0.10e0.90
Domanski and Hermes (2008) R-22, R-410A 3.25e11.63 2.32e8.15 300e900 20.0e25.0 0.10e0.90
Padilla et al. (2009) R-12, R-134a, R-410A 3.25e8.00 3.18e8.15 150e900 10.0e39.0 0.01e0.94
Fig. 1 e Sketch of the experimental facility.
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 8 5 4e1 8 6 51856
and not two-phase flow). Azzi and Friedel (2005), based on
experimental pressure loss data during airewater flow in
vertical 90� plexiglas bends with an internal pipe diameter of
30 mm and curvature ratios (2R/D) from 8 to 30, had empiri-
cally reported that the distance for the outlet flow to be fully
recovered is about 30 diameters. With a higher system pres-
sure, the required pressure recovery length could be shorter.
Azzi and Friedel (2005) also mentioned the two-phase
recovery length by Sekoguchi et al. (1968). The later carried out
experiments with airewater in a 25.7 mm inner tube diameter
with a curvature ratio (2R/D) of 4.8 in 90� bendswith horizontal
plane. They claimed that in the case of 90� bends the
minimum downstream recovery length is about 150 times the
pipe diameter. Mandal and Das (2001) measured the static
pressure of gas and liquid flow starting to deviate from steady
value within 30 pipe diameters for the 45�, 90�, 135�, and 180�
bends upstream of the inlet of the bend, depending on the
flow rate. In the downstream of the bend, the pressure
recovery lengthswere found to bewithin 35 pipe diameters for
the 45�, 90�, 135�, and 180� bends, depending on the flow rate.
Mandal and Das (2001) mentioned that pressure drop given by
Ito (1960) starts to deviate from the developing flow 5e10 pipe
diameters upstream of the inlet and gradually approaches the
developing flow in the downstream straight section about
40e50 pipe diameters from the bend exit.
As a conclusion, the flow recovery length depends on the
curvature ratio (2R/D), fluid properties and flow conditions.
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 8 5 4e1 8 6 5 1857
There is a lack of experimental data on this topic in the liter-
ature, especially for synthetic refrigerants; as a result, exper-
imental testswill be performed to determine the flow recovery
length in our conditions.
The purpose of this experimental investigation is to extend
the existing available database in the literature toward
different tube diameters and curvature ratios for two-phase
flowof refrigerants inhorizontal returnbends.The secondstep
is to compare the datawith existing predictionmethods (Table
1) in order to guide engineers in their choice of correlations.
2. Experimental facility and experimentalconditions
2.1. Test facility
Fig. 1 shows a sketch of the present experimental facility. It
consists of two parallel loops: the refrigerant loop and the
watereglycol loop. The test facility is designed to allow single-
a
b
Fig. 2 e (a) Details of the test section. L0 [ 1000 mmz 92D, L1 [
L4[ 165mmz 20D, L5[ 1000mmz 127D. (b) Sketchof the section
the return bend.
phase and two-phase tests using various refrigerants. The
refrigerantflowloopconsistsofagearpumpwhichdeliverssub-
cooled refrigerant totheheater.Therefrigerant ispreheatedand
partially evaporated in the heater to the desired vapor quality.
Thevaporqualityentering thetest section iscalculatedfromthe
energy balance on the electrical heater given by Eq. (1):
Dx ¼
� _Qheater
_m
�þ hheater;in � hl
hlv(1)
where hlv ¼ hv � hl is the latent heat of vaporization and
�(hheater,in � hl) corresponds to the subcooling sensible heat._Qheater is the electrical power of the heater.
The fluid passes through the test section and is cooled and
condensed in the condenser. Before returning to the pump,
the refrigerant is sub-cooled to ensure that no vapor flows into
the pump. The refrigerant mass flow rate is adjusted by the
operator using a by-pass and measured by means of a Cori-
olis-type flow meter. All components and tubes are well
insulated with foam material.
110mmz 10D, L2 [ 210mmz 20D, L3 [ 120mmz 15D,
s used to determine the flowrecovery lengthdownstreamof
0 0.2 0.4 0.6 0.8 1
0
2000
4000
6000
8000
10000
12000
14000
16000
Vapor quality [−]
Fric
tio
na
l p
re
ss
ure
g
ra
die
nt [P
a/m
]
D = 7.9 mm
G = 560 kg/m2s
Tsat
= 15 °C
20D
50D
Müller−Steinhagen and Heck (1986) Model
Moreno Quibén and Thome (2007) Model
0 0.1 0.2 0.3 0.4 0.5 0.6
0
5000
10000
15000
20000
25000
30000
35000
Vapor quality [−]
Frictio
nal p
ressu
re g
rad
ien
t [P
a/m
]
D = 7.9 mm
G = 1140 kg/m2s
Tsat
= 15 °C
20D
50D
Müller−Steinhagen and Heck (1986) Model
Moreno Quibén and Thome (2007) Model
a
b
Fig. 3 e Straight tube frictional pressure gradients vs. vapor
quality for two flow recovery lengths downstream of the
return bends, namely 20D and 50D. Comparisons to two-
well-known frictional pressure gradient prediction
methods in straight tubes. (a) D[ 7.9 mm, G[ 560
kg$mL2$sL1, Tsat [ 15�C. (b) D[ 7.9 mm, G[ 1140
kg$mL2$sL1, Tsat [ 15�C.
0.1 0.2 0.3 0.4 0.5 0.6 0.7
0.1
0.2
0.3
0.4
0.5
0.6
m Δ hL [kW]
Ele
ctric
al p
ow
er [
kW
]
Energy balance
86.7 % of the data within ± 5 %
MAE = 2.5 %
MRE = 0.8 %
.
a
b
1000 10000 100000 1000000
0.001
0.01
0.1
Liquid Reynols number [−]
Fric
tio
n fa
cto
r [−
]
f = 0.046*Re−0.2
L
Single−phase flow
in straight tubes
f = 0.0791*Re−0.25
L
MAE = 5.3 %
MRE = 0.4 %
D=10.85 mm (R−410A)
D=7.9 mm (R−410A)
D=5.3 mm (R−134a)
Fig. 4 e Energy balance and single-phase pressure drop
measurements. (a) Energy balance (b) Friction factor vs.
Liquid Reynolds number for straight tube.
Table 3 e Experimental conditions and uncertainties ofthe present database.
Parameters Range Uncertainties
Fluid R-410A
D 10.85 and 7.90 mm �0.6%
R 20.00 and 16.00 mm �0.6%
G 179.18e1695.26 kg m�2 s�1 �1.3%
Tsat 4.6e20.7 �C �0.1 K_Q 0.00e10.00 kW �1 W
x 0.045e0.960 �0.82%
p 10.85e12.92 bar �0.1%
Dp 0e23.98 kPa �0.1%
L0 1000.00 mm z 92D �0.5%
L1 110.00 mm z 10D �0.5%
L2 210.00 mm z 20D �0.5%
L3 120.00 mm z 15D �0.5%
L4 165.00 mm z 20D �0.5%
L5 1000.00 mm z 127D �0.5%
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 8 5 4e1 8 6 51858
The pressure is controlled in the condenser by means of
a water e glycol flow in the watereglycol loop, with
a temperature comprised between �5.0 �C and 20.0 �C, thatcan be chosen by the operator. This water e glycol flow
controls the two-phase conditions in the liquid reservoir.
2.2. Test section
The test section for pressure drop measurements (Fig. 2(a)) is
made of copper and includes two straight tubes, two return
bends and one sudden contraction. The test tubes are set up
horizontally. The saturation pressure is measured using an
absolute pressure transducer located at the test section outlet.
In addition, two thermocouples are placed at the inlet and the
outlet of the test section in the center of the flow. The desired
vapor quality at the inlet of the test section is obtained by
adjusting the power of the electrical heater.
A straight entrance tube of inner diameter of 10.85mmand
550.00 mm (50D) of length is located upstream of the first
straight tube of the test section to achieve a fully developed
flow condition. A differential pressure transducer is used to
measure the pressure drop across the first straight tube
0 0.2 0.4 0.6 0.8 1
0
2000
4000
6000
8000
10000
12000
14000
Sin
gu
la
r p
re
ss
ure
d
ro
p [P
a]
D = 7.9 mm
2R/D = 4.05
T sa t
= 15 ° C
G = 700 kg/m 2 s
G = 1150 kg/m 2 s
a
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 8 5 4e1 8 6 5 1859
(D ¼ 10.85 mm, L0 ¼ 1000.00 mm). The pressure gradient along
the first return bend (2R/D ¼ 3.68) is measured from a second
differential pressure transducer. The pressure tap is located
210 mm z 20D (L2) downstream of the return bend.
300 mm z 28D downstream of the pressure tap the flow
passes across a sudden contraction to obtain a new tube
diameter. A straight tube of length 650.00 mm z 82D is
directly connected downstream of the sudden contraction for
the flow recovery. Two differential pressure transducers are
used to measure the pressure drop across the second return
bend (2R/D ¼ 4.05) and the second straight tube (D ¼ 7.90 mm,
L5 ¼ 1000.00 mm). The pressure tap is located 165 mm z 20D
downstream of the second return bend. In order to check the
flow recovery length necessary downstream of return bends
to make a correct pressure drop measurement, two pressure
drop tests in straight tubes were carried out by considering
two different inlet pressure tap locations. Fig. 2(b) presents the
test section used to determine the flow recovery length
downstream of the return bend. In the first test, the pressure
drop was measured along the straight tube (D ¼ 7.90 mm,
L5 ¼ 1000.00 mm) with the first pressure tap located approxi-
mately 50Dz 400mmdownstream of the return bend. For the
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
100
200
300
400
500
G = 370 kg/m2s
Slug I
Slug+SW
S
SW
A
Mass velo
city [kg
/m
2s]
Vapor quality [−]
1
0
150
300
450
600
P
ressu
re d
ro
p [P
a]
Return bend
Straight tube
Singularity
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
0
100
200
300
400
500
600
700
800
900
G = 700 kg/m2s
Slug I
Slug+SW
S
SW
A
Ma
ss
v
elo
city
[k
g/m
2s]
Vapor quality [−]
0
1000
2000
3000
4000
P
re
ss
ure
d
ro
p [P
a]
P
re
ss
ure
d
ro
p [P
a]
Return bend
Straight tube
Singularity
a
b
Fig. 5 e Flow patterns fromWojtan et al. (2005) and return
bend, straight tube and singular pressure drops (over the
length pR) vs. vapor quality. (a) Flow patterns and pressure
drop forD[10.85mm,2R/D[3.68,G[370.00kg$mL2$sL1,
Tsat [ 15.0�C and q[ 0 kW$mL2. (b) Flow patterns and
pressure drop for D[ 7.90 mm, 2R/D[ 4.05, G[ 700
kg$mL2$sL1, Tsat [ 15.0�C and q[ 0 kW$mL2.
second test, the first pressure tap was located approximately
20Dz 160mmdownstream of the return bend. Fig. 3(a) and (b)
show the results of these tests. The straight tube pressure
gradient measured for a recovery length of 20D does not
deviate significantly (�5%) from the straight tube pressure
gradient measured at 50D. In this sense, to minimize the test
Vapor quality [−]
0 0.2 0.4 0.6 0.8 1
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Vapor quality [−]
Sin
gu
la
r p
re
ss
ure
d
ro
p [P
a]
T sa t
= 15 ° C
G = 600 kg/m 2 s
2R/D = 3.68
2R/D = 4.05
b
c
0 0.2 0.4 0.6 0.8 1
0
100
200
300
400
500
600
700
Vapor quality [−]
Sin
gu
lar p
ressu
re d
ro
p [P
a]
D = 10.85 mm
2R/D = 3.68
G = 300 kg/m2s
Tsat
= 5 °C
Tsat
= 20 °C
Fig. 6 e Effect of the mass velocity, the temperature and the
curvature ratio on the singular pressure drop. (a) Effect of
the mass velocity G. (b) Effect of saturation temperature
Tsat. (c) Effect of the curvature ratio 2R/D.
Fig. 7 e Experimental pressure drop data in return bends (over the length pR) compared to prediction methods (238 points).
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 8 5 4e1 8 6 51860
section size, the minimal flow recovery length of 20D was
selected to locate the pressure taps downstream of the return
bends. In addition, we have compared the straight tube
pressure gradients to the models of Muller-Steinhagen and
Heck (1986) and Moreno Quiben and Thome (2007). As can be
seen, the data are comprised between these two models. This
corroborates the reliability of our two-phase flow experiments
and pressure drop measurements.
2.3. Experimental conditions
Table 3 summarizes the experimental conditions of the
present database along with the corresponding uncertainties.
Table 4 e 238 experimental pressure drop data points forreturn bends compared to different correlations from theliterature.
�30 % error band MAE MRE
Chisholm (1983) and Idelshik
(1986)
54.3% 79.0% 59.9%
Chen et al. (2004) 45.7% 87.2% 76.3%
Domanski and Hermes (2008) 52.9% 63.7% 47.2%
Padilla et al. (2009) 15.5% 56.3% �34.4%
The 238 experimental tests have been carried out using two
different tube diameters (10.85 and 7.90 mm), saturation
temperatures from 4.6 �C to 20.7 �C, and over the entire range
of the vapor quality. The mass velocity ranges from 179.18 to
1695.26 kg m�2 s�1. The working fluid is R-410A.
2.4. Single-phase experiments
In order to check the measurements made with the present
experimental facility, an energy balance and single-phase
pressure drop measurements have been carried out. The
energy balance (Fig. 4(a)) depicts a Mean Relative Error (MRE)
less than 1%. The single-phase pressure drop data have been
compared to the well-known Blasius equations for turbulent
flow in smooth tubes ( fst ¼ 0.079Re�0.25 for Re < 20 000 and
fst ¼ 0.046Re�0.20 for Re > 20 000) with an MRE less than 0.5%
(Fig. 4(b)). The test facility is thus validated.
3. Data reduction
As some ambiguities can sometimes be detected in the liter-
ature, we wish to underline here that our approach is to study
the singular pressure drop (Dpsing), which is obviously
different from the pressure of the whole return bend (Dprb).
0 0.2 0.4 0.6 0.8 1
0
500
1000
1500
Pressu
re d
ro
p in
retu
rn
b
en
ds [P
a]
Vapor quality [−]
D = 10.85 mm
2R/D = 3.68
G = 400 kg/m2s
Tsat
= 20 °C
Experimental data
Chisholm & Idelshik
Chen et al.
Domanski & Hermes
Padilla et al.
0 0.2 0.4 0.6 0.8 1
0
1000
2000
3000
4000
5000
6000
7000
Pressu
re d
ro
p in
retu
rn
b
en
ds [P
a]
Vapor quality [−]
D = 7.90 mm
2R/D = 4.05
G = 700 kg/m2s
Tsat
= 15 °C
Experimental data
Chisholm & Idelshik
Chen et al.
Domanski & Hermes
Padilla et al.
a
b
Fig. 8 e Experimental pressure drop in return bends (over
the length pR) as a function of the vapor quality compared
to different prediction methods.
200 400 600 800 1000 1200 1400 1600 1800 2000
0
10
20
30
40
50
60
Mass velocity [ kg/m2s ]
Nu
mb
er o
f d
ata
p
oin
ts
[ −
]
0 5 10 15 20 25 30
0
20
40
60
80
100
120
140
Saturation temperature [ °C ]
Nu
mb
er o
f d
ata
p
oin
ts
[ −
]
0 0.2 0.4 0.6 0.8 1
0
5
10
15
20
25
30
35
Vapor quality [−]
Nu
mb
er o
f d
ata
p
oin
ts
[−
]
a
b
c
Fig. 9 e Distribution of the database.
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 8 5 4e1 8 6 5 1861
However, in order to obtain the values of the singular pressure
drop Dpsing, the pressure drops in straight tubes and in return
bends have beenmeasured. The singular pressure drop due to
return bend is given by the following relation:
Dpsing ¼ Dptot ���dpdz
�st
Leq (2)
where Leq ¼ L1 þ pR1 þ L2 ¼ 0.383 m for the first return bend
and Leq ¼ L3 þ pR2 þ L4 ¼ 0.335 m for the second return bend.
Dptot is the total pressure drop measured over the length Leq.
The straight tube pressure gradient is calculated from the
measurements made along the straight section:��dpdz
�st
¼ Dpst
Li(3)
where Li ¼ L0 ¼ 1000.0 mm for D ¼ 10.85 mm and
Li ¼ L5 ¼ 1000.0 mm for D ¼ 7.90 mm. Finally, the return bend
pressure drop is calculated as follows:
Dprb ¼ Dpsing þ��dpdz
�st
pRð1 or 2Þ (4)
In the experiments, the maximum pressure drop measured
from the outlet of the electrical heater (where the vapor
quality is calculated) to the outlet of the test section can reach
up to 0.84 bar. This pressure drop is not negligible and
provokes a so-called flashing (increase of the vapor quality
due to pressure reduction) and a temperature difference. The
flashing effect may easily be calculated using the relation
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 8 5 4e1 8 6 51862
developed by Revellin et al. (2009), which is expressed (for
constant properties and neglecting the term b(v/vlv)hlv in the
specific heat capacity at constant vapor quality) as follows:
Dx ¼ �vlvTsatcp;tp þ hlvvtp
h2lv
Dp (5)
where vlv ¼ vv � vl, vtp ¼ xvv þ (1 � x)vl. In addition, cp,tpcorresponds to the specific heat capacity of the two-phase
flow at constant pressure, calculated by the following relation:
cp;tp ¼ xcp;v þ ð1� xÞcp;l (6)
The induced temperature difference is obtained using the
Clapeyron equation ðdp=dTsat ¼ hlv=ðTsatnlvÞÞ. The maximum
vapor quality variation Dx due to the flashing effect from the
outlet of the electrical heater to the outlet of the test section is
0.022. As a consequence, the variation of the vapor quality along
the tubes has been taken in to account. The vapor qualities
mentioned in the figures are the inlet vapor qualities of each
measurement length. However, the variation of the vapor
quality due to the flashing effect along the pressure drop
measurement lengths is small enough to assume the vapor
quality to be constant along these lengths. In addition, the
maximum temperature difference due to the pressure drop
along the tube is up to 2.3 K. As a result, the saturation temper-
ature is recalculated at the inlet of each straight tube and return
bend. The values of the temperature given in Appendix A
account for this correction.
Fig. 5(a) shows the results of Dpsing, Dpst and Dprb for
D¼ 10.85mm, 2R/D¼ 3.68, G¼ 370 kgm�2 s�1 and a saturation
temperature of 15.0 �C. As can be seen, the return bend pres-
sure drop corresponds to the sum of the singular pressure
drop plus that in straight tube over the length pR. It is also
interesting to distinguish the maximum in pressure drop, not
only for the straight tube but also for the singular pressure
drop. This maximum corresponds to a vapor quality around
0.72 for the singular pressure drop, which is lower than that
observed for the straight tube. Deriving the expression
developed by Padilla et al. (2009) (Eq. (7)):
�dpdz
�sing
¼ a
�rvJ
2v
R
��J2lR
�b(7)
with respect to x, predicts that themaximumsingularpressure
drop should occur for a vapor quality equal to xmax ¼ 1/(1 þ b).
Since b ¼ 1/3, xmax ¼ 0.75. This value is close to that experi-
mentally found (xmax ¼ 0.75 for Fig. 5(a) and xmax ¼ 0.71 for
Fig. 5(b). Fig. 5(b) shows the results forD¼ 7.90mm,2R/D¼ 4.05,
G ¼ 700 kg m�2 s�1 at the same saturation temperature.
In Fig. 5(a) and (b), the flow pattern map proposed by
Wojtan et al. (2005) is shown for information. This map was
developed for straight tubes only. Therefore, it cannot strictly
be used to determine the flow pattern in the test section.
Nevertheless, it gives an indication of the flow regimes
encountered at the return bend inlet (i.e. the outlet of the
straight tube). In our database, at the inlet of the return bend,
52.5% (125 points) of the experiments are for annular flow,
whereas 44.1% are for intermittent flow. The rest is segregated
between slug (2.98%) and stratifiedwavy (0.42%). Note that the
flow pattern map of Wojtan et al. (2005) was implemented by
setting the heat flux to 0.00 kW m�2, as the present experi-
ment is performed in adiabatic conditions.
4. Results and discussion
Fig. 6 presents the effect of the mass velocity G, the saturation
temperature Tsat and the curvature ratio 2R/D on the singular
pressure drop. As can be observed, when the mass velocity
increases (Fig. 6(a)), the singular pressure drop increases. This
is consistent with the correlation of Padilla et al. (2009). As
a matter of fact, the centrifugal effect acting on both phases,
which was the physical reasoning behind Padilla et al. (2009)
correlation, becomes more and more important when G
increases. Regarding the influence of the saturation temper-
ature (Fig. 6(b)), it can be observed that the singular pressure
drop increases when the saturation temperature decreases.
Finally, in Fig. 6(c) when the curvature radius is lower, the
singular pressure drop increases.
Two-phase pressure drop data were compared against
available correlations (Fig. 7): i.e. the methods developed by
Chisholm (1983) and Idelshik (1986), Chen et al. (2004), the
Domanski and Hermes (2008) and Padilla et al. (2009). All these
methods allow the calculation of the return bend pressure
drop over the length pR. The results of the comparison are
summarized in Table 4. As can be observed, none of these
methods was able to satisfactorily predict the return bend
pressure drop.
Beyond the above statistics, Fig. 8(a) and (b): graphically
show the comparison between the Chisholm (1983) and
Idelshik (1986) method, the Chen et al. (2004), the Domanski
and Hermes (2008) and the Padilla et al. (2009) correlations
with selected experimental data from the present database.
For an eventual use by the readers, all the experimental data
shown for return bends are extensively given in Appendix A.
To check the performance of correlations, the distribution of
influencing parameters in the database are shown in Fig. 9.
Fig. 9(a)e(c) shows the data distribution with respect to mass
velocity, saturation temperature and vapor quality.
5. Conclusions
In this paper, 238 pressure drop data points measured in
horizontal return bends have been presented for R-410A. The
tube diameter (D) varied from 7.90 to 10.85 mm and the
curvature ratio (2R/D) from 3.68 to 4.05. The mass velocity (G)
ranged from 179 to 1695 kg m�2 s�1 and the vapor quality (x)
from 0.045 to 0.960. Saturation temperatures were tested from
4.6 �C to 20.7 �C. The singular pressure drop was determined
by subtracting the regular pressure drop in straight tube from
the return bend pressure drop. It has been shown that the
singular pressure drop increases when the mass velocity
increases because of the increasing effect of the centrifugal
force acting on both phases. Furthermore, the singular pres-
sure drop was higher for a lower saturation temperature and
a lower curvature ratio (2R/D).
A preliminary experimental investigation was carried out
to determine the flow recovery length necessary downstream
of the return bend to make a correct pressure drop measure-
ment. Two different tap locations were tested, namely 20D
and 50D. The results show that the pressure drop determined
for a recovery length of 20D does not deviate significantly
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 8 5 4e1 8 6 5 1863
(�5%) from that for 50D. This result shows that the fully
developed pressure gradient has been reached before 20D.
The 238 experimental data have been compared against
available correlations found in the literature: i.e. the methods
developed by Chisholm (1983) and Idelshik (1986), Chen et al.
(2004), Domanski and Hermes (2008) and Padilla et al. (2009).
None of these methods was able to satisfactorily predict the
return bend pressure drop.
In the future, new tests should be performed using another
fluid (R-134a for instance)and itwouldbe interesting tostudy the
influence of the temperature, the curvature ratio and to better
determine the vapor quality corresponding to the maximum
Table A.1 e Summary of R-410A experimental data on return be
Test G (kg me2 se1) Tsat (�C) x DPrb(Pa)
1 189.98 10.1 0.418 3.45
2 179.18 10.0 0.540 18.44
3 184.43 10.1 0.642 25.09
4 199.67 10.0 0.681 49.25
5 189.45 10.1 0.808 80.13
6 201.43 11.2 0.853 138.69
7 199.11 10.1 0.919 108.63
8 203.26 10.2 0.961 63.77
9 376.21 10.1 0.052 37.33
10 373.51 10.0 0.106 68.30
11 369.29 10.1 0.204 186.25
12 366.20 10.0 0.311 231.74
13 372.37 10.1 0.400 325.43
14 369.83 10.3 0.501 371.02
15 372.39 10.1 0.590 392.52
16 375.05 10.2 0.697 549.48
17 364.73 10.3 0.809 472.56
18 301.03 15.0 0.203 8.89
19 302.71 15.0 0.304 60.26
20 300.59 15.0 0.406 86.72
21 298.30 15.0 0.521 149.17
22 295.70 15.0 0.628 184.07
23 300.53 15.0 0.693 230.62
24 294.96 15.0 0.804 263.81
25 304.36 15.1 0.908 256.26
26 371.54 15.0 0.058 17.93
27 366.26 15.0 0.107 104.02
28 375.38 15.0 0.204 139.82
29 365.23 15.0 0.317 153.16
30 370.91 15.0 0.404 215.48
31 366.43 15.0 0.499 245.31
32 370.42 15.0 0.613 344.84
33 372.79 15.0 0.708 475.21
34 370.30 15.1 0.805 499.71
35 371.96 15.2 0.849 490.43
36 370.53 14.7 0.908 396.50
37 596.34 15.0 0.053 83.15
38 601.05 15.0 0.102 288.16
39 598.03 15.0 0.205 508.49
40 604.19 15.0 0.306 640.03
41 599.51 15.1 0.408 877.99
42 605.00 15.0 0.502 1060.36
43 600.20 15.5 0.619 1236.42
44 608.40 16.3 0.689 1132.95
45 605.70 16.1 0.775 902.46
singular pressure drop. Visualization will be of importance in
order to better understand the effect of the centrifugal forces.
Acknowledgements
The Authors wish to express their gratitude to Prof. Christian
J.L. Hermes (Universidade Federal do Parana, Curitiba Brazil)
for his appreciable help for cross-checking with the Authors
the validity and consistency of the data.
Appendix A.
nds (over the length pR) forD[ 10.85mmand 2R/D[ 3.68.
Test G (kg me2 se1) Tsat (�C) x DPrb(Pa)
59 299.77 19.9 0.951 381.82
60 425.97 19.9 0.046 26.30
61 395.35 19.9 0.116 27.96
62 396.78 19.9 0.208 59.47
63 401.75 19.9 0.318 144.77
64 404.80 19.9 0.407 229.32
65 392.12 19.9 0.521 364.78
66 396.76 19.9 0.601 432.11
67 401.66 19.9 0.701 487.40
68 397.55 19.9 0.800 500.80
69 401.22 20.0 0.855 494.86
70 395.60 19.9 0.913 444.27
71 395.37 19.9 0.948 393.75
72 508.56 19.9 0.056 25.89
73 495.59 19.9 0.106 110.72
74 495.93 19.9 0.209 210.58
75 504.07 19.9 0.303 376.50
76 499.03 19.9 0.399 469.45
77 497.50 19.9 0.514 633.11
78 495.07 19.9 0.619 726.81
79 504.87 20.0 0.689 796.33
80 492.75 19.9 0.810 827.62
81 498.41 20.1 0.849 827.81
82 495.84 20.2 0.904 733.95
83 495.15 20.7 0.951 598.55
84 606.18 19.9 0.099 261.02
85 598.85 19.9 0.196 383.54
86 599.78 19.9 0.286 604.43
87 595.51 19.9 0.405 893.34
88 603.05 19.9 0.490 1065.99
89 600.27 20.0 0.601 1253.30
90 601.27 20.0 0.697 1377.81
91 609.34 20.0 0.790 1511.22
92 898.73 19.9 0.102 751.52
93 833.55 19.9 0.242 1008.03
94 864.40 19.9 0.298 1142.23
95 886.49 20.0 0.395 1490.31
96 888.28 19.8 0.485 2035.98
97 403.61 15.0 0.105 92.31
98 398.78 15.0 0.194 173.88
99 399.63 15.0 0.304 307.16
100 391.53 15.0 0.395 336.04
101 398.17 15.0 0.509 426.96
102 389.32 15.0 0.617 479.36
103 399.70 15.0 0.703 507.37
(continued on next page)
Table A.1 (continued)
Test G (kg me2 se1) Tsat (�C) x DPrb(Pa) Test G (kg me2 se1) Tsat (�C) x DPrb(Pa)
46 704.36 10.1 0.052 120.50 104 394.00 15.1 0.810 507.09
47 697.27 10.0 0.101 413.28 105 402.32 15.7 0.857 489.78
48 699.09 10.1 0.197 725.71 106 407.89 15.0 0.907 459.54
49 698.37 10.1 0.305 900.66 107 409.99 14.9 0.957 417.49
50 292.26 19.9 0.212 58.34 108 288.54 5.0 0.054 64.36
51 306.54 19.9 0.304 121.24 109 308.26 5.1 0.097 119.94
52 298.99 19.9 0.397 235.56 110 309.83 5.1 0.215 211.74
53 305.42 19.9 0.493 297.54 111 308.73 5.0 0.299 276.87
54 296.64 19.9 0.613 430.38 112 293.50 5.0 0.409 381.33
55 298.96 19.9 0.703 506.68 113 273.24 5.1 0.520 486.56
56 286.37 19.9 0.833 543.52 114 299.78 4.6 0.607 523.69
57 300.50 19.9 0.866 508.33 115 294.72 5.6 0.706 522.66
58 301.73 19.9 0.913 442.93
Table A.2 e Summary of R-410A experimental data on return bends (over the length pR) for D[ 7.90 mm and 2R/D[ 4.05.
Test G (kg me2 se1) Tsat (�C) x DPrb(Pa) Test G (kg me2 se1) Tsat (�C) x DPrb(Pa)
116 360.36 10.0 0.045 10.98 178 540.16 19.9 0.833 1615.01
117 356.12 10.1 0.105 33.15 179 566.83 19.9 0.866 1603.01
118 373.02 10.1 0.218 237.97 180 569.14 19.9 0.913 1510.29
119 365.29 10.0 0.294 308.25 181 565.46 19.9 0.951 1311.20
120 358.36 10.1 0.418 421.69 182 803.50 19.9 0.046 298.42
121 337.98 10.0 0.540 563.50 183 745.74 19.9 0.116 520.55
122 347.89 10.1 0.642 687.14 184 748.44 19.9 0.208 955.45
123 376.64 10.0 0.681 635.74 185 757.81 19.9 0.318 1431.56
124 357.36 10.1 0.808 773.47 186 763.57 19.9 0.407 1938.39
125 379.95 11.2 0.853 941.36 187 739.65 19.9 0.521 2431.77
126 375.58 10.1 0.919 868.63 188 748.39 19.9 0.601 2905.95
127 383.40 10.2 0.961 811.54 189 757.65 19.9 0.701 2987.67
128 709.64 10.1 0.052 192.69 190 749.89 19.9 0.800 2823.27
129 704.54 10.0 0.106 491.76 191 756.82 20.0 0.855 2805.75
130 696.58 10.1 0.204 1021.43 192 746.22 19.9 0.913 2446.36
131 690.75 10.0 0.311 1541.31 193 745.77 19.9 0.948 2483.47
132 702.39 10.1 0.400 2180.52 194 959.28 19.9 0.056 405.38
133 697.61 10.3 0.501 2631.43 195 934.82 19.9 0.106 1323.62
134 702.43 10.1 0.590 3004.27 196 935.46 19.9 0.209 1532.71
135 707.44 10.2 0.697 3023.45 197 950.82 19.9 0.303 2513.56
136 687.98 10.3 0.809 2461.35 198 941.31 19.9 0.399 4617.29
137 559.35 15.0 0.099 146.79 199 938.43 19.9 0.514 7556.77
138 567.82 15.0 0.203 530.30 200 933.84 19.9 0.619 8328.32
139 570.99 15.0 0.304 760.11 201 952.33 20.0 0.689 9702.97
140 566.99 15.0 0.406 1097.21 202 929.45 19.9 0.810 10880.98
141 562.67 15.0 0.521 1498.04 203 940.14 20.1 0.849 11046.86
142 557.78 15.0 0.628 1756.67 204 935.29 20.2 0.904 10277.38
143 566.88 15.0 0.693 1912.28 205 933.99 20.7 0.951 9412.59
144 556.38 15.0 0.804 2033.47 206 1132.00 19.9 0.049 1765.82
145 574.11 15.1 0.908 1906.59 207 1143.41 19.9 0.099 2342.30
146 700.82 15.0 0.058 121.79 208 1129.59 19.9 0.196 2894.54
147 690.87 15.0 0.107 432.63 209 1131.35 19.9 0.286 3804.13
148 708.07 15.0 0.204 848.55 210 1123.30 19.9 0.405 4716.52
149 688.93 15.0 0.317 1194.09 211 1137.52 19.9 0.490 5382.47
150 699.63 15.0 0.404 1844.11 212 1132.28 20.0 0.601 5998.70
151 691.19 15.0 0.499 2302.48 213 1134.16 20.0 0.697 6150.06
152 698.72 15.0 0.613 2711.45 214 1149.38 20.0 0.790 5437.79
153 703.18 15.0 0.708 3000.05 215 1695.26 19.9 0.102 4154.84
154 698.48 15.1 0.805 2817.63 216 1572.31 19.9 0.242 5689.50
155 701.62 15.2 0.849 2292.07 217 1630.51 19.9 0.298 7355.92
156 698.92 14.7 0.908 1793.36 218 1672.16 20.0 0.395 9999.93
157 698.00 14.9 0.952 1596.12 219 1675.55 19.8 0.485 11842.95
158 1124.86 15.0 0.053 376.96 220 761.33 15.0 0.105 576.73
159 1133.74 15.0 0.102 1059.32 221 752.21 15.0 0.194 633.83
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 8 5 4e1 8 6 51864
Table A.2 (continued)
Test G (kg me2 se1) Tsat (�C) x DPrb(Pa) Test G (kg me2 se1) Tsat (�C) x DPrb(Pa)
160 1128.05 15.0 0.205 2588.76 222 753.82 15.0 0.304 1617.23
161 1139.67 15.0 0.306 3943.94 223 738.54 15.0 0.395 2035.00
162 1130.84 15.1 0.408 5556.14 224 751.05 15.0 0.509 2862.99
163 1141.19 15.0 0.502 7848.15 225 734.36 15.0 0.617 3319.73
164 1132.14 15.5 0.619 10208.70 226 753.94 15.0 0.703 3128.47
165 1147.62 16.3 0.689 12318.89 227 743.19 15.1 0.810 2584.68
166 1142.51 16.1 0.775 13583.13 228 758.89 15.7 0.857 2445.52
167 1328.63 10.1 0.052 887.98 229 769.40 15.0 0.907 2162.21
168 1315.25 10.0 0.101 1952.86 230 773.35 14.9 0.957 1827.73
169 1318.68 10.1 0.197 3939.44 231 544.26 5.0 0.054 155.52
170 1317.31 10.1 0.305 6574.30 232 581.46 5.1 0.097 210.68
171 563.15 19.9 0.117 322.81 233 584.42 5.1 0.215 631.71
172 551.29 19.9 0.212 470.40 234 582.35 5.0 0.299 920.17
173 578.22 19.9 0.304 661.92 235 553.62 5.0 0.409 1398.29
174 563.99 19.9 0.397 772.62 236 515.40 5.1 0.520 1982.76
175 576.11 19.9 0.493 1011.35 237 565.46 4.6 0.607 2435.52
176 559.54 19.9 0.613 1268.12 238 555.93 5.6 0.706 2449.89
177 563.92 19.9 0.703 1379.09
i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 4 ( 2 0 1 1 ) 1 8 5 4e1 8 6 5 1865
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