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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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