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Pressure drop correlation for oil–refrigerant R134a mixtureflashing flow in a small diameter tube

Heryca O.S. Castroa, Jose Luiz Gascheb,*, Alvaro T. Pratac

aUniversity of Rio Verde, College of Engineering, 75.901-970 Rio Verde, GO, BrazilbUNESP, Sao Paulo State University, Department of Mechanical Engineering, Av. Brasil Centro, 56, 15385-000 Ilha Solteira, SP, BrazilcUFSC – Federal University of Santa Catarina, Department of Mechanical Engineering, 88.040-970 Florianopolis, SC, Brazil

a r t i c l e i n f o

Article history:

Received 9 October 2007

Received in revised form

23 July 2008

Accepted 3 September 2008

Published online 24 September 2008

Keywords:

Refrigeration system

Mixture

R134a

Synthetic oil

Two-phase flow

Tube

Geometry

Experiment

Pressure drop

Correlation

a b s t r a c t

This paper presents an experimental investigation of the ester oil ISO VG10/refrigerant

R134a mixture flashing flow in a 6.0 m long, 3.22 mm ID tube, which is one of the primary

steps towards the construction of a methodology for the study of the lubrication and gas

leakage in refrigeration compressors. The phase change starts with solubility reduction of

the refrigerant in the oil as the pressure decreases due to the friction forces. In this flashing

flow the foam pattern is observed at the end of the tube as vapor quality reaches high

values, and this is a particular phenomenon of this kind of mixture flow. In order to study

this pressure drop, an experimental apparatus was designed to allow the measurement of

both pressure and temperature profiles along the tube as well as the visualization of the

flow patterns. Pressure and temperature distribution along the flow were measured for

saturation pressure ranging from 450 to 650 kPa, mass flux ranging from about 2000 to

3000 kg/(m2s), temperatures around 303 K, and inlet refrigerant concentration varying

between 0.2 and 0.4 kg ref/kg mixt. An available correlation proposed to predict the fric-

tional pressure drop for a mixture composed by the mineral oil SUNISO 1GS and refrigerant

R12 flowing in small diameter tubes yielded large deviations in predicting the ester oil and

refrigerant R134a mixture flow. A new correlation has been proposed that fitted the

experimental data with rms deviations of 24%.

ª 2008 Elsevier Ltd and IIR. All rights reserved.

Correlation de la chute de pression d’un melange defrigorigene R134a et d’huile en ecoulement a l’interieur d’untube de faible diametre

Mots cles : systeme frigorifique ; melange ; R134a ; huile de synthese ; ecoulement diphasique ; tube ; geometrie ; experimentation ; chute

de pression ; correlation

* Corresponding author. Tel.: þ55 18 3743 1035; fax: þ55 18 3742 2992.E-mail addresses: heryca@fesurv.br (H.O.S. Castro), gasche@dem.feis.unesp.br (J.L. Gasche), prata@polo.ufsc.br (A.T. Prata).

www. i ifi i r .org

ava i lab le at www.sc iencedi rec t . com

journa l homepage : www.e lsev i er . com/ loca te / i j r e f r ig

0140-7007/$ – see front matter ª 2008 Elsevier Ltd and IIR. All rights reserved.doi:10.1016/j.ijrefrig.2008.09.001

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1. Introduction

It is well known that, in a vapor refrigeration system, a good

miscibility between refrigerant and lubricant oil is required

to allow easy return of circulating oil to the compressor. This

oil–refrigerant characteristic benefits evaporators,

condensers, and expansion devices. In addition, high refrig-

erant absorption rates in the oil are desirable to diminish the

equalizing pressure, which reduces torque and power

required for compressor start-up (Prata and Barbosa, 2007).

On the other hand, this miscibility can modify the lubrica-

tion of sliding parts, the performance of journal bearings,

and the leakage of refrigerant gas through the compressor

clearances. For a given oil–refrigerant mixture, the solubility

of the refrigerant in the oil depends on the pressure and

temperature, diminishing as temperature increases or pres-

sure decreases. Consequently, as the oil–refrigerant mixture

flows through the several channels inside the compressor,

the refrigerant is released from the mixture (outgassing) due

to the solubility reduction caused by the friction pressure

drop. The resultant two-phase flow, depending on local

conditions, can be quite different from pure oil flow.

Therefore, single-phase flow models usually employed to

design those channels are frequently inappropriate. For

instance, estimations of refrigerant gas leakage through

radial clearance in rolling piston compressors can be quite

different depending if an oil single-phase flow or a mixture

two-phase flow model is employed. It has been found that

the mass flow rate of the refrigerant gas through the radial

clearance calculated using the mixture two-phase flow

model can be up to 30% lower than the mass flow rate

estimated by the single-phase flow model (Gasche et al.,

2000). Reduction in load capacity of compressor journal

bearings has been observed when oil–refrigerant mixture

flow model is used rather than pure oil flow model (Grando

et al., 2005).

Mainly in the 80s and 90s, several studies related to oil–

refrigerant mixture started being developed. Some of these

works were directed towards the determination of the ther-

mophysical properties of the mixtures (Martz et al., 1996;

Grebner and Crawford, 1993; Thomas and Pham, 1992; Baus-

tian et al., 1986; Thome, 1995; Van Gaalen et al., 1990, 1991a,b).

Other researchers concentrated their studies on the behavior

of refrigerant flows contaminated with lubricating oil (refrig-

erant-rich mixtures) with the objective of analyzing the

influence of the oil in the mixture flow and heat transfer

dynamics in evaporators, condensers, and capillary tubes

(Schlager et al., 1987; Jensen and Jackman, 1984; Wallner and

Dick, 1975; Hambraeus, 1995; Motta et al., 2002).

From the point of view of the refrigeration compressor,

some researches have focused on the lubricant–refrigerant

mixture lubricating characteristics. Jonsson (1999) has pre-

sented viscosity and pressure–viscosity data for three ISO VG

32 polyolester lubricants and also a film forming comparison

between two ISO VG 68 polyolester lubricants. The author has

concluded that the reduction in viscosity and pressure–

viscosity coefficient when diluted by refrigerant R134a is far

greater than for normal/linear (not branched) lubricants,

resulting in a poorer film forming ability in applications where

the lubricant is subjected to refrigerant gas with low super-

heat. Chul Na et al. (1997) have performed a tribological study

of refrigeration oils under refrigerant R134a environment,

providing results on compressor lubricity and material

compatibility and suggesting a methodology for the proper

Nomenclature

a constant of Eq. (A.1a)

b constant of Eq. (A.1a)

c constant of Eq. (A.1a)

d constant of Eq. (A.1a)

D inner tube diameter (m)

f friction factor (-)

G mass flux [kg m�2 s�1]

O objective function (-)

p pressure (Pa)

ReG gas Reynolds number ¼ ½rGUGSDhG� (-)

ReL liquid Reynolds number ¼ ½rLULSDhL� (-)

T temperature (�C)

V average velocity (m s�1)

w equilibrium mass fraction of refrigerant in the

liquid (kg ref. kg mixt�1)

x vapor quality (-)

X Martinelli parameter (-)

z longitudinal coordinate (m)

Greek symbols

3 tube roughness

h dynamic viscosity, (kg m�1 s�1)

r density (kg m�3)

n kinematic viscosity (m2 s�1)

F2G gas two-phase multiplier

Subscripts

acc accelerational

calc calculated

exp experimental

f friction

G gas

o overall (inside HPT)

ini initial

L liquid

TP two-phase

Abbreviations

HE Heat exchanger (1 and 2)

HPA High pressure accumulator

HPT High pressure tank

ID Internal diameter

LPA Low pressure accumulator

LPT Low pressure tank

SV Solenoid valve (1 and 2)

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selection of refrigeration oils to improve the durability and

performance of the compressor. Another important aspect of

the interaction between lubricant and refrigerant, that may

play an important role in the compressor lubrication, is the

dynamic of the mixing and separation processes, which has

been treated by Fukuta et al. (2005), who have studied the

transient mixing/separation characteristics of isobutene with

refrigerant oil. However, none of these works have addressed

the issue of the mixture flow with phase change.

There have been very few studies on oil-rich mixture

(mixture with high content of oil) flow with phase change,

which may also be an important issue when the compressor is

the focus of the study. A general understanding of the oil-rich

mixture flashing flow through small channels is important in

order to develop a knowledge basis onto which lubrication and

gas leakage models can be built. One of the primary steps

towards the construction of a methodology for the study of the

lubrication of compressor parts and gas leakage in the pres-

ence of refrigerant outgassing is the investigation of refrig-

erant–lubricant oil flows in a simple geometry as a straight

horizontal tube. The resulting two-phase, two-component

flow possesses very peculiar characteristics and requires

special attention as far as its modeling is concerned. Many

efforts have been done in this direction in the last 8 years.

Computational (Grando et al., 2003; Dias and Gasche, 2006) as

well as experimental (Lacerda et al., 2000; Poiate and Gasche,

2006; Castro and Gasche, 2006) works directed to flashing flow

of oil–refrigerant mixture in small diameter tubes around

3 mm have been reported. The two-phase flow characteristic

is the most important aspect present in all those works. In

addition, foam flow pattern is always observed as the void

fraction reaches high values, usually greater than 0.7.

Together with the pressure drop, a significant temperature

drop due to the outgassing is also noticed.

Attempting to analyze one important feature of this type of

flow, that is, the prediction of the component of the total

pressure gradient due to friction, Barbosa et al. (2004) have

investigated the frictional pressure drop in the two-phase flow

with outgassing of a mixture, composed by refrigerant R12

and oil SUNISO 1GS, flowing through a 5.3 m long, 2.86 mm ID

tube. The authors stated that several two-phase multiplier

correlations (Mishima and Hibiki, 1996; Wang et al., 2000;

Friedel, 1979; Tran et al., 2000; Chen et al., 2001) based on

a variety of experimental conditions including oil–refrigerant

flows and flows in small diameter tubes failed to predict the

database. Based on these results they proposed a new corre-

lation for predicting the frictional pressure drop in this type of

flow, considering an adaptation of the gas pressure drop

multiplier of Chisholm (1973). The authors also suggested, as

a crude approximation, that the correlations could be used to

assess the performance of mixtures such as the ester oil–

refrigerant R134a mixture.

The main purpose of this work is to test the correlation

proposed by Barbosa et al. (2004) using experimental data for

the two-phase flow of another mixture, composed by ester oil

ISO VG 10 and refrigerant R134a, flowing through a 6.0 m long,

3.22 mm ID tube. As it will be observed, that correlation yiel-

ded large deviations in representing the oil/refrigerant R134a

mixture database, indicating that a new correlation should be

proposed for the oil/refrigerant R134a mixture.

2. Experimental method

An experimental apparatus was designed to produce steady

flow of an oil/refrigerant mixture through metallic and glass

6 m long tubes. The metallic tube was instrumented with

pressure transducers and thermocouples in order to measure

the pressure and temperature distributions along the flow.

The glass tube was used to allow for the visualization of the

flow patterns. Because of the main emphasis of the present

work on the pressure drop correlation, visualization results

will not be explored and can be found in Poiate and Gasche

(2006) and Castro and Gasche (2006).

2.1. Apparatus and instrumentation

A scheme of the experimental apparatus is depicted in Fig. 1.

The main components of the test facility are the four tanks, the

test section (two horizontal tubes), a vapor return line, an oil

return line, instrumentation, and a data acquisition system. All

these equipments are connected with each other in order to

produce a steady flow through either of two 6 m long horizontal

tubes. The first tube is made of borosilicate glass (3.0 mm ID)

and allows for flow visualization, whereas the other tube is

a metallic 3.22 (�0.03) mm ID tube equipped with 10 absolute

pressure transducers based on strain-gauge sensor type P8AP

made by HBM� and 14 AWG 36 type-T thermocouples. The

pressure transducers were calibrated using a dead weight

calibrating machine, resulting in a 2-s uncertainty of �2 kPa,

and were installed along the tube through 0.3 mm diameter

pressure taps. Type-T thermocouples were employed and

calibrated using a 0.1 �C-resolution mercury-in-glass ther-

mometer and the 0 �C-electronic reference of the data acqui-

sition system, resulting in a 2-s uncertainty of �0.5 �C; they

were installed through superficial roles made on the tube

surface. Thermocouple and pressure readings were hardwired

into an HBM� data acquisition system (Spider8 and MGCplus)

and routed directly to a personal computer. Data interpretation

and manipulation was performed using the software package

Catman� by HBM�. Specific details regarding the experi-

mental apparatus, instrumentation, calibration procedure,

and data acquisition system can be obtained in Poiate (2001).

The main objective of the four tanks is to maintain

a constant pressure difference between the inlet and outlet of

the tube. Pressure in the high pressure tank (HPT) and in the

low pressure tank (LPT) is kept constant through the high and

HPT

HPALPA

pump

compressor

HE1

HE2

SV1 SV2

glass tube

metallic tube

LPT

refrigerant

vapor

mixture

Fig. 1 – Experimental apparatus.

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low pressure accumulators, HPA and LPA, respectively. The

HPT is filled with oil and refrigerant, and an equilibrium liquid

mixture at the lower part of the tank coexists with the refrig-

erant vapor at the upper part for the desired temperature and

vapor pressure. Pressure and temperature sensors monitor the

conditions of the gas and liquid in both tanks. High and low

pressure accumulators (HPA, LPA) operating at pressures

higher and lower than those at HPT and LPT, respectively, keep

the pressure at constant levels in both tanks using two auto-

matic solenoid valves (SV) controlled by a desktop computer.

During operation the equilibrium liquid mixture existing in

the HPT is driven into either one of the two tubes. The exper-

imental apparatus runs on the blow down mode.

Auxiliary equipment consists of a compressor, an oil

pump, and two heat exchangers (HE1, HE2). The compressor is

employed to return the gas to the HPA and the pump returns

the oil to the HPT. The heat exchangers are used to cool both

fluids if necessary before reaching the HPA and HPT.

2.2. Experimental procedure

Firstly, the parts of the apparatus occupied by the mixture

were cleaned with a solvent fluid to remove impurities, and

the system was evacuated to 10 Pa. After that, about 80 kg of

oil was introduced into the HPT and heated until 60 �C for 3 h

in order to remove impurities (mainly dissolved gases and

water), while the vacuum pump was kept running. Next,

about 60 kg of refrigerant was introduced partly into the HPT

and HPA.

All tests start with the saturation of the oil in the HPT at the

desired test temperature and 10 kPa above the desired test

pressure, po, that is, at an initial pressure, pini¼ poþ 10 kPa. In

order to increase the rate of absorption, the refrigerant is

bubbled into the HPT employing the compressor, which sucks

the refrigerant gas from the top and compresses it at the

bottom of the HPT, as sketched in Fig. 2. As the liquid mixture

absorbs gas in the HPT, the pressure tends to decrease, acti-

vating the automatic solenoid valve (SV1), which releases

refrigerant from HPA to HPT in order to maintain a constant

pressure inside the HPT. This process continues until satura-

tion is achieved in the HPT at the initial pressure, pini. This

saturation process can last up to 6 h. After saturation is

reached at pini, some amount of gas is released from the top of

HPT to decrease the pressure to po, the desired test pressure.

This pressure reduction promotes a fast outgassing and

assures that saturation is indeed established at the pressure

test, po (�1% of the value). This new saturation state is reached

within 30–60 min, and is verified when pressure stops

increasing because of the gas release. The temperature is

controlled at the desired value (�1 �C) during the whole

process.

Depending on whether flow visualization or measurement

run is desired, after the saturation process is finished, the test

section valves are arranged so that the mixture is forced into

the glass or the metallic tube, respectively. The compressor

remains running during the tests in order to circulate gas from

the LPA to the HPA. Data acquisition is initiated after steady

flow is reached. The steady state regime is characterized by

observing the time variation of the mixture temperature in all

measuring positions. When the variation temperature is of

the order of 0.5 �C, it is assumed that the steady state flow is

reached.

Prior to initiating the experiments with the mixture, some

tests were performed with pure oil in laminar flow inside the

metallic tube, and nitrogen pressurizing the tanks and accu-

mulators. Experimental results were then compared to the

available analytical solutions for fully developed laminar flow.

These tests were used to evaluate and validate the experi-

mental loop, instrumentation, and data acquisition. In addi-

tion, these tests validated the methodology to obtain the mass

flow rate of the mixture flows, which was based on the use of

the linear pressure gradient established at the inlet of the

tube. Details about the validation of the experimental appa-

ratus can be found in Poiate (2001).

2.3. Experimental results and data reduction

Table 1 shows the experimental conditions for the tests

carried out using a mixture composed by an ester oil ISO VG10

and refrigerant R134a. Pressure and temperature distribution

along the flow were measured for saturation pressure inside

the high pressure tank (HPT), po, ranging from 450 to 650 kPa

(abs), total mass flux, G, ranging from about 2000 to 3000 kg/

(m2s), temperatures around 303 K, and refrigerant concentra-

tion inside the HPT, wo, varying between 0.227 and 0.443 kg ref/

kg mixt. Figs. 3 and 4 depict pressure and temperature distri-

butions, respectively, for tests 7–9. It can be noticed in these

figures that there is an inlet flow region where pressure

decreases linearly and temperature remains practically

constant. In addition, qualities are low at this region. Close to

the tube outlet, however, pressure and temperature gradients

are much larger and, because of the outgassing, mixture

qualities increase.

The same procedure used by Barbosa et al. (2004) for

obtaining the local frictional pressure gradient at an inter-

mediate position between two adjacent pressure tappings was

utilized in this work, i.e., by subtracting the estimated accel-

erational pressure gradient from the total pressure gradient at

the same intermediate position,�dpdz

�f;TP

¼�

dpdz

�total

��

dpdz

�acc

(1)

HPT

SV1

HE2

compressor

to HE1

to HPA

to test

section

su

ctio

n

compression

Fig. 2 – Sketch of the saturation procedure.

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The total pressure gradient at an intermediate position was

calculated by dividing the difference between two adjacent

pressure readings by the distance of the pressure tappings.

The local accelerational pressure gradient was estimated

assuming a homogeneous flow model (Barbosa et al., 2004),

that is,

�dpdz

�acc

¼ G2

��1rG

� 1rL

�dxdz� x

r2G

drG

dz� ð1� xÞ

r2L

drL

dz

�(2)

Neglecting the oil vapor pressure, the local equilibrium

vapor quality is given by

x ¼ wo �w1�w

(3)

where w is the local refrigerant concentration at the inter-

mediate position estimated by using a linear interpolation

between two adjacent values, which were calculated utilizing

the pressure and temperature readings, and a solubility

correlation, w¼w( p,T ). Neglecting the oil vapor is a very good

assumption due to the low vapor pressure of the oil. The non-

equilibrium model described in Grando et al. (2006) is adopted

to calculate the local refrigerant mass fraction, that is, no gas

is considered to be absorbed after being released. Therefore,

for each run test only the data that produced decreasing local

mass concentration along the flow was accepted as valid.

The local physical properties were estimated using the

local pressure, temperature, and refrigerant concentration.

The derivatives dx/dz, drG/dz and drL/dz at an intermediate

position were estimated by using a linear approximation

and two adjacent values of x, rG, and rL.

In order to avoid an undesired outgassing before the

mixture flow reached the tube entrance, a mass flow meter

was not used; instead, the mass flow rate was calculated by

using the pressure gradient measured at the inlet region of the

flow, where a constant pressure gradient was still observed.

The uncertainty estimated for the mass flow rate calculation

was about 5% of the calculated value. The total mass flux, G,

was estimated by

G ¼ rLV (4)

where rL is the liquid mixture density and V is the average

velocity estimated by:

V ¼�

2DrLf

��dp

dz

�total

�1=2

(5)

where D is the tube diameter, rL is the density of the liquid

mixture calculated at the inlet temperature of the flow, f is the

friction factor estimated by the equation proposed by

Churchill (1977), and (dp/dz)total is the experimental total

0

100

200

300

400

500

600

0 1 2 3 4 5 6z (m)

p(k

Pa

)

Test 8Test 9

Fig. 3 – Longitudinal pressure distribution for tests 8 and 9.

20

22

24

26

28

30

32

0 1 2 3 4 5 6z (m)

T(oC

)

Test 8Test 9

Fig. 4 – Longitudinal temperature distribution for tests

8 and 9.

Table 1 – Experimental conditions

Test number po

(kPa)G

(kg m�2 s�1)wo

(kg ref. kg mixt�1)

01 450 2358 0.231

02 2235 0.234

03 2272 0.230

04 2272 0.227

05 2345 0.227

06 2407 0.227

07 500 2223 0.271

08 2124 0.279

09 2210 0.268

10 2186 0.264

11 2112 0.267

12 2284 0.266

13 2481 0.267

14 550 2210 0.314

15 2260 0.304

16 2124 0.310

17 2100 0.313

18 2321 0.296

19 2124 0.310

20 2284 0.318

21 2395 0.307

22 2468 0.308

23 600 2530 0.352

24 2345 0.376

25 2542 0.347

26 2481 0.343

27 2333 0.399

28 2567 0.319

29 2493 0.342

30 2702 0.344

31 650 2763 0.411

32 2751 0.411

33 2738 0.443

34 2677 0.424

35 2947 0.387

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pressure gradient measured at the inlet region of the flow. The

measurement of the tube roughness ratio, which was used in

the Churchill equation, resulted in 3/D¼ 0.000124 (Poiate,

2001).

2.4. Test of Barbosa et al. (2004) frictional pressurecorrelation

The two-phase multiplier proposed by Barbosa et al. (2004) is

given by:

F2G ¼ 1:24

x1� x

ð1�wÞ þ�1:95 exp

�0:00694

ReG

ReL

��Xþ X2 (6)

which was fitted with an rms error of 26% for a mixture

composed by the mineral oil SUNISO 1GS and refrigerant R12.

The local frictional pressure gradient for the oil–refrigerant

mixture was then predicted by:�dpdz

�f;TP

¼ F2G

�dpdz

�f;G

(7)

where (dp/dz)f,G is the single-phase gas pressure gradient

calculated at the mass flux (Gx). The parameter X2 is the ratio

of the liquid to gas single-phase frictional pressure gradient:

X2 ¼�

dpdz

�L

��dpdz

�G

(8)

The correlation proposed by Barbosa et al. (2004) was tested

with the present experimental database for the ester oil–

refrigerant R134a and the results are plotted in Fig. 5. As can be

seen, the rms error for this mixture was 46% which is much

higher than the rms error of 26% for the oil–refrigerant R12. As

reported by the authors, mentioning Goswami et al. (1998),

caution should be exercised when using the correlation for

ester oil mixtures because the foaming characteristics of HFC/

polyol ester oil mixture are different from CFC/mineral oil and

HCFC/mineral oil mixtures.

3. Proposed correlation for ester oil/refrigerant R134a mixture

Considering the same type of correlation, new coefficients

were obtained for the mixture composed by an ester oil ISO

VG10 and refrigerant R134a by minimizing the objective

function given by the relative quadratic difference between

the experimental pressure, pexp, and the pressure calculated

by the correlation, pcalc,

O ¼X

pexp � pcalc

pexp

!2

(9)

Using the same correlation format suggested by Barbosa

et al. (2004) the new correlation proposed here is given by:

F2G ¼ 9:10

� x1� x

�ð1�wÞ þ

�3:35 exp

�� 0:0867

ReG

ReL

��Xþ X2

(10)

with an rms error of 30%. Fig. 6 shows the comparison

between the experimental and calculated two-phase frictional

pressure gradients. As can be noticed in this figure, the

correlation proposed adjusted better to the experimental

results. However, a large data scatter for experimental two-

phase multiplier ranging from 0 to 1 is observed. It is impor-

tant to mention that this behavior has been also verified to

a lesser extent in Barbosa et al. (2004) database for experi-

mental two-phase multiplier between 10 and 20.

Analyzing the present database it has been noticed that the

gas Reynolds number increases rapidly at the end of the tube,

where foam pattern prevails. This is exactly the region where

the experimental two-phase multiplier scatter arises. Based

on that behavior, a new correlation introducing a non-linear

effect of the gas Reynolds number has been proposed:

F2G ¼ �5:38

� x1� x

�ð1�wÞ þ

�1:36 exp

�7:96 10�5

�ReG

ReL

�2:19��X

þ X2 ð11Þ

The previous equation minimizes the relative quadratic

difference between the experimental and the calculated

pressure, as given by Eq. (9). Fig. 7 depicts the comparison

between the experimental and calculated two-phase multi-

pliers showing that the new correlation given by Eq. (11)

reduced the rms error to 24%. This correlation can be applied

for the following conditions: 0< x< 0.2, 0.8<X<155,

2000<G< 3000 kg/(m2 s), 0.2<wo< 0.4, inlet pressures, po,

ranging from 450 to 650 kPa, and inlet temperatures around

30 �C.

1

10

100

1000

10000

1 10 100 1000 10000Experimental Two-phase Multiplier

Calcu

lated

T

wo

-p

hase M

ultip

lier

rms error = 46 %

Fig. 5 – Comparison of experimental and calculated two-

phase frictional pressure gradients using the correlation

proposed by Barbosa et al. (2004).

1

10

100

1000

10000

1 10 100 1000 10000

Experimental Two-phase Multiplier

Calcu

lated

T

wo

-p

hase M

ultip

lier

rms error = 30 %

Fig. 6 – Comparison of experimental and calculated two-

phase frictional pressure gradients for the correlation

proposed in the present work, Eq. (10).

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It can be observed in Fig. 7 that there is still a certain data

scatter, mainly for experimental multiplier around 10. One

can point out two main reasons for that: metastability and

foam formation (Barbosa et al., 2004).

For obtaining Eq. (3), which determines the vapor quality, it

was supposed that the liquid mixture was always saturated by

refrigerant at the local temperature and pressure, that is, the

local concentration was calculated by using the solubility

curve of the mixture. Nevertheless, if metastability occurred,

the local vapor quality could be lower than the local equilib-

rium vapor quality, which could delay the vaporization

inception. In this case, a supersaturated liquid mixture would

flow whether in a single-phase flow or with the presence of

refrigerant vapor. For pure substances, metastable states can

exist in a non-equilibrium condition when vapor is super-

cooled below its equilibrium saturation temperature or liquid

is superheated above its equilibrium saturation temperature

for a given pressure.

The visualization results of all tests have shown the exis-

tence of intermittent foam formation at the end of the tube. It

is well known that the rheology of foam is much more

complex. Foams are, virtually, the only non-Newtonian

compressible fluid, and the ratio between the stress and the

strain rate is not unique for foams (Winkler et al., 1994). The

parameters that govern the flow pattern change from bubbly

flow to foam flow are not well defined and the correlation’s

inability to capture their behavior and influence on local

pressure and temperature gradients may have also contrib-

uted to the scatter observed in Fig. 7.

Fig. 8 presents a plot of the experimental pressure drop as

a function of the Martinelli parameter in order to provide the

pressure drop characteristics of the oil–refrigerant R134a

mixture flashing flow in the tube.

4. Conclusions

Two-phase flow of a mixture composed by an ester oil ISO

VG10 and refrigerant R134a in a 6.0 m long, 3.22 mm ID tube

has been experimentally investigated. New experimental data

for frictional pressure drop have been obtained. The correla-

tion proposed by Barbosa et al. (2004) to predict the frictional

pressure drop for another mixture, composed by the mineral

oil SUNISO 1GS and refrigerant R12, has been tested with the

present data and failed if the same rms of 26% obtained by the

authors is considered. A new correlation for the ester oil/

refrigerant R134a mixture has been proposed with an rms

error of 24%. Foam formation at the end of the tube was

observed and further considered in the correlation final form.

Acknowledgment

This research was supported by FAPESP-Sao Paulo State

Research Foundation.

Appendix.

This Appendix presents correlations for the physical proper-

ties used in this work.

A.1. Solubility

The mutual solubility of the ester oil ISO VG10/Refrigerant

R134a was provided in graphical form by the oil manufacture.

The curves were fitted by Castro (2006), resulting in the

following correlation:

w ¼ a expð�p=bÞ þ c expð�p=dÞ (A.1.a)

where:

a ¼ 3:74399 10�4 þ 5:78313 10�18 expðTÞ (A.1.b)

b ¼ �9:24928 10�3 expðT=7:20444Þ � 0:0921475 expðT=107:3101Þ(A.1.c)

c ¼ 8:19266� 2:650030 10�3 T2 (A.1.d)

d¼�0:17407expðT=14:27529Þ�0:82779expðT=38:53972Þ (A.1.e)

1.E+00

1.E+01

1.E+02

1.E+03

1.E+04

1.E+05

0 20 40 60 80 100 120 140 160 180X

Exp

erim

en

tal T

wo

-p

hase M

ultip

lier

Fig. 8 – Experimental two-phase multiplier as a function of

the Martinelli parameter.

1

10

100

1000

10000

1 10 100 1000 10000Experimental Two-phase Multiplier

Calcu

lated

T

wo

-p

hase M

ultip

lier

rms error = 24 %

Fig. 7 – Comparison of experimental and calculated two-

phase frictional pressure gradients for the correlation

proposed in the present work, Eq. (11).

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 2 ( 2 0 0 9 ) 4 2 1 – 4 2 9 427

Author's personal copy

in which the concentration is given in (%), pressure in (bar),

and temperature in (�C). The curve fit is applicable for pressure

ranging from 0 to 700 kPa and temperature ranging from 0 to

40 �C.

A.2. Density

The density of the oil/refrigerant mixture was also provided in

graphical form by the manufacture and the data were curve

fitted, resulting in the following correlation:

rL ¼0:94109þ 1:90541 10�3wþ 1:21933 10�18w3 � 7:4 T

103

(A.2)

where concentration is given in (%), temperature in (�C), and

density in (kg m�3). The correlation was fitted by Castro (2006)

for w< 30% and 0< T< 40 �C.

A.3. Kinematic viscosity

Following a similar procedure used to fit concentration and

density data from the manufacture, Castro (2006) also found

the following correlation for the kinematic viscosity of the

liquid mixture, nL,

nL ¼aþ bTþ cT2 þ dT3 þ eT4

�110�6 (A.3.1)

where:

a ¼ a1 þ a2wþ a3w2 þ a4w3 þ a5 expðwÞ (A.3.2)

b ¼ b1 þ b2wþ b3w3=2 þ b4w2 þ b5w3 (A.3.3)

c ¼ c1 þ c2wþ c3w2 þ c4w5=2 þ c5w3 (A.3.4)

d ¼ d1 þ d2wþ d3w2 þ d4w3 þ d5w4 (A.3.5)

e ¼ e1 þ e2wþ e3w2 þ e4w3 þ e5w4 (A.3.6)

in which all constants are listed in Table A.1. In this correla-

tion, the kinematic viscosity is given in (m2 s�1), concentration

in (%), and temperature in (�C). The correlation was fitted for

w< 55% and �10< T< 50 �C.

All refrigerant properties were calculated using the

package REFPROP (NIST, 1998).

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Constant a b c d e

Subscript

1 1.4138 10�2 9.6799 10�4 2.0454 10�5 2.7497 10�9 �5.7896 10�11

2 1.4899 10�3 1.3450 10�4 5.2077 10�6 1.3717 10�8 �2.8533 10�10

3 6.2747 10�5 �4.2158 10�5 �1.1169 10�6 6.6998 10�9 �8.3874 10�11

4 7.7374 10�7 9.4270 10�6 2.8237 10�7 �3.5512 10�12 4.6565 10�12

5 �2.1416 10�27 �6.3823 10�8 �1.9552 10�8 4.3568 10�12 �5.8576 10�14

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