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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 4 1 ( 2 0 1 4 ) 1e1 0

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Two-phase heat transfer and pressure drop ofpropane during saturated flow boiling inside ahorizontal tube

S. Wang a,b, M.Q. Gong a,*, G.F. Chen a, Z.H. Sun a, J.F. Wu a,**aKey Laboratory of Cryogenics, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing

100190, ChinabUniversity of Chinese Academy of Sciences, Beijing 100039, China

a r t i c l e i n f o

Article history:

Received 5 December 2012

Received in revised form

9 March 2013

Accepted 31 March 2013

Available online xxx

Keywords:

Propane

Flow boiling

Heat transfer

Pressure drop

Flow pattern

Correlation

* Corresponding author. Tel./fax: þ86 10 825** Corresponding author. Tel./fax: þ86 10 626

E-mail addresses: gongmq@mail.ipc.ac.cn0140-7007/$ e see front matter ª 2013 Elsevhttp://dx.doi.org/10.1016/j.ijrefrig.2013.03.019

a b s t r a c t

Comprehensive heat transfer coefficient and pressure drop data of the two-phase satu-

rated flow boiling for propane were obtained in a smooth horizontal tube at conditions

covering mass fluxes from 62 to 104 kg m�2 s�1, heat fluxes from 11.7 to 87.1 kW m�2, and

saturated temperatures from �35.0 to �1.9 �C. Results indicate that heat transfer co-

efficients increase with mass and heat flux. For saturation temperature and vapor quality,

distinct variation trends were observed depending on different test conditions. The heat

transfer experimental data were compared with five well-known correlations. Among

those, LiueWinterton correlation shows the best agreement with a mean absolute relative

deviation less than 10%. For two-phase frictional pressure gradients, the influences of

saturation temperature, mass flux and vapor quality were also presented. The predicted

method of Muller-Steinhagen & Heck correlation gives the best fit to the data with a mean

absolute relative deviation less than 20%.

ª 2013 Elsevier Ltd and IIR. All rights reserved.

Transfert de chaleur diphasique et chute de pression dupropane pendant l’ebullition en ecoulement sature al’interieur d’un tube horizontal

Mots cles : Propane ; Ebullition en acoulement ; Transfert de chaleur ; Chute de pression ; Schema d’ecoulement ; Correlation

43728.27843.(M.Q. Gong), jfwu@mail.ipc.ac.cn (J.F. Wu).

ier Ltd and IIR. All rights reserved.

Nomenclature

Bo boiling number

Cp specific heat capacity (J kg�1 K�1)

D inner diameter of the tube (mm)

g gravity (m s�2)

G mass flux (kg m�2 s�1)

h heat transfer coefficient (kW m�2 K�1)

Hlv latent heat (J kg�1)

L length of the pressure drop test section (mm)

m mass flow rate (kg s�1)

p pressure (kPa, MPa)

q heat flux (W m�2)

Q thermal power (W)

Re Reynolds number

T temperature (K)

x vapor quality

Greek symbol

r density (kg m�3)

s surface tension (N m�1)

l30% percentage of experimental points predicted

within �30%

Subscripts

cal calculated value

exp experimental value

frict frictional pressure drop

in inlet of the test section

l liquid phase

mom momentum pressure drop

out outlet of the test section

sat saturation state

sub subcooled state

v vapor phase

w wall

i n t e rn a t i o n a l j o u rn a l o f r e f r i g e r a t i o n 4 1 ( 2 0 1 4 ) 1e1 02

1. Introduction

The increasing awareness of the environmental protection

has led to a demand for natural refrigerants in the refrigera-

tion and air conditioning industries. Hydrocarbons (HC’s), in

particular like propane (R290), are well known as excellent

refrigerants. It has been verified to be used as a long term

alternative refrigerant both as a pure refrigerant or a major

component for several mixed refrigerants due to its good

cooling performance and its less impact on the environment

(Blanco et al., 2005; Cavallini et al., 2010; Fernando et al., 2004;

Jung et al., 2000; Lee et al., 2012; Navarro et al., 2005). With the

substitution of old refrigerants by new environmentally

friendly ones, characteristics of the heat transfer coefficients

are of great significance, as well as the two-phase frictional

pressure drop features.

For recent decades, researches of boiling characteristics on

natural refrigerants have become more active (Thome, 1996).

Some experiments on pool boiling of propane have been un-

dertaken (Shen et al., 1997). However, relevant experimental

data about flow boiling heat transfer and pressure drop

characteristics of pure propane in tubes are still not enough.

A number of studies of mixtures with propane as a

componentwere reported (Thome et al., 2008). Zou et al. (2010)

presented saturated flow boiling heat transfer coefficients in a

horizontal tube of the binary mixtures of R170/R290. The

degradation of mixtures increases as increasing the heat flux

and decreases as the vapor quality or the mass flux increases.

The influence of saturation pressure is unapparent, while the

mass flux does have a significant effect. Amodified correlation

was developed based on their previous pool boiling heat

transfer database, which shows an acceptable agreement

with the experimental data for predicting the heat transfer

coefficients of both pure refrigerants and mixtures. Grauso

et al. (2011) conducted an experimental study on flow boiling

of CO2 and propanemixtures in a smooth horizontal tubewith

an internal diameter of 6 mm. The results confirm a strong

degradation of heat transfer respect to the ideal heat transfer

coefficient for mixtures. Results show the heat transfer

coefficients are only slightly dependent on the mass flux and

the working temperature, while strongly influenced by the

heat flux.

A few researches on pure propane two-phase flow boiling

characteristics were reported. Watel and Thonon (2002) con-

ducted an experimental study on propane flow boiling during

a vertical upflow inside a compact serrated plate-fin

exchanger. The experimental conditions reflect those occur-

ring in industrial applications. An analysis of measured

convective boiling heat transfer coefficients, without nucleate

boiling, shows the separate effects of quality, mass flux, and

pressure. Lee et al. (2005) presented experimental results of

heat transfer characteristic and pressure gradients of such

hydrocarbon refrigerants as R290, R600a, R1270 and HCFC

refrigerant R22 during evaporating inside horizontal tubes.

Similar results were observed that the local evaporating heat

transfer coefficients and pressure drop of hydrocarbon re-

frigerants were higher than those of R22. Moreover, in their

study, the average evaporating heat transfer coefficient in-

creases with themass flux, and a peak point appears at 0.85 as

for the influence of vapor quality. As for the influence of vapor

quality on the pressure drop, a highest value of pressure drop

is shown at 0.6 quality point. Compared with existing corre-

lations, the heat transfer coefficient experimental results are

well matched with Shah’s correlation, Kandlikar’s correlation

and GungoreWinterton’s correlation. Choi et al. (2009) re-

ported the convective boiling pressure drop and heat transfer

experiments of propane in horizontal smooth minichannels

with inner diameters of 1.5 mm and 3 mm. The experimental

results show that pressure drop is a function of mass flux,

inner tube diameter, surface tension, density and viscosity. A

new pressure drop correlation was developed on the basis of

the LockharteMartinelli method as a function of the two-

phase Reynold number and Webber number. Mass flux, heat

flux and saturation temperature have an effect on the heat

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 4 1 ( 2 0 1 4 ) 1e1 0 3

transfer coefficient. Despite the conventional parameters, the

influence of inner tube diameter was also discussed.

Some literature both reported saturation flow boiling

characteristics of pure propane and mixture containing pro-

pane as a component. Shin et al. (1997) conducted an experi-

mental study of convective boiling heat transfer coefficients of

pure refrigerants (R22, R32, R134a, R290, and R600a) and

several refrigerant mixtures inside a 7.7 mm seamless stain-

less steel tube. Their results indicate that the density ratio of

liquid and vapor phases is a weak function of physical prop-

erties, so the influence on heat transfer coefficients is negli-

gible at the same quality. However, they have presented only a

little experimental data for propane. Wen and Ho (2005) con-

ducted an experimental investigation of heat-transfer and

pressure drop behavior of R290, R600, and R290/R600 in a

three-line serpentine small-diameter (2.46 mm) tube bank.

The influences of mass velocity and heat flux to the evapo-

ration heat transfer and pressure drop characteristic were

examined and discussed. The heat transfer coefficients in-

crease with mass flux and heat flux. As the refrigerant mass

flow rate increases, the pressure drop also increases. A new

heat transfer correlation was proposed by using a super-

position model to predict the experimental data for both pure

refrigerants and refrigerant mixtures with a mean absolute

deviation of 11.5%.

The above bibliographic review shows that only a few

studies are available for boiling characteristics of propane,

especially for forced two-phase flow boiling. Moreover,

experimental data in literature mentioned above covers only

near zero centigrade degree ranges or even higher, while

relatively lower saturation temperature ranges have not been

studied. Therefore, more comprehensive and fundamental

experimental data of propane are still required to develop a

widely adaptable correlation. In this study, extensive mea-

surements on the two-phase flow boiling heat transfer coef-

ficient and frictional pressure drop have been performed. The

experimental conditions summarized in Table 1 cover a wide

range of vapor qualities, and some specific mass fluxes, heat

fluxes, and saturation temperatures.

2. Experimental setup

2.1. Test facility

The test rig of this experiment, newly modified on the previ-

ous work (Zou et al., 2010), is shown in Fig. 1. It consists of a

test loop and a condensation loop. The test fluid condensation

Table 1 e Experimental conditions.

Refrigerant Propane

Tube Copper

Internal diameter (D) 6 mm

Length of pressure drop test section (L) 1550 mm

Saturation temperature (T ) �35.0 to �1.9 �CMass flux (G) 62e104 kg m�2 s�1

Heat flux (q) 11.7e87.1 kW m�2

Heating medium Electrical heating

is achieved in a tubular heat exchanger which is also the

evaporator of a low temperature refrigerator (Gong et al.,

2004). The test loop consists of a magnetic gear pump, a

mass flow meter, a preheater, two sight glasses, a diabatic

heat transfer test section and an adiabatic pressure drop test

section. The magnetic gear pump drives the test fluid to

circulate in the test circle. The mass flux can be modified by

varying the electric motor speed. Then a coriolis effect mass

flow meter is used to measure the flow rate. The test fluid at

the outlet of the magnetic pump is kept subcooled to avoid

any vapor flow through the mass flow meter. The refrigerant,

in subcooled condition, passes through the preheater where

heat is supplied to the fluid by a sheathed heater, which is

controlled by a DC regulator; changing the voltage, it is

possible to modify the thermal power and to obtain the

desired inlet vapor quality of the diabatic heat transfer test

section. At the inlet and outlet of the diabatic test section, two

sight glasses with the same inner diameter of the test tube are

separately set to observe the flow pattern.

The test sections are smooth horizontal tubes with an

inner diameter of 6 mm. The refrigerant evaporates in the

diabatic heat transfer test section where the local heat

transfer coefficient can be measured with four individual

heating segments. Each segment is a 50 mm long copper tube

with an inner diameter of 6 mm and an outer diameter of

30 mm. Then four segments are connected by five 60mm long

stainless steel tubes with an inner diameter of 6 mm and an

outer diameter of 6.4 mm.

The wall temperatures of each heating copper segment are

measured with three four-wire PT100 platinum resistance

thermometers embedded in the wall of each heating segment

by drilling a through-hole inside the wall at the top, bottom,

and right side position as shown in Fig. 2. The lead wire is tied

to the wall in the axial direction in order to minimize the heat

conduction through the wire to or from the surroundings. The

heat flux transferred to the test fluid at the test section can be

calculated by the value of voltage and current of thin-film

electric heaters tightly adhered to the tube outer surface.

The locations of the temperature, absolute pressure, and dif-

ferential pressure measurement sensors are also indicated in

Fig. 1.

The two-phase frictional pressure drop test section is set

after the outlet sight glass. The mass flux, saturation tem-

perature and vapor quality at the inlet of the pressure drop

test section are assumed to be the same as the outlet of the

heat transfer test section. To avoid heat gain or heat loss,

heavy insulation is provided by a glass wool insulator for the

heat exchanger, the liquid reservoir, the magnetic gear pump

and the mass flowmeter; by an aluminum plating film for the

preheater and the two test sections which are also placed in a

vacuum chamber with a vacuum consistently less than 6 Pa

during the test. Regarding the single-phase energy balance,

the maximum heat loss is always no more than 3.75% in the

heat flux range of this work.

2.2. Data reduction

For each heating segment of the heat transfer test section, the

local heat transfer coefficient in the flow boiling process can

be calculated by the following equation:

Fig. 1 e Schematic view of the experimental apparatus.

i n t e rn a t i o n a l j o u rn a l o f r e f r i g e r a t i o n 4 1 ( 2 0 1 4 ) 1e1 04

h ¼ qðTw � TsatÞ (1)

where q represents the inner wall heat flux, calculated on the

basis of the total heat input by measuring the voltage and

current of the DC regulator. Tw is the inner wall temperature,

calculated from the measured temperature by applying the

one-dimensional, radial, steady-state heat conduction equa-

tion for a hollow cylinder, based on the assumption that the

heat flux is uniform inside the tube and a negligible heat loss

to the surroundings. Tsat is the local saturation temperature of

the test fluid, which is the thermodynamic equilibrium tem-

perature corresponding to the saturation pressure. An abso-

lute pressure sensor set at the inlet of the test section and a

linear pressure drop assumption along the test section is used

to determine the local saturation pressure. The saturation

temperature and thermophysical properties of the propane

presented in this work are from Refprop v8.0 (Lemmon

et al., 2007).

The vapor quality is obtained from an energy balance

between the enthalpy increment of the fluid and the thermal

power input. The vapor quality at the inlet of the heat transfer

test section can be calculated as follows:

xin ¼ Qpreh � CpmðTin � TsubÞmHlv

(2)

Fig. 2 e Schematic view of the basic unit of the heat transfer te

thermometers; (b) Transversal surface of the heating segment.

Considering the amount of heat applied to the preheater

and the flow rate of the test fluid, and then the vapor quality at

the exit of the first unit x1 is:

x1 ¼ xin þ Q1

mHlv(3)

where Q1 is the thermal power applied to the first test section.

Similarly, the vapor quality at the inlet and outlet of each

heating segment can be obtained. With the linear interpola-

tion method, the average vapor quality for each test section is

acquired.

2.3. Experimental uncertainties

The uncertainty analysis for the present experiments is

summarized in Table 2. The final uncertainties are estimated

with the method suggested by Moffat (1985). Under the

employed operation conditions, the uncertainties for the heat

transfer coefficient with a 95% confidence interval range from

6.5% to 17.2%, and are less than 2% for the vapor quality.

3. Results and discussion

With the apparatus described above, extensive measure-

ments have been carried out. Local heat transfer coefficients

st unit: (a) The location of three platinum resistance

Table 2 e Parameters and estimated uncertainties.

Parameters Instruments Range Uncertainties

Temperature (K) PT100 thermometer 80e300 0.1 K

Absolute pressure (MPa) UNIK 5000 pressure transducers 0e1 0.04%

Differential pressure (kPa) UNIK 5000 differential pressure transducer 0e40 0.04%

Mass flow (kg h�1) ULTRA mass MKII Coriolis mass flow meter 0e180 0.1%

Voltage (V) Keithley 2700 multimeters 0e60 0.005%

Direct current (A) ZW 1659 amperometers 0e5 0.2%

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 4 1 ( 2 0 1 4 ) 1e1 0 5

and two phase frictional pressure gradients were experi-

mentally obtained in this study.

3.1. Local heat transfer coefficients

Local heat transfer coefficients were experimentally obtained

in this study with the method that one experimental param-

eter varied in the predefined range while the others were kept

constant. We obtained 352 experimental local heat transfer

coefficients at 13 different operating conditions. The in-

fluences of the four important parameters: mass flux, heat

flux, saturation temperature and vapor quality on the flow

boiling heat transfer coefficients were discussed individually.

3.1.1. Effect of mass fluxFig. 3 shows the variation of local heat transfer coefficients for

different vapor qualities under three different mass fluxes

(from 63.9 kgm�2 s�1 to 102.7 kgm�2 s�1) at constant saturation

temperature of �35 �C at a heat flux of 33.6 kW m�2. As ex-

pected, the heat transfer coefficients increase with the mass

flux within all the test vapor quality ranges (from 0.14 to 0.75).

At lowvapor qualities, the influence ofmass flux is subtle:more

than 60% mass flux increase leads to only about 5% heat

transfer coefficient increment. But the same mass flux varia-

tion leads to a much more evident influence of 20% increment

at high vapor quality conditions. This behavior can be

Fig. 3 e Variation of local heat transfer coefficients for

different mass fluxes.

conducted that, in the low vapor quality region the nucleate

boiling prevails while the convective boiling contribution is

weak. As a result, small impact of mass flux on the heat

transfer is encountered. In high vapor quality region, the flow

pattern changes from stratified flow to fully developed annular

flow. As fluid velocity increases, the heat input to the tube is

taken away faster which enhances the heat transfer effect.

3.1.2. Effect of heat fluxIn Fig. 4 the effect of heat flux on local heat transfer co-

efficients are shown. Fig. 4-a,-b,-c presents the local heat

transfer coefficients versus vapor qualities under several heat

fluxes (11.7 kW m�2e53.2 kW m�2) at three specific saturation

temperatures (�35.0 �C to �1.9 �C) at a constant mass flux of

73 kg m�2 s�1. For each saturation temperature condition at

constantmass flux, the local heat transfer coefficients have an

evident growth with the increase of heat flux for a certain

vapor quality in the whole range. This variation trend is more

obviously found at high saturation temperature condition.

To investigatemore direct influence of heat flux on the local

heat transfer coefficient, a group of experiments were con-

ducted at constant saturation temperature and mass flux at

almost the same vapor qualities as shown in Fig. 4-d. A linear

approximation increasing tendency of the local heat transfer

coefficient is observedwith the increase of heat flux. In Fig. 4-a,-

b,-c, the increase of vapor quality leads to no evident variations

of the local heat transfer coefficients in thewhole vapor quality

range. It is assumed that the growth in Fig. 4-d is probably due

to the heat flux increase. Many researches in pool boiling show

that with the increase of heat flux, bubble departure frequency

and the nucleation sites number increase rapidly. This com-

bined effects lead to an enhanced nucleate boilingmechanism.

3.1.3. Effect of saturation temperatureFig. 5 shows the local heat transfer coefficients variation under

three saturation temperatures (�35.0 �C to �1.9 �C) at three

specific heat fluxes (11.7 kW m�2e53.2 kW m�2) at a constant

mass flux of 73 kg m�2 s�1. For different heat fluxes, the heat

transfer coefficients versus vapor qualities present diverse

trends. In Fig. 5-a, the increase of saturation temperature leads

to negligible variation of the local heat transfer coefficients

within the whole vapor quality range. In Fig. 5-b and -c, more

obvious variation trend for saturation temperature on the local

heat transfer coefficients is found. For a certain vapor quality,

the increase of saturation temperature causes a strong increase

of the local heat transfer coefficients. Comparing the two

different heat flux conditions, the variation of saturation tem-

perature brings about 30% local heat transfer coefficient in-

crease at the heat flux of 33.6 kWm�2, but about 50% increase at

0.0 0.2 0.4 0.6 0.8 1.01000

2000

3000

4000

5000

6000

7000

8000

0.0 0.2 0.4 0.6 0.8 1.01000

2000

3000

4000

5000

6000

7000

8000

0.0 0.2 0.4 0.6 0.8 1.01000

2000

3000

4000

5000

6000

7000

8000

0 10 20 30 40 50 60 70 80 901000

2000

3000

4000

5000

6000

7000

8000

tsat

=-35.0 oC; G=71.5 kg m-2 s-1;q=11.8 kW m-2

tsat

=-35.0 oC; G=73.5 kg m-2 s-1;q=33.6 kW m-2

tsat

=-35.0 oC; G=70.8 kg m-2 s-1;q=53.2 kW m-2

h [W

m

-2

K

-1

]

Vapor Quality [-]

tsat

=-14.1 oC; G=74 kg m-2 s-1;q=11.7 kW m-2

tsat

=-14.1 oC; G=74 kg m-2 s-1;q=33.6 kW m-2

tsat

=-14.1 oC; G=73 kg m-2 s-1;q=53.1 kW m-2

h [W

m

-2

K

-1

]

Vapor Quality [-]

tsat

=-1.9 oC; G=72 kg m-2 s-1;q=11.7 kW m-2

tsat

=-1.9 oC; G=73 kg m-2 s-1;q=33.6 kW m-2

tsat

=-1.9 oC; G=74 kg m-2 s-1;q=53.2 kW m-2

h [W

m

-2

K

-1

]

Vapor Quality [-]

dc

b

tsat

=-32.6 oC; G=99 kg m-2 s-1; x=0.29-0.35

h [W

m

-2

K

-1

]

Heat Flux [ kW m-2

]

a

Fig. 4 e Comparison of local heat transfer coefficients of propane at constant saturation temperature and mass flux, for

several heat fluxes.

i n t e rn a t i o n a l j o u rn a l o f r e f r i g e r a t i o n 4 1 ( 2 0 1 4 ) 1e1 06

the heat flux of 53.3 kW m�2 at low vapor quality region, and

finally tends to slight distinctions at high vapor quality region.

This can be concluded that the more obvious promotion effect

of saturation temperature on the local heat transfer coefficient

occurs at higher heat flux condition.

3.1.4. Effect of vapor qualityThe influence of vapor quality on the local heat transfer co-

efficient is an important consideration in studying the relative

contributions of the nucleate boiling mechanism and

convective boiling mechanism. Figs. 3e5 also show the local

heat transfer coefficient variation versus vapor quality for

different mass fluxes, heat fluxes and saturation tempera-

tures. It is shown that the local heat transfer coefficient can

either increase with quality, remain constant, or decrease

with quality. Kandlikar and Steinke (2002) considered it

mainly due to two important parameters e Boiling number,

Bo ¼ q/(GHlv), and liquid to vapor density ratio (rl/rv). They

pointed out that for a high density ratio, the convective effects

dominate which leads to an increasing trend for the local heat

transfer coefficient with the increase of vapor quality. On the

other hand, a high boiling number leads to a high nucleate

boiling contribution, which tends to decrease as the vapor

quality increases. This leads to a decreasing trend for the heat

transfer coefficient with increasing vapor quality.

In Kandlikar’s previous work (1991), a flow boiling map is

given, which shows the function relationship between heat

transfer coefficient and vapor quality based on two major

parameters (liquid and vapor density ratio and a modified

boiling number). The map indicates that at rl/rv ¼ 1000, the

heat transfer coefficient increases with vapor quality, while at

rl/rv ¼ 10, the heat transfer coefficient decreases with vapor

quality For the given set conditions in this study, take Fig. 3 for

instance, the liquid and vapor density ratios are within the

range of 50e200. Thus it may cause a slight increase of the

heat transfer coefficient. Meanwhile, the low boiling number

which leads to a heat transfer coefficient increase trend,

eventually strengthen the tiny increasing rate due to the low

liquid and vapor density ratio. Thus the total effect of the

vapor quality increase is still positive. Similar conclusions can

be drawn for Figs. 4 and 5 with litter difference in the

increasing rate.

Fig. 5 e Comparison of local heat transfer coefficients of

propane at constant heat and mass flux, for several

saturation temperatures.

Table 3 e Deviations between calculated and measuredheat transfer coefficients.

Reference Deviation

ARD (%) MARD (%) l30%

Kandlikar (1990) �9.1 15.3 79.1

Liu and Winterton (1991) 2.5 7.5 99.5

Gungor and Winterton (1986) 42.9 43.6 22.7

Bennett and Chen (1980) 85.3 85.3 7.1

Shah (1982) �16.7 18.8 76.3

0 2000 4000 6000 8000 100000

2000

4000

6000

8000

10000Bennett-Chen(1980)Gungor-Winterton(1986)KandlikarLiu-Winterton(1991)Shah(1982)

hc

al[W

m

-2

K

-1

]

hexp

[W m-2

K-1

]

Fig. 6 e Comparison between calculated and experimental

data of the local heat transfer coefficients.

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 4 1 ( 2 0 1 4 ) 1e1 0 7

3.1.5. Assessment of predictive methods for heat transfercoefficientsIn this section a comparison of experimental data with calcu-

lated results of local heat transfer coefficients with five pre-

diction methods is shown in Table 3. The mean absolute

relative deviation (MARD) and average relative deviation (ARD)

of thepredicted results respect to the experimental data, aswell

as the percentage of points predicted within a deviation band-

width of�30%, are considered for the statistical analysis for the

predictive methods. Each parameter is defined as follows:

MARD ¼ 1n

Xn

1

�����hcal � hexp

�hexp

����� 100 (4)

ARD ¼ 1n

Xn

1

��hcal � hexp

�hexp

�� 100 (5)

Fig. 6 shows the comparison of heat transfer coefficients

between experimental data and calculated results using five

well-known correlations predicted by Kandlikar (1990), Liu

and Winterton (1991), Gungor and Winterton (1986), Bennett

and Chen (1980), and Shah (1982). Consider the whole data-

base, Liu and Winterton correlation shows the best agree-

ment, with a mean absolute relative deviation less than 10%,

and over 99% of points in a deviation bandwidth of �30%. The

Kandlikar correlation and Shah correlation also show good

agreements with a mean absolute relative deviation less than

20%, and over 75% of points in a deviation bandwidth of�30%.

The BennetteChen correlation and the GungoreWinterton

correlation show obviously larger predicted results than the

experimental data. Especially for the BennetteChen correla-

tion, the mean absolute relative deviation is over 80%, with

10

1

]

tsat

=-35.0oC, G=62 kg m-2 s-1

t =-35.0oC, G=80 kg m-2 s-1

i n t e rn a t i o n a l j o u rn a l o f r e f r i g e r a t i o n 4 1 ( 2 0 1 4 ) 1e1 08

the percentage of points predicted within a deviation band-

width of �30% less than 10%.

0.0 0.2 0.4 0.6 0.8 1.00

2

4

6

8

Fric

tio

na

l p

re

ss

ure

g

ra

die

nt [k

Pa

m

-

Vapor Quality [-]

sat

tsat

=-35.0oC, G=104 kg m-2 s-1

Fig. 8 e Frictional pressure gradients for different mass

fluxes.

3.2. Two-phase frictional pressure gradients

The two-phase pressure drop for flows inside tubes are the

sum of three parts: the static pressure drop Dpstatic, the mo-

mentum pressure drop Dpmom, and the frictional pressure

drop Dpfrict as:

Dptotal ¼ Dpstatic þ Dpmom þ Dpfrict (6)

For a horizontal tube, the static pressure drop change is

zero. Themomentum pressure drop reflects the phase change

in kinetic energy of the flow, is given by:

�Dpmom ¼ G2

("x2

rvεþ ð1� xÞ2rlð1� εÞ

#out

�"x2

rvεþ ð1� xÞ2rlð1� εÞ

#in

)(7)

where rl and rv is the liquid and vapor density respectively, G

is the mass flux and x is the vapor quality. The void fraction ε

is obtained using the Rouhani and Axelsson (1970) model for

horizontal tubes which is given as:

ε¼ xrv

�ð1þ0:12ð1�xÞÞ

�xrv

þ1�xrl

�þ1:18ð1�xÞ½gsðrl�rvÞ�0:25

Gr0:5l

��1

(8)

where g is gravity, s is the surface tension. After calculating

themomentum pressure drop, hence the two-phase frictional

pressure drop is obtained by subtracting the calculated mo-

mentum pressure drop from the measured total pressure

drop.

3.2.1. Effect of saturation temperatureFig. 7 shows the effect of saturation temperature for propane

at constant mass flux. As expected, the pressure gradients

reduce with the increase of saturation temperature. For a

certain vapor quality, the higher the saturation temperature

is, the lower pressure gradient it obtains. This behavior is

0.0 0.2 0.4 0.6 0.8 1.00

1

2

3

4

5

6

Fric

tio

na

l p

re

ss

ure

g

ra

die

nt [k

Pa

m

-1

]

Vapor Quality [-]

G=73 kg m-2 s-1, tsat

=-35.0 oC;

G=73 kg m-2 s-1, tsat

=-14.1 oC;

G=73 kg m-2 s-1, tsat

=-1.9 oC;

Fig. 7 e Frictional pressure gradients for different

saturation temperatures.

mainly due to the change of thermophysical properties caused

by the variation of saturation temperature. With the

increasing saturation temperature, the liquid viscosity and

vapor density increases,, which lead to conspicuously

decrease for both vapor and liquid velocity. Finally the

degradation of two-phase velocity causes the reduction of the

pressure gradients.

3.2.2. Effect of mass fluxFig. 8 shows the pressure gradients versus vapor quality for

different mass fluxes at constant saturation temperature of

�35 �C. For a certain vapor quality, the increase of mass flux

leads to an evident increase of the frictional pressure gradients.

Comparing the whole vapor quality range, mass flux varying

from 62 to 104 kg m�2 s�1 causes about 100% increase at the

vapor quality of 0.2 but nearly 200% increase at the high vapor

0 3 6 9 12 150

3

6

9

12

15+30%

FriedelLockhart and Martinelli)GronnerudChisholmMüller-Steinhagen and Heck)

Ca

lc

ula

te

d

p [k

Pa

m

-1

]

Experimental p [kPa m-1

]

-30%

Fig. 9 e Comparison between calculated and experimental

data of the two-phase frictional pressure gradients.

Table 4 e Deviations between calculated and measuredpressure gradients.

Reference Deviation

ARD (%) MARD (%) l30%

Friedel (1979) 67.7 67.7 7.9

Lockhart and Martinelli (1949) 33.4 38.1 55.1

Gronnerud (1979) 85.9 87.4 24.7

Chisholm (1973) 88.5 98.6 29.2

Muller-Steinhagen and Heck (1986) �7.5 17.0 91.0

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 4 1 ( 2 0 1 4 ) 1e1 0 9

quality of about 0.7. This is already clear that the increasing

mass flux causes higher two-phase velocity which ultimately

leads to greater pressure gradients. This increasing trend oc-

curs especially obvious in high vapor quality region when the

flow pattern changes into fully developed annular flow.

3.2.3. Effect of vapor qualityBoth Figs. 7 and 8 also show the effect of vapor quality for the

frictional pressure gradient at different test conditions. For

different cases, themaximumvapor quality range covers from

0.1 to 1, and some only reaches up to about 0.7 limited by the

operation condition, along with which the flow pattern

changes from stratified wavy flow, slug flow, annular flow,

and finally dry-out region. Results show that the pressure

gradient obviously increases with the vapor quality within a

wide range of vapor quality. A peak point was observed at the

vapor quality value of about 0.88 at a relatively lower satura-

tion pressure condition. After that, the pressure gradient

finally shows a decrease trend in Fig. 7 when the high vapor

quality condition is acquired. This behavior is mainly attrib-

uted to the flow pattern change. For each experimental

condition, stratified wavy flow is encountered at low vapor

qualities, and then the transition to the slug flow occurs with

the increasing vapor quality. The perturbation effects gradu-

ally strengthen, causing an obvious increase of the frictional

pressure gradients. In addition, as the liquid continually

evaporates, the convergence of bubbles leads to an increasing

pressure to the liquid film which also increases the frictional

pressure gradients. Until the steady annular flow is formed,

the perturbation effect reaches the strongest point. After that,

with the continually increasing vapor quality, the increase

trend for the frictional pressure gradient turns into the steady

state. Finally, when the dry-out transition is found, the rest of

the liquid phase is entrained in the gas core and disperse as

droplets causing a decrease trend for the frictional pressure

gradients as the surface in contact with the tube wall changes

from liquid to vapor.

3.2.4. Comparisons with existing correlationsIn presentwork, the experimental frictional pressure gradients

of propane were compared with five correlations. Fig. 9 shows

a comparison between the measured frictional pressure gra-

dients of propane with the correlation of Friedel (1979),

Gronnerud (1979), Lockhart and Martinelli (1949), Muller-

Steinhagen and Heck (1986), and Chisholm (1973). The results

of the statistical analysis are showed in Table 4. The result

indicates that the Muller-Steinhagen & Heck correlation gives

the best fit to the data with a mean absolute relative deviation

less than 20%, and over 90% points within a deviation band-

width of �30%. The Lockhart & Martinelli correlation shows a

second good agreement with a mean absolute relative devia-

tion about 38%, but only about 50% points within a deviation

bandwidth of �30%. The calculated results by Friedel, Gron-

nerud and Chisholmare obviously lager than the experimental

data with a mean absolute relative deviation over 60%. For

these three correlations, the percentages of points within a

deviation bandwidth of �30% are less than 30%.

4. Conclusion

In this work, an experimental study of two-phase flow boiling

heat transfer and frictional pressure gradients of propane in

smooth horizontal tubes was carried out at various condi-

tions. Some conclusions can be drawn from this study.

(1) Local heat transfer coefficients were found to increase with

mass flux and heat flux at all test conditions. For saturation

temperature, more obvious promotion effects on the local

heat transfer coefficient occurs at high heat flux conditions.

Results also show that the heat transfer coefficient can

either increase with quality, remain constant, or decrease

with quality depending on different test conditions.

(2) Compared with five well-known correlations, Liu and

Winterton correlation shows the best agreement, with a

mean absolute relative deviation less than 10%, and over

99% of points within a deviation bandwidth of �30%.

(3) For adiabatic two-phase frictional pressure gradients, the

influences of saturation temperature, mass flux and vapor

quality were also analyzed. Mass flux has obviously positive

effects on frictional pressure gradients,whilenegative effect

is found for saturation temperature. The pressure gradient

variation tendency as a function of vapor quality lasts for a

long period of increase until it reaches a peak at a relatively

high vapor quality value, and then gradually decreases.

(4) The adiabatic two-phase frictional pressure gradient

experimental results were compared with five existing

correlations. Muller-Steinhagen & Heck correlation gives

the best fit to the data with a mean absolute relative de-

viation less than 20%, and over 90% of experimental points

are in the deviation bandwidth of �30%.

Acknowledgment

This work was supported by the National Science Foundation

of China with the contract number of 50890183 and 51106171.

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