Download Two-phase friction factor in vertical downward flow in high

International Communications in Heat and Mass Transfer 35 (2008) 1147–1152
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International Communications in Heat and Mass Transfer
j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i c h m t
Two-phase friction factor in vertical downward flow in high mass flux region of
refrigerant HFC-134a during condensation☆
A.S. Dalkilic a,⁎, S. Laohalertdecha b, S. Wongwises b,⁎
a
Heat and Thermodynamics Division, Department of Mechanical Engineering, Yildiz Technical University, Yildiz, Istanbul 34349, Turkey
Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Lab. (FUTURE), Department of Mechanical Engineering, King Mongkut's University of Technology Thonburi,
Bangmod, Bangkok 10140, Thailand
b
A R T I C L E
I N F O
Available online 15 July 2008
Keywords:
Condensation
Two-phase pressure drop
Friction factor
Vertical downward flow
HFC-134a
Equivalent Reynolds number model
A B S T R A C T
The two-phase pressure drop of the pure refrigerant HFC-134a during condensation inside a vertical tube-intube heat exchanger was investigated. The double tube test section was 0.5 m long with refrigerant flowing
in the inner tube and cooling water flowing in the annulus. The inner tube was constructed from smooth
copper tubing of 8.1 mm inner diameter and 9.52 mm outer diameter. The test runs were performed at
average condensing temperatures of 40–50 °C. The mass fluxes were between 260 and 515 kg m− 2 s− 1 and
the heat fluxes between 11.3 and 55.3 kW m− 2. The quality of the refrigerant in the test section was calculated
using the temperature and pressure obtained from the experiment. The pressure drop across the test section
was directly measured by a differential pressure transducer. A new correlation for the two-phase friction
factor of R134a flow is proposed by means of the equivalent Reynolds number model. The effects of heat flux,
mass flux and condensation temperature on the pressure drop are also discussed.
© 2008 Published by Elsevier Ltd.
1. Introduction
The heat transfer and pressure drop characteristics of refrigerants
have been studied by a large number of researchers. However, study of
the pressure drop of refrigerants during downward condensation in
small diameter vertical tubes has received comparatively little
attention in the literature. A brief summary of pressure drop studies
of downward condensation is given as follows:
Goodykoontz and Dorsch [1] investigated the local condensation
heat transfer coefficients and pressure distribution of R113 for the
mass fluxes of 21–455 kg m− 2 s− 1 in a 7.4–15.9 mm i.d. vertical tube.
Kim and No [2] developed a turbulent film condensation model
including pressure drop for high pressure steam in a 46 mm i.d.
vertical tube. Ma et al. [3] studied the two-phase friction factors of
downward flow of R113 for the mass fluxes of 400–800 kg m− 2 s− 1 in a
20.8 mm i.d. smooth and micro-fin tubes.
Akers et al. [4] developed a two-phase multiplier by assuming that
two-phase flows are similar to single-phase flows. Their correlation
predicts a frictional two-phase pressure drop by means of a multiplying factor, which uses the same rationale as the Lockhart–Martinelli
multiplier [5]. Their model is known as the “equivalent Reynolds
number model”. It can be used for an annular flow regime. According to
this model, the equivalent all liquid flow produces the same wall shear
☆ Communicated by W.J. Minkowycz.
⁎ Corresponding authors.
E-mail addresses: [email protected] (A.S. Dalkilic), [email protected]
(S. Wongwises).
0735-1933/$ – see front matter © 2008 Published by Elsevier Ltd.
doi:10.1016/j.icheatmasstransfer.2008.06.002
stress as that of the two-phase flow. Several researchers have used this
model in their work, for example, Moser et al. [6].
To the best of the authors' knowledge, there has been insufficient
work dealing with the two-phase pressure drop during downward
condensation in small diameter tubes. Although some information is
currently available on the two-phase friction factor in annular flow,
there still remains room to further discuss whether it gives reliable
predictions of friction factors in the high mass flux region. Therefore, the
main aim of this study was to extend the existing pressure drop data for
R134a during downward condensation to the high mass flux region. The
results from the large amount of experimental data were correlated with
the equivalent Reynolds number and presented as a new empirical
correlation to predict the two-phase friction factor. The effects of various
relevant parameters on pressure drop are also discussed.
2. Experimental apparatus and method
A schematic diagram of the test apparatus is shown in Fig. 1. The
refrigerant loop consists of a pre-heating loop, test section, cooling
loop and chilling loop. The refrigerant is circulated by a gear pump
controlled by an inverter. The refrigerant flows in series through a
filter/dryer, a sight glass tube, a refrigerant flow meter and a preheater and enters the test section. A spiral counter-flow double tube
heat exchanger is designed to supply heat to control the inlet quality
of the refrigerant before entering the test section. After exiting the test
section, the chilling loop condenses and sub-cools the refrigerant and
removes the heat input from the pre-heater and test section, and
ejects it into the surroundings. After leaving the chilling loop, the
1148
A.S. Dalkilic et al. / International Communications in Heat and Mass Transfer 35 (2008) 1147–1152
Nomenclature
cp
d
f
G
f
g
i
ifg
L
m
Re
S
T
Q
q
x
ΔP
ΔT
specific heat, J kg− 1 K− 1
internal tube diameter, m
friction factor
mass flux, kg m− 2 s− 1
friction factor
gravitational acceleration, m s− 2
enthalphy, J kg− 1
latent heat of condensation, J kg− 1
length of test tube, m
mass flow rate, kg s− 1
Reynolds number
slip ratio
temperature, °C
heat transfer rate, W
mean heat flux, kW m− 2
mean vapour quality
pressure drop, Pa
vapour side temperature difference, Tsat − Twi, °C
meters. The uncertainty of the temperature measurements is ±0.1 °C.
All static pressure taps are mounted on the tube wall. The refrigerant
flow meter is a variable area type. The flow meter was calibrated in the
range of 0–2.2 gal min− 1 for HFC-134a by the manufacturer. Pressure
drop is measured by a differential pressure transducer installed
between the inlet and outlet of the test section. The length between
pressure taps is 0.7 m. A low temperature thermostat is used to control
the system pressure of the refrigerant flow. The differential pressure
transducer and pressure gauges are calibrated against a primary
standard, the dead weight tester. All signals from thermocouples and
pressure transducers are recorded by a data logger. Tests are performed
in the steady state.
3. Data reduction
The data reduction of the measured results can be analysed as
follows:
3.1. The inlet vapour quality of the test section (xTS,i)
xTS;i ¼
Greek symbols
ρ
density, kg m− 3
μ
dynamic viscosity, kg m− 1 s− 1
α
void fraction
Subscripts
eq
equivalent
Exp
measured
F
frictional term
g
gas/vapour
G
gravitational term
i
inlet
l
liquid
M
momentum term
o
outlet
ph
pre-heater
ref
refrigerant
sat
saturation
TS
test section
T
total
tp
two phase
w
water
wi
inner wall
refrigerant changes from the two-phase refrigerant to a sub-cooled
state. Eventually, the refrigerant returns to the refrigerant pump to
complete the cycle.
The test section is a vertical counter-flow tube-in-tube heat
exchanger with refrigerant flowing downward in the inner tube and
cooling water flowing upward in the annulus. The inner and outer
tubes are made from smooth vertical copper having inner diameters of
8.1 and 26 mm respectively. The length of the heat exchanger is 0.5 m.
Fig. 2 shows the detailed dimensions of the heat exchanger and the
location of the thermocouples.
T-type thermocouples are used to measure refrigerant temperature
and the tube wall temperatures in the test section. A total of ten
thermocouples are located on the side wall at five points along the test
tube. A thermostat is used to control the inlet temperature of the water.
All the temperature-measuring devices are calibrated in a controlled
temperature bath using standard precision mercury glass thermo-
iTS;i −il@TTS;i
ifg@TTS;i
ð1Þ
where il@TTS,i is the enthalpy of the saturated liquid based on the
temperature of the test section inlet, ifg@TTS,i is the enthalpy of
vapourisation based on the temperature of the test section inlet, and
iTS,i is the refrigerant enthalpy at the test section inlet, given by:
iTS;i ¼ iph;i þ
Qph
mref
ð2Þ
where iph,i is the inlet enthalpy of the liquid refrigerant before
entering the pre-heater, mref is the mass flow rate of the refrigerant,
and Qph is the heat transfer rate in the pre-heater:
Qph ¼ mw;ph cp;w Tw;i −Tw;o ph
ð3Þ
where mw,ph is the mass flow rate of the water entering the preheater, cp,w is the specific heat of water, and (Tw,i − Tw,o)ph is the
temperature difference between inlet and outlet positions of the preheater.
3.2. The outlet vapour quality of the test section (xTS,o)
xTS;o ¼
iTS;o −il@TTS;o
ifg@TTS;o
ð4Þ
where iTS,o is the refrigerant enthalpy at the test section outlet, il@TTS,o is
the enthalpy of the saturated liquid based on the temperature of the
test section outlet, and ifg@TTS,o is the enthalpy of vapourisation. The
outlet enthalpy of the refrigerant flow is calculated from
iTS;o ¼ iTS;i −
QTS
mref
ð5Þ
where the heat transfer rate, QTS, in the test section is obtained
from:
QTS ¼ mw;TS cp;w Tw;o −Tw;i TS
ð6Þ
where mw,TS is the mass flow rate of the water entering the test
section, and (Tw,o − Tw,i)TS is the temperature difference between water
at the outlet and inlet positions.
A.S. Dalkilic et al. / International Communications in Heat and Mass Transfer 35 (2008) 1147–1152
1149
Fig. 1. Schematic diagram of experimental apparatus.
Fig. 2. Schematic diagram of test section.
3.3. The equivalent Reynolds number model approach for two-phase
friction factor
tum pressure gradient and the frictional pressure gradient as
follows:
The two-phase pressure gradient is the sum of three
contributions: the gravitational pressure gradient, the momen-
dP
¼
dz
dP
dP
dP
þ
þ
:
dz G
dz M
dz F
ð7Þ
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A.S. Dalkilic et al. / International Communications in Heat and Mass Transfer 35 (2008) 1147–1152
Fig. 5. Effect of various mass fluxes of R134a on measured total pressure drop at Tsat = 50 °C.
Fig. 3. Comparison of heat flux for various mass fluxes of R134a at Tsat = 50 °C.
Pressure drop due to gravity can be determined from [3]:
ðΔP ÞG ¼ g αρg þ ð1−α Þρl L
ð8Þ
where the void fraction, α, can be determined from the Chisholm [7]
correlation below:
α¼
1þ
1
1−xρg x
ρ S
ð9Þ
l
where
S¼
1−x þ x
ρl
ρg
!1=2
:
ð10Þ
The momentum transfer term contributes to the overall pressure
drop during condensation due to the mass transfer that occurs at the
phase's interface. Honda et al. [8] and Sami and Schnotale [9] reported
that the momentum pressure gradient can be ignored for condensation. On the other hand, the momentum pressure gradient can be
Fig. 6. Effect of various mass fluxes of R134a on measured total pressure drop at
Tsat = 40 °C and xinlet = 1.
written according to the results of the one-dimensional two-phase
separated-flow analysis which can be defined as follows [10]:
"
#
dP
x2
ð1−xÞ2
2 d
þ
:
¼ −G
dz M
dz ρg α ρ1 ð1−α Þ
ð11Þ
Eq. (11) can be rearranged as follows:
"(
ΔPM ¼ G2
ð1−xÞ2
x2
þ
ρl ð1−α Þ ρg α
) (
−
o
ð1−xÞ2
x2
þ
ρl ð1−α Þ ρg α
)#
:
ð12Þ
i
The two-phase frictional pressure drop can be obtained by
subtracting the gravitational and momentum terms from the total
measured pressure drop as follows:
dP
dP
dP
dP
¼
−
¼
:
dz F
dz Exp dz G
dz M
ð13Þ
The two-phase friction factor is calculated by the following
equation based on the all liquid Reynolds number [3]:
3
Fig. 4. Change in measured total pressure drop for all mass fluxes of R134a at Tsat = 40 °C
and various condensation temperature differences.
ftp ¼
ðΔP ÞF d
ðΔP ÞF 2ρl d
¼
G2eq =2ρl 4L
Re2eq μ 2l 4L
ð14Þ
A.S. Dalkilic et al. / International Communications in Heat and Mass Transfer 35 (2008) 1147–1152
Fig. 7. Effect of various mass fluxes of R134a on measured total pressure drop at
Tsat = 40 °C and xinlet = 1.
where the all liquid equivalent Reynolds number is determined
from:
Reeq ¼
Geq d
μl
and equivalent liquid mass flux is defined as:
0
!0:5 1
ρl
@
A:
Geq ¼ G ð1−xÞ þ x
ρg
ð15Þ
1151
Fig. 9. Comparison of friction pressure drop for various mass fluxes of R134a at
Tsat = 40 °C.
temperature of 50 °C at various mass fluxes in a smooth tube. It can be
seen that heat flux increases with increasing temperature difference
(or condensation rate). The increase in heat flux increases the
condensation rate. In other words, film thickness on the tube wall
increases due to the constant latent heat of condensation for a specific
saturation temperature of condensation (Eqs. (5)–(6)). It can also be
seen that heat flux increases with increasing mass flux due to the
ð16Þ
3.4. Correlation development
The two-phase friction factor of R134a in a copper smooth tube
having an inner diameter of 8.1 mm and length of 0.5 m during
downward condensation was developed by means of Eqs. (14)–(15).
The equivalent Reynolds number is considered to be the significant variable for the experiment. Regression analysis was performed with this variable and gave a convincing correlation. Based
on 380 smooth tube data points, the following correlation was
developed:
ftp ¼ 0:0144Re−0:0087
:
eq
ð17Þ
4. Results and discussion
Fig. 3 shows the relationship between the mean heat flux and the
condensation temperature difference (Tsat − Twi) for the condensation
Fig. 10. Comparison of friction pressure drop for various mass fluxes of R134a at
Tsat = 50 °C.
Fig. 8. Effect of condensation temperatures of R134a on measured total pressure drop
for G = 260 and 515 kg m2 s− 1 and xinlet = 1.
Fig. 11. Comparison of friction factors for various mass fluxes of R134a at Tsat = 40 °C.
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A.S. Dalkilic et al. / International Communications in Heat and Mass Transfer 35 (2008) 1147–1152
calculated frictional pressure drop values at 50 °C are lower than those
at 40 °C for the same mass flux.
Figs. 11–12 show the variation in two-phase friction factor versus
the equivalent Reynolds number. The sequence of lines is consistent
for all mass fluxes. It can be seen that the two-phase friction factor
increases with decreasing equivalent Reynolds numbers. The same
trend was also seen by Ma et al. [3] with different experimental
conditions and parameters. It is clear that the two-phase friction
factors at 50 °C are lower than those at 40 °C. The majority of the
measured data falls within ±20% using the proposed correlation
(Eq. (17)) for all mass fluxes and condensing saturation temperatures.
5. Conclusion
Fig. 12. Comparison of friction factors for various mass fluxes of R134a at Tsat = 50 °C.
increase in condensation rate. Fig. 4 shows the change in total
pressure drop with various mass fluxes for the condensation
temperature of 40 °C at various temperature differences. Due to the
increase in shear stress at the interface of the phases, total pressure
drop increases with increasing mass fluxes. Hence, increasing heat
flux increases with increasing condensation rate, decreases the vapour
quality, and as a result, pressure drop is decreased. Similar results
were presented in [11–13].
Fig. 5 shows the relationship between total measured pressure
drop and quality at the condensation temperature of 50 °C at various
mass fluxes. At high vapour quality, the higher velocity of vapour flow
causes more shear stress at the interface of the vapour and the liquid
film. As a consequence, the total pressure drop increases with
increasing vapour quality.
The pressure drop per unit length shown in Figs. 6–8 is obtained
from dividing the measured pressure drop by the length between
pressure taps. In our apparatus, the length between pressure taps is
0.7 m. The test runs were conducted at average inlet qualities between
0.77 and 1.
Figs. 6–7 show the effect of mass fluxes of R134a on the total
measured pressure drop per unit length. It can be seen that at the
same condensing temperature difference, total pressure drop
increases with increasing mass flux. At a specific vapour quality, the
increase in mass flux will increase the vapour velocity and flow
turbulence. Hence, the shear stress at the interface of the vapour and
liquid film increases and, as a result, the pressure drop is increased.
Fig. 8 shows the effect of condensation temperature (40–50 °C)
on the total measured pressure drop per unit length for low and
high mass fluxes (260 kg m− 2s− 1 and 515 kg m− 2s− 1). Low mass
flux conditions give less condensation pressure drop per unit
length than high mass flux conditions at the same condensing
temperature. In addition to this, an increase in system pressure or
condensing temperature leads to some decrease in pressure drop
at the same mass flux. Yan and Lin [14] found similar results.
Figs. 9–10 illustrate the dependence of the frictional pressure drop
determined from Eq. (13) on the average quality along the test
tube for the condensation temperatures of 40–50 °C. It is clear that
frictional pressure drop increases with increasing mass flux.
The increase in saturation temperature decreases the specific volume
of R-134a vapour, and the vapour velocity is decreased. It also
decreases the viscosity of R134a, as a result of which the flow
resistance is decreased. When the condensing saturation temperature
increases, all of these factors lower the pressure drop. As expected, the
Accurate and repeatable pressure drop data for the condensation
of R134a in downward flow at high mass flux inside a smooth tube
were obtained. Chisholm's [7] void fraction correlation was used to
calculate the gravitational and momentum pressure drop. Frictional
pressure drop was obtained from measured total pressure drop data.
The effects of various relevant parameters such as condensing
temperature, condensation temperature difference, vapour quality
and mass flux on the pressure drop are discussed and investigated. A
new correlation of the two-phase friction factor, determined using the
equivalent Reynolds number model, was developed from a large
amount of data.
Acknowledgements
The authors are indebted to the Department of Mechanical
Engineering, King Mongkut's University of Technology Thonburi
(KMUTT) and the Thailand Research Fund (TRF) for supporting this
study. Especially, the first author wishes to thank KMUTT for providing
him with a Post-doctoral fellowship.
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