Post on 25-Jun-2020
transcript
Condensation Heat Transfer and Pressure Drop in Horizontal
Rectangular Multiport Minichannels and Small Diameter
Microfin Tubes
By
Md. Mostaqur Rahman
A dissertation submitted in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy (Ph.D) in
Mechanical Engineering
Department of Science and Advanced Technology
Graduate School of Science and Engineering
Saga University
Japan
March 2018
i
ACKNOWLEDGEMENTS
First of all, Alhamdulillah, I should be grateful to Almighty, Gracious and Merciful
Allah. The words are not enough to praise Him for his comfort, strength and courage.
His presence is the main source of my inspiration, without His help; I would not
achieve this goal.
I would like to express my deep appreciation to my research advisor Professor Dr. Akio
Miyara who accepted me as his Ph.D student without any hesitation. It was my
privilege to work with him, who completely showed me what a wonderful advisor
should be like. Without his expert supervision, sincere and tireless supports,
appreciation, continuous inspiration, and trust, it would be impossible for me to achieve
this milestone. My special thanks are due to Dr. Keishi Kariya for making a number of
helpful suggestions. Without their valuable input, this thesis would not have been this
current quality.
I also would like to extend my sincere thanks to the members of my dissertation
committee, Professor Dr. Shigeru Matsuo and Professor Dr. Yuichi Mitsutake for their
time, comments and valuable ideas. I am grateful for their generous and suggestions
that helped improve this work significantly.
I would like to thank to my home university, Dhaka University of Engineering and
Technology, Gazipur-Bangladesh, for allowing me the opportunity to continue my
studies at the doctoral level. I would also like to express special thanks to the MEXT
(Ministry of Education, Culture, Sports, Science and Technology), Japan to grant me as
a Japanese Government sponsored student. Without their grant and support, this would
not have been possible.
I wish to thank to my beloved parents, my father, Md. Helalur Rahman Tarafder, is the
person who put the fundament my learning character, showing me the joy of intellectual
pursuit ever since I was a child; and my mother, Mrs. Morium Begum, is the one who
sincerely raised me with her caring and gently love. Their prayers, encouragement, and
advice have been and will always be a fortune for my life. I be obliged them everything
and wish I could show them just how much I love and appreciate them. I would like to
convey my heartfelt thanks to my beloved wife, Niger Sultana, whose love, support,
patience, encouragement and sacrifice allowed me to finish this journey. Without love
and sacrifice from her, I would not be able to complete my study today. I also want to
ii
be thankful to my only daughter, Musthasfia Mostaq, for her love, patience and
sacrifice.
Thanks are due to all the personnel at the Thermal Energy Engineering Miyara Lab.
They were a constant source of help when I was working with this work group. Thanks
to Kyosuke Nakaiso and Yasuhiro Kudo for helping me to collect experimental data in
the early stage of this study. Finally, I would like to thank all of my lab mates for their
supports. I would also like to express my gratitude to all Bangladeshi friends, Saga
Moslem Society and international students in Saga for making my Japan life more
comfortable and enjoyable. I also would like to thank everybody who was important to
the successful realization of my study, as well as expressing my apology that I could not
mention personally one by one.
iii
Abstract
Multiport minichannels and microfin tubes are increasingly being used for the
fabrication of compact and high performance heat exchangers in air-conditioning,
refrigeration, automotive, heat pump systems and some other industrial applications for
a wide variety of applications. The main target of using compact heat exchanger is to
improve the performance of the system and reduce the charge amount of refrigerant.
The charge reduction is very important in recent air-conditioning, refrigeration and heat
pumping systems because of the great impact of HCFC and HFC refrigerants on the
direct greenhouse effects. However, the pressure drop and heat transfer characteristics
in multiport minichannels and small diameter microfin tubes are questionably to be
different from the conventional tubes of diameter greater than 3.0 mm. The behavior of
the most important parameters such as pressure drop and heat transfer characteristics in
reduced geometry is not clarified sufficiently yet for the design of compact and high
performance heat exchangers. Although, several researchers extensively investigated
the pressure drop and heat transfer in multiport minichannels and small diameter
microfin tubes, but the design engineer still facing problem for accurate predictive tools
for pressure drop and heat transfer prediction in two-phase flow.
To investigate the effects of different parameters on the pressure drop and heat
transfer, a new experimental apparatus to obtain explicit pressure drop and local
condensation heat transfer coefficient measurements over a range of test conditions has
been fabricated. Multiple variables were recorded in order to calculate pressure drop
and local heat transfer coefficient in two-phase adiabatic and condensing flow within
multiport minichannels and microfin tube, respectively. The effects of mass flux,
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saturation temperature, vapor quality and channel geometry on adiabatic frictional
pressure drop and condensation heat transfer coefficient were investigated and clarified.
The experimental results discovered that the mass flux, saturation temperature, vapor
quality, and channel geometry play an important role in increasing or decreasing an
adiabatic frictional pressure drop and condensation heat transfer coefficient in both
multiport minichannels and microfin tubes. Some models over-predicted the
experimental frictional pressure drop and condensation heat transfer data, some are
under-predicted and few models captured the trend correctly within the limits of
experimental error. Due to the variety in operating condition consideration during the
models development and complex characteristics of two-phase flow, most of the
existing models were failed to capture the experimental data with a high degree of
accuracy.
In addition, a new two-phase frictional pressure drop correlation is developed for
multiport minichannels to predict the frictional pressure drop correctly. The correlation
has been developed using the experimental data by considering the effects of inertia,
viscous force, fluid properties, channel geometry and surface tension. A new
condensation heat transfer correlation was also proposed to improve the accuracy of the
condensation heat transfer coefficients prediction of two-phase flow in horizontal
rectangular multiport minichannels.
Furthermore, the newly proposed correlations for frictional pressure drop and
condensation heat transfer coefficients prediction has also been validated with the
available frictional pressure drop and heat transfer data collected from the open
literature. Both frictional pressure drop and condensation heat transfer coefficient
correlations showed good agreement with the collected data.
v
Table of Contents
Acknowledgements i
Abstract iii
Table of Contents v
List of figures ix
List of tables xii
Nomenclature xiii
1 Introduction 1
1.1 Background 2
1.1.1 Minichannels 2
1.1.2 Microfin tube 7
1.1.3 Two-phase flow regimes (Flow pattern) 11
1.1.4 Two-phase flow mapping 14
1.2 Literature review 15
1.2.1 Condensation heat transfer in minichannels 15
1.2.2 Two-phase pressure drop in minichannels 22
1.2.3 Condensation heat transfer and pressure drop in microfin tube 27
1.3 Objectives of the present research 33
1.4 Overview of the thesis 34
References 35
2 Experimental Methods 50
2.1 Experimental Facility 51
2.1.1 Experimental Apparatus 51
2.1.2 The test sections
2.1.1.1 Multiport minichannels with and without fins
2.1.1.2 Smooth and microfin tubes
52
52
54
2.1.3 Range of test conditions 56
2.2 Data Reduction 58
2.2.1 Two-phase frictional pressure drop 58
vi
2.2.2 Condensation heat transfer 61
2.3 Experimental measurement uncertainties analysis 65
References 67
3 Adiabatic Frictional Pressure Drop Analysis 68
3.1 Two-phase frictional pressure drop in rectangular multiport
minichannels with and without fins
68
3.1.1 Effect of the mass flux and vapor quality 68
3.1.2 Effect of saturation temperature 70
3.1.3 Effect of channel hydraulic diameter 73
3.2 Two-phase frictional pressure drop in circular microfins and smooth
tubes
74
3.2.1 Influence of mass flux and vapor quality 74
3.2.2 Influence of microfins 76
3.2.3 Influence of saturation temperature 76
3.3 Conclusions 78
References 79
4 Condensation heat transfer 80
4.1 Condensation heat transfer in rectangular multiport minichannels with
and without fins
80
4.1.1 Effect of mass velocity and vapor quality 82
4.1.2 Effect of saturation temperature 83
4.1.3 Effect of minichannels diameter 85
4.2 Condensation heat transfer in circular microfins and smooth tube 86
4.2.1 Effect of the mass flux and vapor quality 86
4.2.2 Effect of tube diameter 87
4.3 Conclusions 90
References 91
5 Comparison of two-phase frictional pressure drop 93
5.1 Models review and comparison of frictional pressure drop in multiport
minichannels with the well-known correlations
93
vii
5.1.1 Models review 94
5.1.1.1 Correlation developed for convensional channels 94
5.1.1.1.1 Homogeneous model (Thome, 2006) 94
5.1.1.1.2 Lockhart and Martinelli correlation (1949) 95
5.1.1.1.3 The Friedel Correlation (1979) 96
5.1.1.1.4 The Müller-Steinhagen and Heck
correlation (1986)
97
5.1.1.1.5 The Wang et al. correlation (1997) 97
5.1.1.2 Correlations developed for minichannels 98
5.1.1.2.1 The Mishima and Hibiki correlation (1996) 98
5.1.1.2.2 The Lee and Lee correlation (2001) 98
5.1.1.2.3 The Koyama et al. correlation (2003) 99
5.1.1.2.4 The Lee and Mudawar correlation (2005) 99
5.1.1.2.5 The Hwang and Kim correlation (2006) 100
5.1.1.2.6 The Sun and Mishima correlation (2009) 100
5.1.1.2.7 The Zhang et al. correlation (2010) 101
5.1.1.2.8 The Li and Wu correlation (2010) 101
5.1.1.2.9 The Kim and Mudawar correlation (2012) 102
5.1.1.2.10 The Jige et al. correlation (2016) 103
5.1.2 Comparison with existing correlations 104
5.2 Models review and comparison of frictional pressure drop in microfins
tube with the well-known correlations
113
5.2.1 Models review 113
5.2.1.1 The Miyara et al. correlation (2000) 113
5.2.1.2 The Koyama and Yonemoto correlation (2006) 114
5.2.1.3 The Müller-Steinhagen and Heck correlation (1986) 115
5.2.1.4 The Goto et al. correlation (2001) 115
5.2.1.5 The Haraguchi et al. correlation (1994) 116
5.2.1.6 The Olivier et al. correlation (2004) 116
5.2.1.7 The Kedzierski and Goncalves correlation (1999) 117
5.2.2 Comparison of experimental frictional pressure drop of
microfins tube with existing correlations
117
5.3 Conclusions 120
viii
References 121
6 Comparison of Condensation Heat Transfer 124
6.1 Models review and comparison of heat transfer coefficients in
minichannels with existing correlations
124
6.1.1 Models review 125
6.1.1.1 Correlations developed for convensional tube 125
6.1.1.1.1 The Shah correlation (1979) 125
6.1.1.1.2 The Haraguchi et al. correlation (1994) 125
6.1.1.1.3 The Dobson and Chato correlation (1998) 126
6.1.1.2 Correlations developed for mini and microchannels 126
6.1.1.2.1 The Wang et al. correlation (2002) 126
6.1.1.2.2 The Koyama et al. correlation (2003) 128
6.1.1.2.3 The Park et al. correlation (2011) 129
6.1.1.2.4 The Bohdal et al. correlation (2012) 129
6.1.1.2.5 The Kim and Mudawar correlation (2013) 129
6.1.1.2.6 The Shah correlation (2016) 130
6.1.1.2.7 The Jige et al. correlation (2016) 131
6.1.2 Comparison with existing correlations 133
6.2 Comparison of condensation heat transfer coefficients in microfin tube
with existing correlations
139
6.3 Conclusions 144
References 145
7 Development of New Correlations 147
7.1 Development of new pressure drop correlation for minichannels 147
7.2 Development of new heat transfer correlation for minichannels 153
7.3 Conclusions 157
References 158
8 Conclusions and recommendations 162
8.1 Conclusions 162
8.2 Future works 164
ix
List of Figures
1.1 Examples of minichannels 3
1.2 Cross-section of different geometry of minichannels 4
1.3
1.4
1.5
1.6
1.7
1.8
Examples of applications of minichannels cooling (Kim and Mudawar,
2014)
Microfin tube (Photo Ref. http://www.wieland-industrierohre.de/)
Characteristic geometrical parameters of inside microfin tube (Cavallini
et al., 2000)
Shabtay microfin tube (Shabtay et al., 2014)
Examples of different microfin tube (Cavallini et al., 2000, 2003)
Schematics of flow patterns and variation of heat transfer coefficient in
minichannels with uniform circumferential heat flux (Kim and Mudawar,
2014).
6
9
9
10
11
12
2.1 A photograph of the test sections. 50
2.2 Schematic diagram of the experimental apparatus 52
2.3 Test section (Multiport minichannels) 54
2.4 Photograph of the test tube 55
2.5 Test section (Circular tube) 56
2.6
2.7
2.8
Abrupt contraction and expansion nonmentcluture
Error of heat balance of all test conditions
Schematic diagram of local heat transfer coefficient calculation.
59
62
64
3.1
3.2
Effects of mass flux and vapor quality on frictional pressure gradient in
rectangular multiport minichannels with fins.
Effects of mass flux and vapor quality on frictional pressure gradient in
rectangular multiport minichannels without fins
69
70
3.3 Effect of saturation temperature on frictional pressure gradient 72
3.4 Comparison of frictional pressure drop between minichannels with fins
and without fins.
73
3.5 Effects of mass flux and vapor quality on frictional pressure drop: (a)
Microfin tube; (b) Smooth tube.
75
x
3.6 Comparison of frictional pressure drop between smooth and microfin
tubes
76
3.7 Frictional pressure drop penalty factor 77
3.8 Effects of saturation temperature on Frictional pressure drop. 77
4.1 Experimental data of condensation heat transfer spread on modified
Baker two-phase flow pattern map (Scott, 1964)
81
4.2 Experimental data of condensation heat transfer overlaid on Taitel and
Dukler (1976) two-phase flow pattern map
81
4.3 Effects of mass flux and vapor quality on average heat transfer
coefficient: (a) Minichannel with fins; (b) Minichannel without fins
83
4.4 Effect of saturation temperature on average heat transfer coefficient; (a)
Minichannels with fins; (b) Minichannels without fins.
84
4.5 Comparison of average heat transfer coefficient between multiport
minichannels with and without fins: (a) G = 50 kg/m2s; (b) G = 100
kg/m2s; (c) G = 150 kg/m2s; (d) G = 200 kg/m2s.
86
4.6 Effects of mass flux and vapor quality on condensation heat transfer
coefficient in: (a) Microfins tube; (b) Smooth tube.
87
4.7 Condensation heat transfer coefficient of microfin tube compared with
condensation heat transfer coefficient of smooth tube.
88
4.8 Condensation heat transfer coefficient enhancement factor. 89
5.1 Comparison of frictional pressure drop with existing; (a) Homogeneous
Model; (b) Lockhart and Martinelli (1949) correlation; (c) Friedel (1979)
correlation; (d) Muller-Steinhagen and Heck (1986) correlation; (e)
Mishina and Hibiki (1996); (f) Wang et al. (1997); (g) Lee and Lee
(2001); (h) Koyama et al. (2003); (i) Lee and Mudawar (2005); (j)
Hwang and Kim correlation; (k) Sun and Mishima (2009); (l) Li and Wu
105
xi
(2010); (m) Zhang et al. (2010); (n) Kim and Mudawar (2012); and (o)
Jige et al. (2016) correlation.
5.2 Frictional pressure drop of the microfin tube compared with existing
correlations: (a) G = 50 kg/m2s; (b) G = 100 kg/m2s; (c) G = 200 kg/m2s
119
6.1 Comparison of experimental average heat transfer coefficient with
existing; a) Shah (1979); b) Haraguchi et al. (1994); c) Dobson and
Chato (1998); d) Wang et al. (2002); e) Koyama et al. (2003); f) Park et
al. (2011); g) Bohdal et al. (2012); h) Kim and Mudawar (2013); i) Jige
et al. (2016); and j) Shah (2016) correlation.
135
6.2 Condensation heat transfer coefficient of microfin tube compared with
existing correlations; (a) Carnavos (1980); (b) Cavallini et al. (1999); (c)
Kedzierski and Goncalves (1999); (d) Goto et al. (2003); (e) Koyama
and Yonemoto (2006).
143
7.1 Comparison of present experimental frictional pressure drop data with
proposed correlation
151
7.2 Validation of proposed frictional pressure drop correlation with available
experimental data collected from the open lituratures.
152
7.3 Comparison of experimental average heat transfer coefficient with
proposed correlations
154
7.4 Validation of proposed condensation heat transfer coefficient correlation
with available experimental data collected from the open literature.
155
xii
List of Tables
2.1 Tube charecteristics of multiport minichannels 54
2.2
2.3
2.4
Detail dimensions of the circular tube with and without microfins
Test conditions for condensation experiments
Test conditions for adiabatic experiments
56
57
57
2.5 Relationship between cC and c 60
3.1
4.1
Thermophysical properties of R134a (Lemmon et al. 2013)
Thermophysical properties of R134a (Lemmon et al. 2013)
71
85
5.1 Appropriate values of C for Lockhart and Martinelli correlation 96
5.2 Deviations of frictional pressure drop for multiport minichannels 113
5.3 Average errors and Mean absolute errors of frictional pressure drop of
microfin tube
118
6.1 Deviations of Heat transfer coefficients during condensation 134
6.2 Condensation heat transfer correlations for microfin tubes 139
6.3
7.1
Average errors and Mean absolute errors of condensation heat transfer
coefficient in microfin tube.
Two-phase frictional pressure drop data for proposed correlation
validation
142
153
7.2 Condensation heat transfer coefficient data for the proposed correlation
validation
156
xiii
Nomenclature
Aa Actual heat transfer area (m2)
An Nominal heat transfer area based on fin root diameter (m2)
Aaf
Anf
Actual flow area (m2)
Nominal flow area based on fin root diameter (m2)
Bo Bond number 2l v hg d
Cc coefficient of contraction
Cp
C
isobaric specific heat (J/kgK)
chisholm’s parameter
d
e
diameter (m)
fin height (m)
E enhancement factor
F heat transfer enhancement factor
Fr Froude number 2
2h
G
gd
f friction factor
G mass velocity (kg/m2s)
g gravitational acceleration (m/s2)
pw Wetted perimeter of tested tube (m)
h
h
h
enthalpy of refrigerant (J/kg)
enthalpy of cooling water (J/kg)
heat transfer coefficient (kW/m2K)
Nconf Confinement number
2h
l v
h
g
n
N
number of fins
number of data points
Nu Nusselt number h
l
hd
k
xiv
p pressure (Pa)
pr reduced pressure
P pressure drop (Pa)
Ph
Ga
phase change number ,p l R wi
lv
C T T
h
Galileo number 3 2
2h l
l
gd
Pr Prandtl number pC
k
Q Sensible heat gain or loss for the whole test section (J/s)
q heat transfer rate for the subsection (J/s)
q heat flux (W/m2)
Re Reynolds number hGd
Rel liquid Reynolds number (1 ) h
l
G x d
Relo liquid only flow Reynolds number h
l
Gd
Rev vapor Reynolds number h
v
Gxd
Revo vapor only flow Reynolds number h
v
Gd
Sulo liquid only flow Suratman number 2
2orl h lo
l lo
d Re
We
Suvo vapor only flow Suratman number2
2orv h vo
v vo
d Re
We
T temperature (°C)
T temperature difference (°C)
t fin tip thickness (m)
u velocity of the working fluid (m/s)
xv
u mean velocity (m/s)
We Weber number 2
h
v
G d
w
z
Width of the test section (m)
Test section wall thickness (m)
x
k
l
vapor quality
thermal conductivity (W/mK)
length of a subsection (m)
Xtt Lockhart-Martinelli parameter
0.5 0.10.91 v l
l v
x
x
z
Z
w
v
∆v
pressure drop measuring length (m)
effective heat transfer length (m)
distance between wall thermocouple (m)
specific volume (m3/kg)
specific volume difference between saturated vapor and liquid (m3/kg)
Greek letters
ξ void fraction
aspect ratio
ψ
apex angle of fin ( º )
helix angle ( º )
area ratio
angle (rad)
Φ two-phase frictional multiplier
geometry constant
HB
A
heat balance factor
Enlargement factor of surface area
surface tension (N/m)
μ dynamic viscosity (Pa s)
density (kg/m3)
shear stress (N/m2)
xvi
κ kinetic viscosity (m2/s)
Subscripts
a
al
A
A,F
A,S
adiabatic condition
aluminium
annular flow
annular with vapor shear stress
annular with surface tension
c abrupt contraction/coolant
cr
cu
Critical
copper
e abrupt expansion
eq equivalent
exp experimental
FC forced convective condensation term
F
GC
Frictional
gravity control convection term
h
HB
hydraulic diameter
heat balance
i inner
in inlet
l saturated liquid
lo
ll
lt
L
liquid-phase with total flow
laminar liquid-laminar vapor
laminar liquid-turbulent vapor
intermittent flow/lower side water flow
NC free convection condensation term
o outer
out outlet
pred predicted
R refrigerant
r
ref
reduced pressure
refrigerant
s subsection
xvii
sat saturation
tp
tt
tl
T
U
two-phase
turbulent liquid-turbulent vapor
turbulent liquid-laminar vapor
Total
upper side water flow
v
vo
saturated vapor
vapor-phase with total flow
w wall
wo outer wall surface of tested tube
wi inner wall surface of tested tube
1
CHAPTER 1
Introduction
Minichannels and small diameter microfin tubes for two-phase flow applications are
widely being used for the fabrication of compact and high performance heat
exchangers. Unlike single-phase flow system, two-phase flow system absorb far greater
amounts of heat by utilize the coolant’s combined sensible and latent heat. They are
very commonly used in air conditioning, refrigeration, automotive and heat pump
systems to improve the performance of that system. System performance enhancement
and charge of refrigerant reduction is decisive in the present day refrigeration, air
conditioning and heat pump systems.
Global warming is already underway with consequences that must be faced today as
well as tomorrow. Evidence of changes to the Earth's physical, chemical and biological
processes is now evident on every continent. The average temperature of Earth’s
atmosphere and oceans are rising due to the global warming. Since the early 20th
century, Earth's mean surface temperature has increased by about 0.8 °C, with about
two-thirds of the increase occurring since 1980 (America's Climate Choices, 2011).
According to the Intergovernmental Panel on Climate Change (IPCC) report, within the
21st century the global surface temperature is likely to rise a further 1.1 to 2.9 °C for
their lowest emissions scenario and 2.4 to 6.4 °C for their highest (Anowar Hossain,
2013, Forster et al., 2007). Therefore, the world will lose up to 39% of its land by 2100
because rising the sea level, if continue global warming (APA, University of
Wisconsin-Madison, 2007).
Air conditioning, refrigeration, automotive and heat pump sectors are prior
responsible for the man made global warming problem directly and indirectly. The
direct impacts are due to the emissions of high global warming potential refrigerants
emissions to the environment and the indirect impacts are for the greenhouse gas
emissions associated with the energy uses by those systems. Thus, the charge reduction
2
of refrigerant is very important in recent automotive, refrigeration, air conditioning and
heat pumping equipment to enhance the safety measure of flammable refrigerant and
meet the environmental concerns of using high global warming potential (GWP)
refrigerant.
Several previous study of different researchers found that the system performance
such as heat transfer is significantly empowered by either reducing the channel diameter
or employing finned tube. The use of the minichannels and small diameter microfins
tubes may imply a large reduction of the refrigerant charge of the system. Despite those
advantages, unfortunately, a higher pressure drop is obtained which may degrade the
overall efficiency of the two-phase system (Kim and Mudawar, 2012; Lopez-Belchi et
al., 2014).
The heat transfer during condensation and adiabatic frictional pressure drop for two-
phase flow system in minichannels and small diameter microfins tubes has been a
research subject for several decades. Many researchers extensively investigated two-
phase friction pressure drop and the heat transfer characteristics during condensation in
minichannels and small diameter microfins tubes experimentally and theoretically but
the information on two-phase pressure drop is still inadequate. The flow phenomena is
not clarified sufficiently yet.
Design engineers of compact and high performance heat exchangers in automotive,
refrigeration, air-conditioning and heat pump systems are facing problems to obtain
preliminary information on the heat transfer and pressure drop characteristics of two-
phase flow in minichannels and small diameter microfins tubes. Hence, the design of
the compact and high performance minichannels and microfins tube heat exchanger
essentially requires accurate predictive tools for pressure drop and heat transfer
prediction in two-phase flow.
The present study is a challenge to contribute better information and developed
prediction method of heat transfer and frictional pressure drop for the design of
compact and high performance heat exchanger.
1.1 Background
1.1.1 Minichannels
Minichannels are defined as flow passages that have hydraulic diameters in the range of
3
0.2 mm to 3 mm. The minichannel could be single or multiport as shown in Fig. 1.1 and
different in shape. There are more than 25 different geometries are studied by different
researchers (Shahsavari et al., 2012). A very few of the geometries are depicts in Fig.
1.2. The channel dimension and geometry has important effects on two-phase flow heat
transfer and pressure drop, which has been proved in a number of studies. Quite a few
classifications of channels have been proposed by different researchers based on
various criteria. Many of them have been discussed briefly by Cheng and Mewes
(2006). First definition was proposed by Shah (1986). He defined a compact heat
exchanger as an exchanger with a surface area density ratio >700 m2/m3. This limit
translates into a hydraulic diameter of <6 mm. According to this definition, the
distinction between small diameter channels and normal size channels is 6 mm.
Photo source: http://www.fcx.com
Photo source, Shabtay et al., 2014
Fig. 1.1 Examples of minichannels
4
Fig. 1.2 Cross-section of different geometry of minichannels
A most widely used classification is proposed by Kandlikar (2002) and Kandlikar and
Grande (2003) according to which:
Conventional or macro channels: dh > 3 mm
Minichannels: 3mm ≥ dh > 200 µm
Microchannels: 200 µm ≥ dh > 10 µm
Transitional channels: 10 µm ≥ dh > 1 µm
Molecular Nanochannels: 0.1 µm ≥ dh
This classification was developed mainly based on the flow of gases. They also
recommended it for both liquid as well as two-phase flow application such as boiling
and condensation flow application to provide uniformity in the channel classification.
Mehendail et al. (2000) proposed the classification of small channel dimensions in
terms of hydraulic diameter as:
Conventional or macro channels: dh > 6 mm
Compact passage channels: dh =1-6 mm
Meso channels: dh = 0.1-1 mm
Microchannels: dh = 1-100 µm
This classification is based simply on the dimensions of the channels. Although, this
classification has some acceptance.
Cheng and Wu (2006) provided a classification based on an analysis considering the
magnitude of gravity and surface tension effects as:
Star-shap Rhombus Circle Polygon Ellipse Tringle
Rectangle withround corners
Trapezoidal Square Rectangle Semi-circle Diamond
5
Conventional or macrochannels: Bo > 3.0 (Surface tension is small in compared
to gravitational force).
Minichannels: 0.05 < Bo < 3.0 (surface tension effect becomes dominant and
gravitational effect is small)
Microchannel: Bo < 0.05 (gravity effect is negligible)
Later on, Ghiaasiaan (2008) mention another classification as:
Conventional channels: dh ≥ 3 mm
Minichannels: 100 µmm ≤ dh ≤ 1000 µm
Microchannels: 10 µm ≤ dh ≤ 100 µm
This classification is also mainly based on the channels diameter and it does not
consider the effects of fluid properties.
Minichannels offers the following advantages over conventional tubes:
High thermal efficiency
Reduced pressure drop
Low refrigerant charge
Good surface temperature uniformity
Light weight
Low cost (material saving potential)
Effectiveness and compactness
Due to the above mentioned advantages, two-phase flow minichannel have gained
unprecedented popularity in many modern technologies demanding the removal of
highly concentrated heat loads from small surface areas. In recent day, minichannels in
two-phase flow has become increasingly important in many applications such as:
Industrial and automobile air conditioning, refrigeration and heat pump system
Compact heat exchanger
Biomedical instrumentation
Water cooled turbine blades
Computer data centers
Rocket nozzle cooling
Fusion reactor blanket cooling
Avionics cooling
Cooling of satellite electronics
6
Cooling of hybrid vehicle
Power electronics
Heat exchangers for hydrogen storage systems
Fig. 1.3 Examples of applications of minichannels cooling (Kim and Mudawar, 2014)
Those applications are also depicts in Fig. 1.3 collected from Kim and Mudawar, 2014.
From a practical standpoint, minichannel cooling and heating has shown great
7
versatility in design and construction, including isolated tubes, tubes that are soldered
upon a heat dissipating surface and channels that are formed into a conducting
substrate. There is also the added flexibility in minichannel shape, including circular,
rectangular, triangular, trapezoidal, diamond cross sections and so on as shown in Fig.
1.2 (Kim and Mudawar, 2014).
1.1.2 Microfins tube
Improved thermal performance of heat exchanger by enhancement technique has
become more popular and standard practices nowadays. The enhancement technique
can significantly improve the thermal efficiency of the heat exchange systems as well as
the economics of their design and operation. Generally, enhancement techniques can be
divided into two groups: namely, (1) active and (2) passive techniques. The active
techniques require external forces such as electric field, acoustic or surface vibration
whereas the passive techniques require special surface geometries such as rough surface
or extended surface etc. If two or more of these techniques are utilized together to
achieve enhancement, the term is called as compound enhancement. Both techniques
have been used by researchers for 140 years to increase heat transfer rates in heat
exchangers (Dalkilic and Wongwises, 2009). Bergeles have been identified several
enhancement techniques (Bejan & Kraus, 2003) which are given in below and their
brief description can be found in (Bejan & Kraus, 2003).
(1) Passive enhancement techniques:
Treated surfaces
Rough surfaces
Extended surfaces
Displaced enhancement devices
Swirl flow devices
Coiled tubes
Surface tension devices
Additives for liquids
Additives for gases
(2) Active enhancement techniques:
Mechanical aids
Surface vibration
8
Fluid vibration
Electrostatic fields
Injection
Suction
Jet impingement
Among the above mentioned heat transfer enhancement techniques, extended or
finned surface are perhaps the most widely used and researched enhancement technique
(Afroz, 2008). Microfin tubes are the best example of extended surface enhancement
techniques that have recently been used intensively because of their high condensation
heat transfer performance and low pressure drop.
The microfin on an internal wall surface of the tube is called microfin tube as depict
in Fig. 1.4. The microfin tube was first developed by Fujie et al. (1977) of Hitachi
Cable Ltd. As mentioned by Kim (2016). The microfin tubes have received special
attention as they significantly empowered the heat transfer coefficient with relatively
low pressure drop increases in commercial refrigeration and air conditioning
applications since the 1980s. Microfins improve the heat transfer in both two-phase and
single-phase applications, and are one of the most efficient and common heat transfer
enhancement mechanism for the heat exchangers due to their superior heat transfer
performance. The heat transfer performance of the tubes is increased in an effective
manner by the presence of the microfins on the internal wall surface of the horizontal
tubes (Dalkilic and Wongwises, 2009). The heat transfer enhancements are mainly
caused by the increase in the surface heat transfer area, surface tension effect on the
condensate drainage and induced turbulence by microfin. The refrigeration, air
conditioning and heat pumps industry is developing very compact machinery, and this
requires the use of heat exchangers with enhanced surfaces. Air cooled condensers for
refrigeration and heat pumps are manufactured with enhanced surfaces both on the
external and on the refrigerant side (Cavallini et al., 2000).
The microfin tubes are typically made of copper as it offers several advantages such as:
cost effective fabrication and assembly
Smaller size, less weight and lower material costs
Higher heat transfer coefficients
Naturally corrosion resistant metal
9
Environmentally friendly
Well suited for new refrigerants
Mechanical strength is high enough.
Fig. 1.4 Microfin tube (Photo Ref. http://www.wieland-industrierohre.de/)
Fig 1.5 Characteristic geometrical parameters of inside microfin tube (Cavallini et al.,
2000)
Typical microfin tubes available for industrial applications have an outside diameter
from 4 to 15 mm, a single set of 50-70 spiral fins with spiral angle from 6 to 30 0, fin
Fin
tip
dia
met
er (
d)
Spiral angle
Fin height
Apex angle
10
height from 0.1 to 0.25 mm, triangular or trapezoidal fin shapes with an apex angle
from 25 to 90 0 (Cavallini et al., 2000). The characteristic geometrical parameters of
microfin tubes are shown in Fig. 1.5.
A variety types of microfin tube based on the fin geometry studied by different
researchers since at the end of 1970s. The common and commercially available
microfin tubes include (Fig. 1.6-1.7):
Helical or spiral or axial grooved microfin tube
Cross-grooved microfin tube
Herringbone microfin tube
Different studies of several researchers on the microfin tubes show a heat transfer
enhancement compared to equivalent smooth tubes from 80 to 200% and over, with an
increasing pressure drop from 20 to 80% (Cavallini et al., 1999; Miyara et al., 2000; Yu
and Koyama, 1998; Kedziersky and Goncalves, 1999; Cavallini et al., 2000)
Fig. 1.6 Shabtay microfin tube (Shabtay et al., 2014)
11
Fig. 1.7 Examples of different microfin tube (Cavallini et al., 2000, 2003)
1.1.3 Two-phase Flow regimes (Flow pattern)
Flow regimes are among the most intriguing, challenging and difficult aspects of
two-phase flow and have been investigated over many decades. Two-phase flow can
form a variety of morphological flow configuration. Flow regimes are extremely
important as it strongly influence the heat and momentum transfer processes. According
to Ghiaasiaan (2008), some of the physical factors that lead to morphological variations
include the following:
The density difference between the phases; as a result the two phases respond
differently to forces such as gravity and centrifugal force;
Helical microfin tube
Cross-grooved microfin tube
Helical microfin tube Herringbone microfin tube
12
The deformability of the gas–liquid interphase that often results in incessant
coalescence and breakup processes; and
Surface tension forces, which tends to maintain one-phase dispersal.
Flow regimes and their ranges of occurrence are thus sensitive to fluid properties,
system configuration/and orientation, size scale of the system, occurrence of phase
change, and so on. Heat transfer coefficient and pressure drops are closely related to the
local two-phase flow structure of the fluid and thus two-phase flow pattern prediction is
an important aspect of modeling evaporation and condensation (Thome, 2006). To
predict heat transfer and pressure drop, it is important for designers to identify what
flow pattern exists at the local flow condition. Fig. 1.8 shows a schematic representation
of flow regimes and heat transfer coefficient variation in a horizontal minichannels
heated by a uniform heat flux.
Fig. 1.8 Schematics of flow patterns and variation of heat transfer coefficient in
minichannels with uniform circumferential heat flux (Kim and Mudawar, 2014).
In two-phase flow, different flow patterns are established at different regions of
the minichannels as the fluid undergoes a transition from vapor to liquid along the
length of the tube. Several studies already observed that the flow patterns of
minichannels are different from those observed in conventional tube due to the different
relative magnitudes of gravity, shear and surface tension forces. Those forces determine
the particular flow regime established by a given combination of liquid and gas phase
13
velocities (Coleman and Garimella, (1999, 2003)). With an order of magnitude
reduction in the channel diameter from conventional to minichannel and minichannel to
microchannel, significant changes in the two phase flow characteristics are expected.
The flow in minichannels results in the appearance of different flow regimes and some
of the flow regimes transition boundaries are also shifted. In minichannels, the
gravitational effect is insignificant so that the channel orientation no longer has a
significant effect on the two phase flow regimes (Kawahara et al., 2002). Flow regimes
in minichannels are controlled mainly by surface tension and inertia or vapor shear
forces. Based on the relative importance of the surface tension over vapor shear forces,
three overall flow regimes were identified by Shao et al., 2009, namely surface tension
dominated, vapor shear forces dominated and transitional regimes. The surface tension
forces dominate at low flow velocities corresponding to bubbly and intermittent (also
known as Taylor, segmented, slug, plug or elongated flow) flow and vapor shear forces
dominate at high velocities corresponding to annular flow.
There are many authors observed the existence of flow patterns in minichannels
(Suo and Griffith, 1964, Shao et al., 2009, Kawahara et al., 2002, Satitchaicharoen and
Wongwises, 2004, Rebrov, 2010, Coleman and Garimella, 1999, Coleman and
Garimella, 2003, Serizawa et al., 2002, Xu et al., 1999, Yang and Shieh, 2001, Zhao et
al., 2004). Most of the researchers were observed different flow patterns in horizontal
minichannel namely, bubbly flow, intermittent flow, annular flow and dispersed flow.
Bubbly flow: bubbly flow is characterized by distinct bubbles and sometimes non-
spherical bubbles of the equivalent diameter smaller than the channel diameter. Bubbly
flow is usually occurs in relatively small gas superficial velocity. Bubbles are separated
from the walls of the channel with the film of the liquid and have a wide scatter in size.
Intermittent flow: The intermittent flow is characterized by discontinuities in the
gas and liquid flow for further increasing the gas velocity. Due to further increasing the
gas velocity, the interfacial waves become large enough to wash the top of the tube.
Large amplitude waves often contain entrained bubbles. The top wall is nearly
continuously wetted by the large amplitude waves and the thin liquid films left behind
(Thome, 2006). The intermittent flow regime composite of the slug and plug flow
regimes. In plug flow, the flow regime has liquid plugs that are separated by elongated
gas bubbles. The diameters of the elongated bubbles are smaller than the tube such that
the liquid phase is continuous along the bottom of the tube below the elongated
bubbles. In slug flow, at higher gas velocities, the diameters of elongated bubbles
14
become similar in size to the channel height. The liquid slugs separating such elongated
bubbles can also be described as large amplitude waves (Thome, 2006).
Annular flow: When the mass flow rate is high enough, the condensate forms a
continuous annular film around the inside of the tube walls, almost similar to that in
vertical flow but the condensate film is thicker at the bottom than the top. The interface
between the liquid annulus and the vapor core is distributed by small amplitude waves
and droplets may be dispersed in the gas core (Thome, 2006). A significant portion of
most condensers operate in this flow regime.
Dispersed flow: with further increase of liquid superficial velocity or when the
liquid flow is turbulent and the gas phase is in either laminar flow or turbulent flow, all
the liquid may be stripped from the wall and entrained as smalled droplets in the gas
core to form the dispersed pattern. In most cases the liquid film is left in contact with
the wall (Shao et al., 2009).
1.1.4 Two-phase flow mapping
Flow pattern maps are the most widely used predictive tools for two-phase flow
pattern. A flow pattern map is used to predict the local flow pattern in a tube. The flow
pattern map is a graphical presentation that displays the transition boundaries between
the flow patterns. It is typically plotted on two-dimensional maps with coordinates
using dimensionless parameters to represent the liquid and gas velocities. The flow
pattern maps for wide variety of scales, geometric configurations, orientations and
properties are available in open literature. Baker (1954), Scott (1963), Mandhane et al.
(1974), Wambsganss et al. (1991), Kattan et el. (1998a,b,c), Xu (1999), Xu et al.
(1999), Coleman and Garimella (1999, 2003), Yang and Shieh (2001), Ould Didi et al.
(2002), Zurcher et al. (2002a,b), Thome et al. (2003), El Hajal et al. (2003), Zhao et al.
(2004), Wojtan et al. (2005a,b) and Shao et al. (2009) have all described the importance
of using flow pattern information in the determination of accurate two-phase flow
models. There are three main types of two-phase flow maps in the literature:
Baker/Mandhane type, Taitel-Dukler type, and Steiner type (Hossain, 2013). Baker
(1954) developed one of the first two-phase flow regime maps with air-water and air-oil
data in large tubes. Baker (1954) used superficial vapor mass flux times a fluid property
scaling factor on the vertical axes and superficial liquid mass flux times a different fluid
15
property scaling factor on the horizontal axis. Mandhane et al. (1974) later developed a
similar map with huge database of 5935 air water data, but used superficial gas and
liquid velocities on the horizontal and vertical axes respectively. Dobson and Chato
(1998) then made modifications to the flow map of Mandhane et al. (1974) by
multiplying the axis by the square root of the vapor to air density ratio. They observed
flow regimes with R134a, R22 and nearly azeotropic mixtures of R32/R125 condensing
inside tubes having 3.1 mm, 4.6 mm and 7.1 mm inside diameter. Taitel-Dukler (1976)
developed a mechanistic type flow map with the Lockhart- Martinelli parameter on the
horizontal axis and a modified Froude rate times a transition criteria on the vertical axis.
For typical heat exchangers, Wojtan et al. (2005a) proposed a modification of the
Kattan et al. (1998a) map, which itself is a modified Steiner (1993) map, and included
a method for predicting the onset of dry out at the top of the tube in evaporating flows.
Most of the recent two-phase flow regime maps found in the literature is Steiner
(1993) type flow maps. Ould Didi et al. (2002), Coleman and Garimella (2003), El
Hajal et al. (2003) and Wojtan et al. (2005) all use similar Steiner (1993) style flow
maps with quality on the horizontal axis and mass flux on the vertical axis. In this
research work, three well-known flow pattern maps namely, modified Baker (Scott,
1963) and Taitel-Dukler (1976) are used for plotting and visualize the experimental
data.
1.2 Literature review
1.2.1 Condensation heat transfer in minichannels
Heat transfer characteristics in single or multiport minichannels during
condensation have been strongly researched in the last fifty years. The heat transfer
characteristics in minichannles are different from those of conventional tubes. In
conventional channels, the heat transfer is dominated by vapor shear stress and
gravitational forces but in minichannels, gravitational forces are negligible. Instead of
them, surface tensions play an important role. However, several researchers extensively
investigated the condensation heat transfer characteristics in single and multiport tubes
with different shaped minichannels experimentally and theoretically in the last decade.
The available studies on heat transfer characteristics in minichannels during
condensation are summarized below:
16
Thome et al. (2003) developed a new flow pattern based model for condensation
heat transfer in the horizontal tube of diameter ranging from 3.1 to 21.4 mm based on
simplified flow structures of the flow regimes and also considered the effect of liquid-
vapor interfacial roughness. The model predicted experimental database, contained
4621 data points from 15 fluids of different flow regimes reasonably.
Koyama et al. (2003a, b) experimentally measured the condensation heat transfer
coefficients of R134a in two multiport tubes having eight channels and nineteen
channels with 1.1 mm and 0.8 mm hydraulic diameters at the saturation temperature 60
C. They proposed a correlation for heat transfer coefficient by combining convective
and film condensation term based on the same functional form as the correlation of
Haraguchi et al. (1994). The author also concluded that the heat transfer enhancement
effect of micro-fins is mainly due to the enlargement of heat transfer area.
Agarwal et al., (2010) carried out experiments of HFC134a condensation heat
transfer in six non-circular horizontal multiport tubes whose hydraulic diameter ranged
from 0.424 to 0.839 mm. The channels included barrel-shaped, N-shaped, rectangular,
square, triangular extruded tubes, and a channel with a W-shaped corrugated insert that
yielded triangular minichannels. They developed correlation for heat transfer during
condensation in horizontal non-circular minichannels and suggested to use annular flow
based model for square, barrel-shaped and rectangular channels, while the mist-flow
based model for channels with sharp corners.
Goss and Passos (2013) experimentally studied the convective condensation of
R134a inside eight horizontal and parallel tubes of 0.77 mm diameter. Their results
show that mass velocity and vapor quality have an important influence on the heat
transfer coefficient. The consideration that all of the resistance to heat transfer is due to
the conduction through the liquid film is a good approximation, mainly for xv < 0.95.
Kim et al. (2003) performed an experimental investigation of condensation heat
transfer in a smooth multiport minichannel with 1.56 mm hydraulic diameter and in a
microfin multiport minichannel with 1.41 mm hydraulic diameter using R410A and
R22 as working fluids. Results showed that the effect of surface drainage on the fin
surface is more pronounced for R22 than R410A because of smaller Weber umber. In
addition, they modified Yang and Webb (1997) correlation to predict microfins tube
data adequately.
Wang et al. (2002) investigated the condensation heat transfer and flow regime
17
measurements of R134a in a rectangular multiport minichannel with a hydraulic
diameter of 1.46 mm. Existing correlations were failed to predict their experimental
data. The author developed a correlation by weighting the regime-specific correlations
with an annular flow length fraction to account for the effect of flow regime transitions
over a range of condenser flow conditions.
Wang and Rose (2005, 2006) theoretically investigated the film condensation heat
transfer from a vapor flowing in horizontal non-circular minichannel. They developed a
theoretical model based on fundamental analysis which assumes laminar condensate
flow on the channel walls and takes account of the effects of the interfacial shear stress,
surface tension, and gravity. The author presented results for fluids of R134a, R22, and
R410A in square and triangular section minichannels in the range of hydraulic diameter
0.5-5 mm.
Yang and Webb (1997) proposed a semi empirical model by considering the effects
of vapor share and surface tension forces to predict the condensation heat transfer inside
multiport minichannel having microgrooves. At low mass velocity, surface tension
force is effective in enhancing the condensation heat transfer as long as the fin tips are
not flooded by condensate. The surface tension effect is strongly depends on the fin
geometry. The flow is vapor share controlled and contribution of surface tension is very
small at high mass velocity.
Park and Hrnjak (2009) investigated the CO2 flow condensation heat transfer in
multiport tubes of 0.89 mm hydraulic diameter at low temperature. They were measured
at mass velocity from 200 to 800 kg/m2s, saturation temperature of -15 and -25 0C, and
wall sub-cooling temperature from 2 to 4 0C. The author observed that the measured
heat transfer coefficient increased with the increase of mass fluxes and vapor qualities,
whereas it is almost independent of wall sub-cooling.
Yang and Webb (1996) conducted experiments of condensation heat transfer using
R12 in a flat extruded aluminum plain tube of hydraulic diameter 2.63 mm and microfin
tube of hydraulic diameter of 1.56 mm. The condensation heat transfer coefficient in
both plain and microfin tubes increases with increasing heat flux. The authors propose
that the heat transfer coefficients in a microfin tube are slightly greater than that of plain
tubes due to the surface tension drainage force becomes effective and provide additional
enhancement, which is apparently additive to the effect caused by vapor shear. This
effect is not so strong at high mass velocity.
Sakamatapan et al., (2013) conducted experiments of condensation heat transfer
18
characteristics of R134a in multiport minichannels have fourteen channels with a 1.1
mm hydraulic diameter and eight channels with a 1.2 mm hydraulic diameter. Results
showed that the heat transfer coefficient increased with the increase of heat flux, mass
flux and vapor quality but decreased as saturation temperature increases. They found
that when the hydraulic diameter is decreased; the heat transfer coefficients increased
up to 15%.
Kim and Mudawar (2013) proposed a new universal approach to predict the
condensation heat transfer coefficient for predominantly annular flows, and slug and
bubbly flows in mini/microchannels. The proposed approach is capable of tackling
many fluids with different thermophysical properties, flow parameters and broad ranges
of all geometry with hydraulic diameter from 0.424 to 6.22 mm. The author amassed a
consolidated database consisting of 4045 condensation data points from 28 sources for
mini/microchannels. The data points consists of 1964 data points for single channel
from 17 sources and 2081 data points for multiport channel from 13 sources includes 17
different working fluids.
Derby et al. (2012) experimentally measured the condensation heat transfer
coefficients of R134a in 1 mm square, triangular and semi-circular multiport
minichannels with smaller measurement uncertainties. The author concluded that the
mass flux and vapor quality had significant effects on condensation process but
saturation temperature, heat flux and channel shape had no significant effects.
Illan-Gomez et al., (2015) investigated the flow condensation heat transfer
coefficients of R1234yf and R134a in a minichannel multiport tube of 1.16 mm
hydraulic diameter. The test were conducted over a range of mass flux 350 to 940
kg/m2s and saturation temperature range of 30 to 55 0C. Test results showed that the
thermal conductivity, density ratio and viscosity ratio are playing an important role in
the variation of the heat transfer coefficient. The refrigerant R134a has shown higher
heat transfer coefficient than its potential substitute refrigerant R1234yf. The variation
of saturation temperature and mass flux produces similar effects in both refrigerants.
Cavallini et al. (2005) investigated the pressure drop and condensation heat transfer
characteristics of R134a and R410A in a multiport minichannel with 1.4 mm hydraulic
diameter. They have been compared their data against models available in the literature.
All of the existing models were failed to predict the experimental heat transfer
coefficient at high values of mass velocity and high values of the dimensionless gas
velocity.
19
Cavallini et al. (2006) reviewed experimental works on condensation flow regimes;
heat transfer and pressure drop in minichannels of different cross-section geometries
with hydraulic diameters ranging from 0.4 to 3 mm. They compared the available
experimental data for high pressure refrigerant (R410A), medium pressure refrigerant
(R134a) and low pressure refrigerant (R236ea) with semi-empirical and theoretical
models developed for conventional and minichannels. Based on the review and
experimental data, they discussed and evaluated opportunity for a new heat transfer
model for condensation in minichannels. In the new model, they considered the effects
of the entrainment rate of droplets from the liquid film.
Cavallini et al. (2011) reported an experimental data for condensation heat transfer
and adiabatic frictional pressure drop of the refrigerants R32 and R245fa in a single
circular minichannel of inside diameter 0.96 mm. The author’s compared the
experimental heat transfer data with predicting models to provide a guideline for design
of minichannel condenser. They concluded that most of the experimental data points of
condensation heat transfer coefficient were shear stress dominated.
Del Col et al. (2010) experimentally measured the local heat transfer coefficients
during condensation of R1234yf and R134a in a single circular minichannel of 0.96 mm
inside diameter. The refrigerant R1234yf displayed lower heat transfer coefficients that
R134a at the same operation conditions.
Shah (2016a) presented a correlation for heat transfer during condensation in
horizontal single and multiport mini/microchannels of many shapes with hydraulic
diameter from 0.10 to 2.8 mm. They collected 1017 data points from 31 source
covering 13 fluids. The author suggested a simple new boundary between conventional
channels and minichannels for condensation heat transfer.
Shah (2016b) proposed two alternative comprehensive correlations for heat transfer
during condensation in plain conventional channels and micro/minichannels in all
orientations. Both correlations were developed by modifying the Shah (2009)
correlation. They have been validated both the correlations with a database contained
4063 data points collected from 67 source that includes 33 fluids, diameters 0.10 to 49.0
mm, various shapes and all orientations.
Zhang et al. (2012) experimentally investigated condensation heat transfer and
pressure drop of R22, R410A and R407C in two single round tubes with inner diameter
of 1.088 mm and 1.289 mm. The results indicated that condensation heat transfer
coefficients increase with mass flux and vapor quality, increasing faster in the high
20
vapor quality region. They compared the experimental data with the correlations for
large diameter tubes and minichannels. Almost all of the correlations for large diameter
tubes overestimated the experimental data. The correlations for minichannels showed
better prediction but still had large discrepancy.
Lui et al. (2013) conducted experimental measurements of condensation heat
transfer and pressure drop of R152a in circular and square minichannel with hydraulic
diameters of 1.152 mm and 0.952 mm, respectively. The results showed that the
condensation heat transfer and pressure drop increase with mass flux and vapor quality
while decrease with the saturation temperature in both tubes. The author observed that
the square minichannel showed higher heat transfer coefficient than the circular
minichannel due to the effect of surface tension.
Zhang et al. (2015) presented a comprehensive review of correlations for heat
transfer during condensation in horizontal conventional tube and minichannels. They
compiled a database containing 2563 data points of condensation heat transfer,
including 1462 data points for conventional tube and 1101 for minichannels from 26
sources covering 17 working fluids. Total 28 correlations including 7 correlations for
minichannels were evaluated using compiled database. The evaluation results indicated
that more attention is needed to improve the prediction method for minichannels.
Zhang et al (2016) numerically investigated the heat transfer and pressure drop
characteristics during condensation for R410A in minichannels with hydraulic
diameters of 0.25, 1, and 4 mm, respectively at different saturation temperatures. The
results indicated that the heat transfer coefficients and pressure drop increase with
increasing mass flux and vapor quality and decreasing with tube diameter and saturation
temperature. The shear dominated flow regime was observed at higher mass flux, vapor
quality and in smaller diameter tube. Further, the author proposed a new correlation
based on numerical simulation.
Heo et al. (2013) investigated the in-tube condensation heat transfer characteristics
of CO2 in three different rectangular minichannels of hydraulic diameters 1.5, 0.78 and
0.68 mm having 7, 23 and 19 numbers of ports, respectively. The author’s found that
the condensation heat transfer coefficients increased with the decrease in hydraulic
diameter. Increasing and decreasing the heat transfer coefficient at critical vapor quality
was also observed in minichannel of hydraulic diameter 0.78 mm. The existing models
for the prediction of heat transfer coefficients over predicted the experimental data
except Thome et al. (2003) model.
21
Oh and Son (2011) carried out experimental study on the condensation heat transfer
of R22, R134a and R410A in a single circular horizontal copper minichannel of 1.77
mm inner diameter. The results showed that the condensation heat transfer coefficient
of R410A was higher than that of R22 and R134a at the same test condition. Most of
the existing correlations whose were proposed for conventional tube and minichannels
failed to predict their experimental data reasonably.
Huai and Koyama (2004) experimentally studied the local characteristics of heat
transfer and pressure drop of CO2 during condensation in a multiport extruded
aluminum minichannel with 1.31 mm equivalent diameter having 10 circular channels.
The results indicated that the heat transfer coefficient in the two-phase region is higher
than that in the single-phase and mass flux has significant effect on condensation heat
transfer characteristics. During the comparison of experimental data with previous
existing correlations, the authors were observed large discrepancies.
Shin and Kim (2004) developed a new experimental technique to measure the
condensation heat transfer and pressure drop of R134a in a horizontal single round
minichannel with an inner diameter of 0.691 mm. The authors concluded that the
condensation heat transfer increased with the refrigerant quality as expected except for
low mass fluxes. The comparisons of experimental data with existing heat transfer
coefficient revel that all of the correlations failed to predict the experimental data
reasonably.
Shin and Kim (2005) presented an experimental study of condensation heat transfer
characteristics of R134a in horizontal single circular minichannels (d =0.493, 0.691,
and 1.067 mm) and rectangular minichannels (dh =0.494, 0.658, and 0.972 mm). The
tests were conducted over a mass flux range of 100-600 kg/m2s, a heat flux range of 5-
20 kW/m2, and at saturation temperature of 40 0C. The heat flux was shown
insignificant effects on heat transfer coefficient and pressure drop. A clear
enhancement of heat transfer coefficients was observed as the hydraulic diameter
decreased. All of the existing correlations failed to predict the experimental data.
Jige et al. (2016) performed the experimental study of condensation heat transfer
characteristics of refrigerants R134a, R32, R1234ze (E), and R410A in a horizontal
rectangular multiport minichannel of hydraulic diameter 0.85 mm. The tests were
performed for mass flux from 100 to 400 kg/m2s and a saturation temperature from 40
to 60 0C. The author clarified the effects of mass velocity, vapor quality, saturation
temperature, refrigerant properties and hydraulic diameter of a rectangular channel on
22
condensation. The authors concluded that the effects of the vapor shear stress and
surface tension on the condensation heat transfer surpass the gravity effect with
decreasing channel size. Particularly, in the case of low mass velocity, the condensate
film is attracted to the corners of the cross sectional area in the rectangular
minichannels because of the effect of the surface tension. Therefore, the condensate
film is kept thin between the corners for comparatively low vapor quality. The authors
also proposed a model for condensation heat transfer in rectangular minichannels
considering the flow patterns and effects of vapor shear and surface tension.
Recently, Rahman et al. (2017) reported an experimental study of condensation heat
transfer of R134a in horizontal rectangular multiport minichannel with and without fins
having 20 channels with hydraulic diameters of 0.64 and 0.81 mm, respectively. The
measurements were done over a mass flux range from 50-200 kg/m2s and at saturation
temperature of 30 and 35 0C, respectively. The authors found that the condensation heat
transfer coefficient of R134a tended to increases with increasing mass flux and vapor
quality in both minichannels with and without fin. The heat transfer coefficient is
increases faster at higher vapor quality. The saturation temperature has significant
influence on heat transfer coefficient which decreases with increasing the saturation
temperature. The heat transfer coefficient of rectangular multiport minichannel with
fins was approximately 10-39% higher than those of rectangular multiport minichannel
without fin for the same operating conditions due to the surface tension force. They
compared their experimental data with ten well known correlations that were developed
for the conventional tube, minichannels and microchannels. All of the existing
correlations were failed to capture the experimental heat transfer coefficient data within
a high degree of accuracy. In addition, the author proposed a new correlation to predict
the experimental data. The proposed correlation agreed well with the experimental data
with mean average error 17.4%.
1.2.2 Two-phase pressure drop in minichannels
In the last seventy years, much experimental and analytical research were devoted
to measuring the two-phase frictional pressure drop in small diameter tubes and
minichannels of circular or rectangular geometry with single or multiport channels
configurations. Very few of them will be reviewed here.
Yang and Webb (1996) measured an adiabatic single-phase and two-phase pressure
23
drop of R12 flowing in 1.56 and 2.64 mm hydraulic diameters extruded aluminum with
and without fin tube, respectively. The frictional pressure gradient of tube with fin was
higher than that of the tube without fin at same test conditions. Their works showed that
the pressure drop is dominated by vapor shear in both tube with and without fins. The
author also developed the pressure drop correlation on the basis of equivalent mass
velocity concept according to Akers et al. (1959).
Revellin and Thome (2007) experimentally measured an adiabatic two-phase
frictional pressure drop of R134a and R245fa in two sizes of circular minichannels
having inner diameters of 0.509 mm and 0.790 mm. Similar to the classic Moody
diagram in single-phase flow, they distinguished three different zones for laminar,
transition and turbulent flow. Only the turbulent zone was best predicted by the Muller-
Steinhagen and Heck (1986) correlation. They also proposed a new homogeneous two-
phase frictional pressure drop model for a limited range of application.
Koyama et al. (2003) investigated the pressure drop characteristics of R134a in four
types of multiport minichannel tubes. They found that the Friedel (1979) correlation
was able to predict well their data, except at low mass velocity. They also developed a
new model for frictional pressure drop based on the Mishima and Hibiki
(1996) correlation.
Zhang and Webb (2001) measured adiabatic two-phase flow pressure drops for R-
134a, R-22 and R-404a flowing in a multi-port extruded aluminum tube with a
hydraulic diameter of 2.13 mm, and in two copper tubes having inside diameters of 6.25
and 3.25 mm, respectively. They found that the Friedel correlation did not predict the
two-phase data accurately, especially for high reduced pressure. Using the data taken in
their present and in a previous study, a new correlation for two-phase friction pressure
drop in small tubes was developed by modifying the Friedel correlation.
Tran et al. (2000) carried out an experimental study of two-phase flow pressure drop
of R134a, R12 and R113 at six different pressures in two round tube (2.46 mm and 2.92
mm inside diameter) and one rectangular channel (2.40 mm hydraulic diameter). The
data were compared with the large-tube correlations but all of the correlations were
failed to predict the experimental data.
Li and Wu (2010, 2011) collected the experimental data of adiabatic two phase
pressure drop in micro/minichannels for both single and multiport channel
configurations covering 12 fluids for a wide range of operational conditions and
channel dimensions. Based on the whole database, the Bond number and the Reynolds
24
number were introduced to modify the Chisholm parameter to develop a new generalize
correlation for the two-phase pressure drop. To indicate the relative importance of
surface tension, a particular trend was observed with the Bond number that
distinguished the entire database into three ranges.
Lee and Lee (2001) presented an experimental study of two-phase pressure drop of
water and air through horizontal rectangular channels having hydraulic diameter 0.78
mm, 1.91 mm, 3.64 mm and 6.67 mm, respectively. The authors found that the pressure
drop increased with increase in superficial velocities of the liquid and gas but decrease
with hydraulic diameter. They expressed the two-phase frictional multiplier using the
Lockhart-Martinelli type correlation with the modification on parameter C considering
the effects of mass flux and channel dimension.
Agarwal and Garimella (2009) measured the pressure drop and presented a multiple
flow-regime model during condensation of refrigerant R134a in horizontal minichannel.
Condensation pressure drop were measured in two circular and six noncircular channels
having hydraulic diameter from 0.42 mm to 0.8 mm.
Cavallini et al. (2005) experimentally studied the frictional pressure drop
characteristics in multiport minichannel of hydraulic diameter 1.4 mm during adiabatic
two-phase flow of R134a, R236ea and R410A. In their study, R410A presents a
significantly lower pressure drop in comparison with R134a and R236ea at the same
operating conditions. The low pressure fluid R236ea shows the highest pressure
gradient among the three fluids. The experimental data were compared against several
models available in the literature, finding that the correlations by Friedel et al., Zhang
and Webb, Mishima and Hibiki, and Mueller-Steinhagen and Heck are in good
agreement with the R134a experimental data. All of the correlations were failed to
predict the R410A data. The R236ea data are in good agreement with the predictions by
Mueller-Steinhagen & Heck (1986).
Cavallini et al. (2009) presented a model for calculation of the frictional pressure
gradient during condensation or adiabatic liquid-gas flow inside minichannels with
different surface roughness. The researchers used new experimental frictional pressure
gradient data associated to single-phase flow and adiabatic two-phase flow of R134a
inside a single horizontal mini tube with rough wall in their modelling to account for
the effects of surface roughness. It was a Friedel based model and it took into account
fluid properties, tube diameter, mass flux, vapor quality, reduced pressure, entrainment
ratio and surface roughness. With respect to the flow pattern prediction capability, they
25
built for shear dominated flow regimes inside pipes, thus, annular, annular-mist and
mist flow were here predicted. However, they extended the suggested procedure to the
intermittent flow in minichannels and applied it also with success to horizontal macro
tubes.
Bohdal et al. (2012) performed the experimental investigation of condensation
pressure drop of R134a, R404a and R407C refrigerants in circular minichannels with
internal diameter 0.31-3.30 mm. They found that the pressure drop in a two-phase flow
during condensation of refrigerants depends on the refrigerant type, process parameters
and the structure of two-phase flow. The authors compared the experimental results
with the correlations proposed by other researcher. Based on the experimental results,
the authors developed a new correlation for the calculation of the local value of the
frictional pressure drop in the range of two-phase flow structures.
Zhang et al. (2010) explored alternative correlations of two-phase friction pressure
drop and void fraction by applying the artificial neural network for round and
rectangular minichannels based on the separated flow and drift-flux model. They
collected 2201 data points for adiabatic and diabetic conditions from 13 source covering
9 working fluids and hydraulic diameters from 0.007 mm to 6.25 mm.
Kim and Mudawar (2012) developed a new universal approach to predict a two-
phase frictional pressure drop for adiabatic and condensing mini/microchannel flow
based on 7115 data points from 36 sources consisting 17 working fluids. In their
universal approach, they incorporated appropriate dimensionless relations in a separated
flow model to account for both small channel size and different combinations of liquid
and vapor states. This approach is shown to provide excellent predictions of the entire
consolidated database and fairly uniform accuracy against all parameters of the
database. It is also capable of tackling single and multiple channels as well as situations
involving significant flow deceleration due to condensation.
Kim and Mudawar (2013) also proposed a new technique to predict the frictional
pressure gradients for saturated flow boiling considering a consolidated database
consisting 2378 data points which were amassed from 16 sources. The database
considered data for both single and multiport channel, consists of 9 working fluids,
hydraulic diameters from 0.349 to 5.35 mm, mass velocities from 33 to 2738 kg/m2s,
liquid-only Reynolds numbers from 156 to 28,010, qualities from 0 to 1, reduced
pressures from 0.005 to 0.78. A separated flow technique previously developed by the
authors for adiabatic or condensation mini/micro-channel flows is modified to account
26
the different flow structure between boiling and adiabatic or condensing flows.
Lopez-Belchi et al. (2014) experimentally studied condensing two-phase frictional
pressure drop inside a minichannel having 1.16 mm hydraulic diameter with R1234yf,
R134a and R32. They analyzed experimental data to show the effect of saturation
temperature, mass fluxes, vapor quality and fluid properties on pressure drop. In
addition, they presented a new correlation model for “C” calculation.
Jige et al. (2016) investigated the condensation heat transfer and adiabatic pressure
drop characteristics of refrigerants R134a, R32, R1234ze (E) and R410A in a 0.85 mm
hydraulic diameter horizontal rectangular multiport minichannel. They concluded that
the frictional pressure drop increases with decreasing hydraulic diameter due to the
increase in shear stress with increasing velocity gradient. Moreover, they developed the
frictional pressure drop correlation for multiport tube considering the effect of channel
geometry.
Tapia and Ribatski (2017) conducted an experimental investigation on the effects of
refrigerant and channel geometry on the frictional pressure drop during condensing
two-phase flow in minichannels. The researchers used 4 refrigerants, R134a, R1234ze
(E), R1234yf and R600a as a working fluid and three cross-sectional geometries
namely, circular, square and triangular sections as minichannels with hydraulic
diameters 1.1 mm, 0.868 mm and 0.634 mm, respectively. The author concluded that
the two-phase frictional pressure drop for R600a is higher compared to the other fluids.
Moreover, the two-phase frictional pressure drop gradient of R1234ze(E) is higher than
that of R134a and R1234yf. Highest pressure drop were also observed for the triangular
geometry followed by square and circular geometries. Based on the 1468 experimental
data points, they proposed a new predictive method for two-phase friction pressure drop
using Muller-Steinhagen and Heck (1986) model.
Recently, Rahman et al. (2017) examined the experimental adiabatic two-phase
frictional pressure drop of R134a in rectangular multiport minichannel with and without
fins having 20 channels with hydraulic diameters of 0.64 mm and 0.81 mm,
respectively. The pressure drop measurements were done over the mass flux range of
50–200 kg/m2s, saturation temperature range of 20–35 °C, and inlet vapor quality range
of 0.1–0.9. The effects of mass flux, saturation temperature, inlet vapor quality and
channel geometry on frictional pressure drop were clarified. The results discovered that
the mass flux, inlet vapor quality, saturation temperature and channel geometry play an
important role in increasing or decreasing the two-phase frictional pressure drop. The
27
present experimental data were compared with available existing well known frictional
pressure drop correlation. In addition, the researcher developed a validated new two-
phase frictional pressure drop correlation considering the effects of inertia, viscous
force, fluid properties, channel geometry and surface tension.
1.2.3 Condensation heat transfer and pressure drop in microfin tube
Condensation heat transfer and pressure drop in microfin tube has been a research
subject since the end of 1970s due to higher heat transfer enhancement with low
pressure drop. Some of the available studies are reviewed here:
Koyama and Yonemoto (2006) performed experimental studies on condensation
heat transfer and pressure drop of R22, R123 and R134a in eleven different horizontal
microfin tubes. They developed the heat transfer correlations using Yu and Koyama
(1998) correlation based on the void fraction.
Yu and Koyama (1998) conducted an experimental study on condensation heat
transfer of pure refrigerant R134a, R123 and R22 in microfin tubes. The authors
concluded that the local condensation heat transfer characteristics in a horizontal
microfin tube were found to be about 2 times higher than those of a smooth tube with
the same inner diameter. This enhancement seems mainly caused by the enlargement
ration of heat transfer area. By considering the enlargement ratio of heat transfer area, a
modified correlation, from the correlation of Haraguchi et al. (1994) for smooth tubes,
was proposed for the condensation heat transfer in microfin tube with pure refrigerant.
Nozu et al (1998) measured pressure drop during condensation of CFC11 in
horizontal helical microfin tubes and proposed a correlation Eq. (3.1.20) for the local
frictional pressure gradient in which the effect of refrigerant mass velocity was
introduced on the basis of the flow regime consideration.
Goto et al. (2003) experimentally measured the condensation heat transfer
coefficients of R410A and R22 in five different internally helical microfins and
herringbone microfins tubes of about 8.0 mm outer diameter. The obtained results
indicated that the condensation heat transfer coefficients of the herringbone microfins
tube are twice as large as those of helical one. The authors developed a new empirical
correlations based on Koyama and Yu (1996) correlations for both the helical and
herringbone microfins tube to predict the condensation heat transfer coefficients of
28
R410A and R22.
Newell and Shah (1999) recommended a method of predicting two-phase pressure
drop inside helical microfin tubes where they multiplied smooth tube pressure drop
correlation of Souza and Pimenta (1995) with a pressure drop penalty factor.
Han and Lee (2005) experimentally studied the condensation heat transfer and
pressure drop characteristics of refrigerants R134a, R22 and R410A in four different
microfin tubes with 4.0, 5.1, 6.46, and 8.92 mm inside diameters, respectively. The
effects of mass flux, vapor quality and refrigerants on condensation were clarified in
terms of the heat transfer enhancement factor and the pressure drop penalty factor. The
dependence of heat transfer enhancement factors with vapor quality and mass flux
showed similar trend as those of the pressure drop penalty factors. In addition, the
authors proposed a correlation for condensation heat transfer coefficients and frictional
pressure drops in an annular flow regime for microfin tube based on the experimental
data and the heat-momentum analogy.
Mori et al. (1999) measured the frictional pressure gradient of R410A inside a
herringbone microfin tube varying the mass velocity 100-500 kg/m2s. They used
adiabatic condition for measuring the pressure drop and the inlet saturation temperature
was 50 0C. Their data can be used for necessary comparison of two-phase frictional
multiplier as they use adiabatic condition. For the fixed test section length they supplied
the liquid-vapor mixture of the refrigerant maintaining constant quality and mass
velocity and measured the frictional two-phase pressure drop.
Honda et al. (2005) showed the experimental results that described the effects of
mass flux and condensation temperature difference on the local condensation heat
transfer characteristics of R407C in a horizontal microfin tube having 6.35 mm outside
diameter. The experiments were performed over a range of mass velocity of 50-300
kg/m2s, at the saturation temperature of 40 0C, and condensation temperature difference
of 1.5, 2.5 and 4.5 K.
Jung et al. (2004) performed an experiment on flow condensation heat transfer
coefficients of R22, R134a, R407C and R410A inside horizontal plain and microfin
tube of 9.52 mm outside diameter. The condensation heat transfer coefficients of R134a
and R410A in plain tube were similar to those of R22 while the heat transfer coefficient
of R407C was 11-15% lower than those of R22. In microfin tube, the condensation heat
transfer coefficients of R134a were similar to those of R22 while the heat transfer
coefficient of R407C and R410A were 23-53% and 10-21% lower than those of R22.
29
The different heat transfer characteristics between tested refrigerants were mainly
because of different fluid properties and flow pattern. The authors observed 2-3 times
higher heat transfer coefficients in microfin tube than those of a plain tube. They also
concluded that the condensation heat transfer enhancement factor decreased as the mass
flux increased for all the tested refrigerants.
Kedzierski and Goncalves (1999) presented the local convective condensation heat
transfer measurements of refrigerants R134a, R410A, R125 and R32 in a microfin tube
of 9.5 mm outer diameter. The refrigerant R32 exhibited the higher heat transfer due to
its higher thermal conductivity. The authors proposed a single expression correlation
from the measured convective condensation Nusselt number for all of the tested
refrigerants. The correlation was shown to predict existing condensation Nusselt
numbers for microfin tubes from the literature acceptably well excluding the Nusselt
numbers for microfin tubes with cross-grooves. They found that the microfins enhanced
the heat transfer with a combination of liquid-vapor interface mixing and turbulent
mixing near the wall. Moreover, surface tension drainage and swirl effects are
presumed to have little influence on the heat transfer.
Cavallini et al. (2003) reviewed some research relating to condensation inside and
outside smooth and enhanced tubes. They concluded that within smooth circular tubes,
adequate predicting procedures for heat transfer are in general available to designers,
even in the presence of lubricating oils. Experimental data are needed for condensation
of halogenated refrigerants near the critical temperature to possibly extend the
confidence on available design tools. In addition, condensation of CO2 at low
temperature should be investigated to help designing cascade systems with this natural
refrigerant.
Dalkilic and Wongwises (2009) reviewed a large number of existing studies of heat
transfer and pressure drop during in-tube condensation according to the tube orientation
(horizontal, vertical, inclined tubes) and tube geometry (smooth and enhanced tubes),
flow pattern studies of condensation, void fraction studies, and refrigerants with the
effect of oil.
Kim and Shin (2005) experimentally investigated the condensation heat transfer of
R22 and R410A in a horizontal smooth and seven different microfin tubes having 9.52
mm outer diameter. The authors found that the average heat transfer coefficient of the
microfin tube was 1.7-3.19 times higher than that of the smooth tube. This is mainly
due to the larger heat transfer area of microfin tube.
30
Miyara et al. (2003) studied the effects of fin height and helix angle on
condensation heat transfer inside five types of horizontal herringbone microfin tubes.
The authors found that the heat transfer in herringbone microfin tubes is approximately
2-4 times higher than that of the helical microfin tubes under high mass velocity
conditions. The authors suggested that the fin height is better to be 0.18 mm or smaller.
The larger helix angle yields higher heat transfer coefficient and larger pressure drop.
Although the heat transfer enhancement is degraded for shorter fin or smaller helix
angle, it is still higher than that of a conventional helical microfin.
Miyara and Otsubo (2002) carried out an experiment on condensation heat transfer
of R410A in a smooth tube, a helical microfin tube and three different herringbone
microfin tubes, respectively. They found in their study that micro fins were working at
fin-diverging parts in order to remove liquid and they were working at fin-converging
parts in order to collect liquid in the herringbone micro fin tube. Thinning the film at
the diverging parts and mixing the liquid at the converging parts increase the heat
transfer. The removal of the liquid and collection by herringbone micro fins does not
take effect in the low mass velocity region but only in the high mass velocity region.
Kim et al. (2009) investigated the condensation heat transfer of CO2 at low
temperature inside a horizontal smooth and microfin tubes with 5.0 mm and 4.34 mm
outer diameter, respectively. The test was conducted over a mass flux range of 200-800
kg/m2s and at saturation temperatures of -25 0C and -15 0C, respectively. The effects of
various factors on the heat transfer coefficient and enhancement factor were analyzed.
Based on the average enhancement factors and penalty factors, they discovered that the
internally finned geometry do not always guarantee the superior in tube condensation
performance of the microfin tube in refrigeration and air-conditioning systems. Due to
the complexity, variety of fin geometry and flow mechanisms all most all of the
existing correlations were failed to predict the experimental data.
Sapali and Patil (2010) experimentally investigated the heat transfer coefficients
during condensation of R134a and R404A in a smooth and microfin tubes having inner
diameters of 8.56 mm and 8.96 mm, respectively. The experimental results indicated
that the average heat transfer coefficients increase with mass flux but decrease with
increasing temperature for both tubes. The authors found that the average heat transfer
coefficients of R134a and R404A in microfin tube were 1.5-2.5 and 1.3-2 times higher
than that in smooth tube, respectively.
Son and Oh (2012) investigated the heat transfer characteristics of CO2 during
31
condensation in a horizontal smooth and microfin tube at higher saturation temperature
of 20-30 0C. The outer diameters of the tested smooth and microfin tubes were 6.35 and
5.0 mm, respectively. The experimental results indicated that the annular flow almost
dominated the condensation flow in both tubes. The heat transfer coefficients for the
microfin tube were higher than those for the smooth tube in the entire vapor quality
range approximately 1.006 to 1.48 times. The enhancement of condensation heat
transfer were mainly due to the large effective heat transfer area in microfin tube,
turbulence induced in the liquid film and the surface tension effect on the liquid
drainage. The author’s found that most of the existing correlations failed to predict the
experimental data. Furthermore, they suggested necessity to develop accurate and
reliable correlation to predict condensation heat transfer coefficients at high saturation
temperatures in the horizontal smooth and microfin tubes.
Wang et al. (2002) presented a modified model of film condensation from
previously proposed theoretical models in horizontal microfin tubes. The surface
tension force in stratified flow regime and the interfacial shear stress in the annular flow
regime were incorporated in the modified model to describe the characteristics of
condensing two-phase flow more accurately.
Wang et al. (2003) performed a comprehensive comparison of eight previously
proposed correlations with available experimental data for the frictional pressure drop
during condensation of refrigerants of R11, R123, R134a, R22, R32, R125 and R410A
inside eight helical microfin tubes with mass velocity from 78 to 459 kg/m2s. The
results show that the overall root means square deviations of relative residuals of
frictional pressure drop for all tubes and all refrigerants taking together decreased in the
order of the correlations of Nozu et al. (1998), Newell and Shah (1999), Kedzierski and
Goncalves (1997, 1999), Cavallini et al. (1997), Goto et al. (2001), Choi et al. (2001),
Haraguchi et al. (1993), Goto et al. (2001). The best among those correlations is Goto et
al. (2001) which shows r.m.s relative deviation of 23.6%.
Li et al. (2012) performed an experimental study of condensation characteristics
and pressure drop of R22 inside five different microfin tubes with 5.0 mm outer
diameter. The results suggested that the small hydraulic diameter tube (among five
different tubes) has the highest heat transfer coefficient and pressure drop penalty. The
mass flux has nonlinear relation with the condensation heat transfer coefficients for 2
different microfin tubes. The complex nonlinear mass flux effect may be explained by
the complex interactions between microfins and fluid, including liquid drainage by
32
surface tension and interfacial turbulence. Most of the existing correlations were failed
to predict their experimental data accurately.
Wu et al. (2014) experimentally studied convective condensation inside one smooth
tube and six microfin tubes of different geometries. They concluded that the heat
transfer coefficient in the microfin tubes decreases at first and then increases or flattens
out gradually as mass flux decreases due to the surface tension and interfacial
turbulence effects.
Kim (2016) experimentally investigated the condensation heat transfer and pressure
drop of R410A in a 7.0 mm OD smooth and microfin tube at low mass flux. He found
that the heat transfer coefficient of the microfin tube shows a minimum behavior with
the mass flux. Below the mass flux of 100 kg/m2s, the heat transfer coefficient
decreases as mass flux increases. The flow pattern was stratified below the mass flux
100 kg/m2s and the condensation induced by surface tension by microfins. The flow
pattern was annular at high mass flux and condensation induced by share stress.
Therefore, the heat transfer coefficients increased as mass flux increased.
Recently, Rahman et al. (2017) conducted an experimental study of adiabatic
pressure drop and condensation heat transfer characteristics of refrigerant R134a in a
small diameter smooth and microfin tubes. The outer diameters of the tested smooth
and microfin tubes were 2.5 mm. The authors performed this test in the mass flux range
of 50 to 200 kg/m2s, range of vapor quality of 0 to 1 and range of saturation temperature
of 20 to 35 0C. They found that both the condensation heat transfer coefficient and
frictional pressure drop were increases with the mass flux and vapor quality but the
frictional pressure drop decreases with saturation temperature. The microfin tube has
slightly influence on the frictional pressure gradients. The frictional pressure drop of the
microfin tube was higher than those of smooth tube about 10-15%. The higher heat
transfer coefficient was obtained in microfin tube about 2-68%. The present
experimental data were compared with the existing well-known condensation heat
transfer and frictional pressure drop models available in the open literature. The Goto et
al. (2001) pressure drop correlation gives fairly good prediction with 26.1% mean
absolute error. The heat transfer correlation of Cavallini et al. (1999) can predict the
present experimental heat transfer data reasonably.
33
1.3 Objectives of the present research
Through the literature review, it is clear that the results of different studies shown
different effects. That suggests needs for systematically measured heat transfer and
pressure drop data to understand the phenomenon of condensation in minichannels and
microfin tubes and developing models. Although, heat transfer and frictional pressure
drop has been a research subject for several decades and many researchers extensively
investigated the heat transfer and pressure drop characteristics in minichannels and
large diameter microfin tubes experimentally and theoretically. But consistent
information on heat transfer and pressure drop characteristics in multiport rectangular
minichannels and small diameter microfin tubes are still inadequate. Hence, the design
of high performance multiport rectangular minichannels and small diameter microfin
tubes heat exchanger essentially requires accurate predictive tools for heat transfer
coefficient and pressure drop prediction in two-phase flow. The main objectives of the
present studies are:
1. To investigate the effects of all of the involved parameters such as mass
velocity, vapor quality and saturation temperature on adiabatic frictional
pressure drop characteristics of two-phase flow inside rectangular multiport
minichannels experimentally.
2. To developed a new frictional pressure drop prediction model for rectangular
multiport minichannel based on the experimental data and validate with the
existing data available in open literature
3. To investigate the effects of all of the involved parameters such as mass
velocity, vapor quality and saturation temperature on condensation heat transfer
coefficients of two-phase flow inside rectangular multiport minichannels
experimentally.
4. To developed a new heat transfer coefficient during condensation prediction
model for rectangular multiport minichannels based on the experimental data
and validate with the existing data available in open literature
5. To investigate the effects of all of the involved parameters on frictional pressure
drop of R134a inside small diameter microfin tube experimentally.
6. To investigate the effects of all of the involved parameters on condensation heat
transfer coefficients of R134a inside small diameter microfin tube
experimentally.
34
1.4 Overview of the thesis
This thesis is organized as follows:
The present chapter presents the fundamental background, literature reviews and outline
of the objectives of the research and the method used. In the background, the
fundamentals of the minichannels, microfin tubes, flow regime and flow regimes maps
have been discussed inherit. In the literature survey, previous studies relating to heat
transfer and pressure drop have been discussed.
The description of the experimental setup and experimental methodology together with
data reduction and uncertainty measurement are presented in Chapter 2.
Chapter 3 addresses the experimental results of two-phase frictional pressure drop at
adiabatic condition inside rectangular multiport minichannels and microfin tube.
Chapter 4 reports the experimental results of condensation heat transfer of R134a in
rectangular multiport minichannels and microfin tubes.
Chapter 5 contains a review of some of the models available in the open literature for
frictional pressure drop prediction in both minichannels and microfin tubes. The chapter
also contains the comparison of present experimental frictional pressure drop data with
review models.
Chapter 6 presents a review of some of the models available in the open literature for
condensation heat transfer prediction in both minichannels and microfin tubes. The
chapter also contains the comparison of present experimental heat transfer coefficients
data with review models.
Chapter 7 reports a new frictional pressure drop and condensation heat transfer
coefficient prediction models. Both models are validating using the existing pressure
drop and heat transfer data available in open literature.
Finally, Chapter 8 presents the summary and concluding remarks of all findings of the
present research together with future recommendations.
35
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50
CHAPTER 2
Experimental Methods
The experimental test facility, the test sections, data reduction procedures and
measurements uncertainty analysis will be described in the present chapter. A new
experimental test facility was constructed in the MIYARA & KARIYA Thermal
Energy Engineering Lab, Department of Mechanical Engineering at the Saga
University, Japan. The main purpose of this test facility construction is to measure the
heat transfer and pressure drop during condensation and vaporization of refrigerants
inside horizontal rectangular multiport minichannels, smooth tubes and microfin tubes.
In this test facility, three different test sections have been installed in parallel mode as
shown in Fig. 2.1. The first one consists of a microfin tubes, second one consists of a
rectangular multiport minichannels with fins and third one consists of a rectangular
multiport minichannels without fins.
Fig. 2.1 a photograph of the test sections.
51
2.1 Experimental Facility
2.1.1 Experimental Apparatus
The experimental setup has been specifically fabricated to measure the heat transfer
and pressure drop of refrigerants during condensation and boiling. Fig. 2.2 shows the
schematic diagram of the experimental apparatus used in this study. The experimental
test facility consists of a test section, refrigerant loop, cooling/heating water loop, sub-
cooling loop and data acquisition system. The liquid refrigerant is pumped by an
independently controlled gear pump magnetically coupled to a variable speed electric
motor through a filter, mixer, preheaters, sight glass tube, test section, cooler and
accumulator. To complete the cycle, refrigerant from the cooler is then recirculated,
collected in an accumulator and returned to the refrigerant pump. The pump is also used
to set the mass flow rate measured by a Coriolis-effect mass flow meter. Any dust and
foreign materials contained in the refrigerant are separated through the strainer installed
after the pump.
For the condensation, the quality of refrigerant before entering the test section is
controlled by first pre-heater and superheat by second pre-heater. The hot refrigerant (in
the thermodynamic state known as a superheated vapor and it is at a temperature and
pressure at which it can be condensed with typically available cooling water) is then
enter the test section to get experimental data in the vapor quality range 0-1. The test
section consists of a tube-in-tube heat exchanger where the tested refrigerant is
cooled/heated using cooling/heating water flowing in a closed cooling/heating loop.
Cooling/heating water kept at a constant temperature is supplied to the test section from
the cooling/heating unit with constant flow rate. After the test section, refrigerant flows
through the cooler, where the refrigerant is fully subcooled by the brine which is kept at
a constant temperature in the heat source unit. Three mixing chambers are installed at
the inlet of first preheater and test section and outlet of the test section to measure the
bulk temperature of refrigerant. The system pressure of the test apparatus is controlled
by the accumulator. The absolute pressure transducer, differential pressure transducer
and K-type thermocouple at various positions and sight glass at inlet and outlet of the
test section are installed as shown in Fig. 2.2 to monitor the refrigerant’s state. All of
the signals from the pressure transducer and thermocouples are collected by a, Keithley
52
3706, data acquisition system. The whole test apparatus is well insulated with special
attention given to the test section.
Fig. 2.2 Schematic diagram of the experimental apparatus
2.1.2 The test sections
Four test sections have been used in the different experimental investigations, two
are rectangular multiport minichannels and others two is circular tube with and without
fins.
2.1.1.1 Multiport minichannels with and without fins
Fig. 2.3 depicts the schematic diagram of the multiport minichannels. The test
Heating
water bath
53
section for the multiport rectangular minichannels consists of horizontally installed
aluminum rectangular multiport minichannels without fins having 20 channels in 0.813
mm hydraulic diameter and aluminum rectangular multiport minichannels with fins
having 20 channels in 0.645 mm hydraulic diameter, two heder and six cooling water
channel. The photographs and details of the test tube are presented in Fig. 2.3-2.4 and
Table 2.1. The both test tubes are made of aluminum alloy. The hydraulic diameters dh
of rectangular multiport minichannels are calculated as follows:
4h
p
Ad
w (2.1)
Where A and wp are the total cross-sectional area and wetted perimeter length of the
tube, respectively.
There are 8 fins inside the each channel inner surface (2 fins on each side of the
inner surface) of the rectangular multiport minichannel with fins. The fin size is
mentioned in Fig 2.4. The cooling water channels are attached on both upper and
bottom side of the test section. Each cooling water channel is subdivided by three
subsections. Mixing chamber is installed at the inlet and the outlet of the each water
channel to measure the bulk water temperature as shown in Fig. 2.2. The length of each
subsection is 250 mm. The cooling water channels are designed as a rectangular
channel and used to supply heat flux to the tested tubes. The total length of the each test
section is 852 mm and effective cooling length is 750 mm. A differential pressure
transducer with calibrated accuracy of ±0.1 kPa is installed in the header to measure the
pressure difference. The inlet and outlet refrigerant temperature are measured by two K-
type thermocouples with calibrated accuracy of ±0.03K installed in the inlet and outlet
mixing chambers The inlet and outlet pressure are measured by two absolute pressure
transducer with calibrated accuracy of ±0.1 kPa inserted in the inlet and outlet mixing
chambers. Twenty four T-type thermocouples with a calibrated accuracy of ±0.03K are
attached at four points along the multiport minichannel outer wall of each subsection,
both upper and bottom side, to measure the outer wall temperature. For measuring the
inlet and outlet cooling water temperatures, K-type thermocouples with calibrated
accuracy of ±0.03K are also installed at inlet and outlet of each subsection of the water
channel.
54
Table 2.1 Tube characteristics of multiport minichannels
Multiport
Minichannel
Tube
Width
(mm)
Tube
Thickness
(mm)
Outer
tube thickness
(mm)
Tube
Inner
pillar thickness
(mm)
No. of
channel
Channel
Width
Channel
Height
Hydraulic
diameter
(mm)
With fins 19.0 2.0 0.37 0.30 20 0.61 1.24 0.64
Without fins 19.0 2.0 0.37 0.30 20 0.62 1.24 0.81
Fig. 2.3 Test section (Multiport minichannels)
55
Fig. 2.4 Photograph of the test tube
2.1.1.2 Smooth and microfin tubes
Fig. 2.5 illustrates the schematic diagram of the test section for the circular tube
with and without fins. The details dimensions of the test tube are summarized in Table
2.2. The test section consists of horizontally installed copper tube, two headers and
three cooling water channels. The test tubes are small-diameter circular tubes with and
without microfins. The equivalent diameter of the tube with microfins is 2.68 mm. The
equivalent diameter of the microfins tube is calculated as follows:
4eq
Ad
(2.2)
where A is the flow area of refrigerant.
The inner diameter of a tube without microfins is 2.14 mm. The cooling water
channels are designed as a tube in tube heat exchanger and used to supply heat flux to
the tested tubes. The total length of the each test section is 852 mm and effective
cooling and heating length is 744 mm. A differential pressure transducer with calibrated
accuracy of ±0.1 kPa is installed in the header to measure the pressure difference. The
inlet and outlet refrigerant temperature are measured by two K-type thermocouples with
calibrated accuracy of ±0.03K installed in the inlet and outlet mixing chambers. The
56
inlet and outlet pressure are measured by two pressure transducer with calibrated
accuracy of ±0.1 kPa inserted in the inlet and outlet mixing chambers. For measuring
the inlet and outlet cooling water temperatures, K-type thermocouples with calibrated
accuracy of ±0.03 K are also installed at the inlet and outlet of each subsection of the
water channel.
Table 2.2 Detail dimensions of the circular tube with and without microfins
Circular tube with microfins
Circular tube without fins
Outer diameter, do 3.0 mm 2.5 mm Inner diameter, di - 2.14 mm Diameter at fin root, dr 2.7 mm - Diameter at fin tip, dt 2.5 mm - Equivalent diameter, de 2.68 mm - Fin height, e 0.1 mm - No. of fins, n 25 - Apex angle, γ 330 - Helix angle, ψ 100 -
Fig. 2.5 Test section (Circular tube)
2.1.3 Range of test conditions
The experiments covered a wide range of test conditions for all test section studied in
the present work to investigate the effect of the following parameters on the
experimental condensation heat transfer coefficients and frictional pressure drop: the
57
mass velocity, saturation temperature, vapor quality, and tube geometry. Table 2.3 and
Table 2.4 listed the range of the test conditions of the present research for condensation
and adiabatic experiments, respectively.
Table 2.3 Test conditions for condensation experiments
Test Section Minichannel
with fins
Minichannel
without fin Smooth tube Microfin tube
Channel
Diameter dh = 0.64 mm dh = 0.81 mm di = 2.14 mm deq = 2.68 mm
G [kg/m2s] 50-200 50-200 50-200 50-200
Tsat (C) 30, 35 30, 35 30 30
x 0.1-0.9 0.1-0.9 0.1-0.9 0.1-0.9
Table 2.4 Test conditions for adiabatic experiments
Test Section Minichannel
with fins
Minichannel
without fin Smooth tube Microfin tube
Channel
Diameter dh = 0.64 mm dh = 0.81 mm di = 2.14 mm deq = 2.68 mm
G [kg/m2s] 50-200 50-200 50-200 50-200
Tsat (C) 20, 30, 35 20, 30, 35 20, 30, 35 30
x 0.1-0.9 0.1-0.9 0.1-0.9 0.1-0.9
58
2.2 Data reduction
2.2.1 Two-phase frictional pressure drop
The two-phase pressure drop is composed of pressure drop due to momentum change or
acceleration (deceleration), gravity or static, abrupt contraction, abrupt expansion, and
friction. The gravitational or static pressure drop is zero due to horizontal flow. The
pressure drop due to momentum change or acceleration (deceleration) was not included
in the measured pressure drop as the pressure drop was obtained at adiabatic conditions.
Therefore, the total measured pressure drop TP at adiabatic condition is expressed as
the sum of frictional pressure drop FP , pressure drop due to the abrupt contraction
cP and expansion eP at the inlet and outlet of the test section,
T F c eP P P P (2.3)
The pressure drop due to abrupt contraction and expansion in the headers should be
taken into account in addition to the pressure drop in the channel. In the case of a
sudden contraction and enlargement in the cross-sectional area of the pipe flow
separation occurred and the general method used in single-phase flow is still applicable
to a one-dimensional separated two-phase flow (Collier and Thome, 1994). Fig. 2.6
depicts a two-phase flow passing through a sudden contraction and expansion. The
subscript 1, 2 and 3 has been used to denote the conditions at planes 1, 2 and 3,
respectively as laid in Fig. 2.6.
59
Fig. 2.6 Abrupt contraction and expansion nomenclature.
According to Collier and Thome (1994), the pressure drop due to the abrupt contraction
is given by
22
2
1 11 1 1
2l v
c
c c l
G v vP x
C v
(2.4)
And the pressure drop in the case of sudden expansion is given by
2 2
2 (1 )1 ( )
(1 )v
e e e l
l
vx xP G v
v
(2.5)
where, δ is the area ratio ( 1 2 2 3/ , /c eA A A A ) and the coefficient of contraction, Cc
is a function of δ. Perry (1963) suggested the relationship between Cc and δc as listed in
Table 2.5.
The void function is assumed as a constant and calculated by the homogeneous
model.
1
11 v
l
x
x
(2.6)
60
The pressure drop due to abrupt contraction and abrupt expansion was found to be less
than 2% of the total two phase pressure drop.
Table 2.5 Relationship between cC and c
1
c 0 0.2 0.4 0.6 0.8 1.0
cC 0.586 0.598 0.625 0.686 0.790 1.0
2
11
cC
0.5 0.45 0.36 0.21 0.07 0
The vapor quality before entering the test section is expressed as:
outh hx
h h
(2.7)
out in
Wh h
G
(2.8)
The saturated liquid enthalpy, h and enthalpy of saturated vapor, h at the preheater
outlet are calculated with its temperature. The K-type thermocouple at outlet of the
preheater gives the refrigerant temperature. The enthalpy of refrigerant before the
preheater is calculated with its bulk temperature and pressure. The amount of heat, W,
is supplied by the electricity into the preheater in the direct heating method. The
experimental study was conducted at adiabatic condition (the temperature of flowing
refrigerant in the test section and water flowing upper and lower side of the test section
was same). The vapor quality does not change along the test section because no further
heat is added to the refrigerant flowing in the test section.
61
Then from the experimental frictional pressure drop, the experimental two-phase
frictional multiplierl is obtained, based on Lockhart-Martinelli (1949) method, from
the following equation as:
2l
F l
PP
z z
(2.9)
where F
P
z
is the frictional pressure gradient for the two-phase flow; l
P
z
is the
frictional pressure gradient when only liquid flows through the test tube.
The value of l
P
z
is estimated by
222 1l
l h l
f G xP
z d
(2.10)
where the friction factor lf is calculated by Colburn’s Eq. for single-phase flow in a
tube.
0.2
0.046
Rel
l
f (2.11)
2.2.2 Condensation heat transfer
The sectional two-phase average local heat transfer coefficient of each thermocouple
location, i (i=1, 2, 3,…………..,12), during the condensation of R134a in horizontal
rectangular multiport minichannels with and without fins was calculated by
,
,
stp i
R,i wi i
qh
T T
(2.12)
where sq is the heat flux of each subsection based on the actual heat transfer surface
area inside the channel, ,R iT is the refrigerant temperature inside the channel and ,wi iT is
the inner wall temperature.
62
The heat flux of each subsection is calculated as
c HBs
p
w Z
(2.13)
To get better data reduction, sq is modified by HB due to the error of heat balance as
shown in Fig. 2.7.
Fig. 2.7 Error of heat balance of all test conditions
The heat transfer rate of the coolant side of each subsection is
, ,( )c c s out s inq m h h (2.14)
The heat balance factor, HB is
RHB
c
Q
Q (2.15)
The sensible heat gain of the coolant of the whole test section is
0 0.2 0.4 0.6 0.8 1.00
0.2
0.4
0.6
0.8
1.0
50100200
-10%
50 100 150 200
QR [
kW
]
QC [kW]
G [kg/m2s]
+10%
Minichannels
G [kg/m2s]
Microfin and smooth tubes
63
[ ( )] [ ( )]c c out in U c out in LQ m h h m h h (2.16)
The heat release of refrigerant of the whole test section is
( )R R out inQ m h h (2.17)
The inner wall temperature, ,wi iT of the multiport minichannel at each thermocouple
location was calculated from the measured outer wall temperature and the heat flux
using one-dimensional Fourier’s heat conduction equation
, ,s
wi i wo i
al
q zT T
w Z k
(2.18)
In the case of horizontal microfins and smooth circular tubes, the inner wall temperature
was calculated by
0
, ,
ln
2
s
iwi i wo i
cu
dq
dT T
z k
(2.19)
The refrigerant temperature at each thermocouple location, ,R iT , was determined from
the corresponding saturation pressure assuming saturated state. The pressure drop in the
test section was recorded by a differential pressure transducer. Based on the recorded
pressure drop, a new frictional pressure drop correlation was developed in order to
identify the saturation conditions on each thermocouple location. The local heat transfer
coefficient calculation process for multiport minichannel is schematically depicted in
Fig 2.8.
64
Fig. 2.8 Schematic diagram of local heat transfer coefficient calculation
The refrigerant equivalent vapor quality at each thermocouple location is given by
,b i l
i
v l
h hx
h h
(2.20)
Where, ,b ih is the local enthalpy at each test section wall thermocouple location. The
local enthalpy of each thermocouple location “i” was obtained from the local enthalpy
in the location “i-1” using the following equation:
, ,i 1R
b i b
R
q wh h
l m
(2.21)
For the first thermocouple location Eq. (2.9) becomes:
,1 ,R
b b in
R
q wh h
l m
(2.22)
The i+1th point local enthalpy of a thermocouple point is the ith point local enthalpy
of the next thermocouple point.
The thermodynamic properties and transport properties of R134a were obtained
from NIST REFPROP 9.1 (Lemmon et al., 2013).
65
2.3 Experimental measurement uncertainties analysis
The experiments were conducted over a range of test conditions. The effects of different
parameters on the condensation heat transfer and adiabatic pressure drop were clarified.
The vapor quality, mass flux and saturation temperature were varied. The experimental
uncertainty of the condensation heat transfer and adiabatic pressure drop were
calculated following the method by JCGM 100 (2008). The experimental uncertainty is
consisted of two parts, type A uncertainty that derives from repeated observation and
type B uncertainty that derives from instruments calibration and manufacturer’s
specifications. The resulting u of each parameter x is expressed as:
2 2
A Bu x u x u x (2.23)
The combined standard uncertainty is obtained by combining the standard uncertainty
of the measured quantities 1 2, ,....., Nx x x , through a functional relationship f as follows:
1 2, ,.........., Ny f x x x (2.24)
2
2
1
N
ii i
fu y u x
x
(2.25)
The expanded uncertainty U is obtained by multiplying the combined uncertainty u (y)
by a coverage factor k = 2 with a level of confidence of 95%.
U u y k (2.26)
The uncertainty analysis of heat transfer coefficient can be carried out based on the
basic equation of condensation heat transfer mentioned in Eq. 2.12.
2 2 2
2 2 2s wi R
s wi R
h h hu h u q u T u T
q T T
(2.27)
66
Similarly, the uncertainty analysis of frictional pressure drop can be carried out from
the basic equation of frictional pressure drop calculation as mentioned in Eq. 2.3.
2 22
2 2 2F F FF T c e
T c e
P P Pu P u P u P u P
P P P
(2.28)
67
References
Collier, J. G., Thome, J. R., 1994. Convective Boiling and Condensation, Third edition,
Oxford University Press, Oxford, UK.
JCGM 100, 2008. Evaluation of measurement data-Guide to the expression of
uncertainty in measurement.
Lemmon, E.W., Huber, M.L., McLinden, M.O., 2013. Reference Fluid Thermodynamic
and Transport Properties, In: NIST Standard Reference Database 23, REFPROP,
Version 9.1, Gaithersburg, April.
Lockhart, R.W., Martinelli, R.C., (1949). Proposed Correlation of Data for Isothermal
Two-Phase, Two-Component Flow in Pipes. Chemical Engineering Progress 45, 39-
48.
Perry, 1963. Chemical Engineers Handbook, 4th Edition, McGraw-Hili, 5-30.
68
CHAPTER 3
Two-phase Frictional Pressure Drop Analysis
The two-phase frictional pressure drop of R134a in horizontal rectangular multiport
minichannels and microfin tubes at the adiabatic condition is analyzed and discussed in
this chapter. The experimental study conducted over the mass flux range of 50-200
kg/m2s, vapor quality range of 0 to 0.9 and at the saturation temperature of 20, 30 and
35 0C, respectively.
3.1 Two-phase frictional pressure drop in rectangular multiport
minichannels with and without fins
3.1.1 Effect of the mass flux and vapor quality
The analysis of an experimental pressure drop results reveals several important
trends. Most notably, the mass flux and vapor quality has shown significant effect. Fig.
3.1 and Fig. 3.2, respectively shows the effects of mass flux and vapor quality on the
frictional pressure drop in rectangular multiport minichannel with and without fins. The
frictional pressure drop in both multiport minichannels significantly increases with
increasing mass flux and vapor quality. Starting from the beginning with a vapor quality
of 0.1, frictional pressure drop increases almost nearly linearly for all of the vapor
quality range. The increase of the frictional pressure gradient is mainly due to the
higher vapor shear stress which increases with increasing mass flux and vapor quality.
The vapor shear stress increases with increasing vapor flow velocity which increases as
mass flux and vapor quality increases. Similar trends are also observed some previous
studies by Hwang and Kim (2006), Pamitran et al. (2010), Park and Hrnjak (2007) and
Sakamatapan et al (2014).
69
Fig. 3.1 Effects of mass flux and vapor quality on frictional pressure gradient in
rectangular multiport minichannels with fins
0
5
10
15
20
25
30
50 100 150 200
P
/z)
F [
kP
a/m
]
Minichannel with fins (dh= 0.64 mm) G [kg/m2s]
R134a, Tsat
= 30 0C
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
Vapor quality
P
/z)
F [
kP
a/m
]
R134a, Tsat
= 35 0C
Minichannel with fins (dh= 0.64 mm)
50 100 150 200
G [kg/m2s]
70
Fig. 3.2 Effects of mass flux and vapor quality on frictional pressure gradient in
rectangular multiport minichannels without fins.
3.1.2 Effect of saturation temperature
Saturation temperature also plays an influential role in two-phase frictional pressure
drop. In order to investigate the effect of saturation temperature on the frictional
pressure drop, experimental investigation was conducted by changing the saturation
temperature from 20 0C to 35 0C at mass flux 50, 100 and 200 kg/m2s, respectively as
shown in Fig. 3.3. There is no noticeable change in frictional pressure drop with
0
5
10
15
20
25
30
P
/z)
F [
kPa/
m]
R134a, Tsat
= 30 0C
Minichannel without fins (dh= 0.81 mm) G [kg/m2s]
50 100 150 200
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
P
/z)
F [
kPa/
m]
Vapor quality
R134a, Tsat
= 35 0C
Minichannel without fins (dh= 0.81 mm) G [kg/m2s]
50 100 150 200
71
saturation temperature at low mass flux. However, at high mass fluxes, the
experimental results confirmed that the saturation temperature had a significant effect
on frictional pressure drop which decreased with increasing saturation temperature. The
physical explanation of these effects is that the saturation temperature changes fluid
properties such as viscosity, density and surface tension as well as shear stress. When
increasing the saturation temperature, the viscosity ratio /l v , density ratio /l v
and surface tension decreases as a consequence the frictional pressure drop decreases.
The physical properties of selected working refrigerant are shown in Table 3.1. The
frictional pressure drop trend is fully consistent with Revillin and Thome (2007),
Pamitran et al. (2010) and Sakamatapan et al (2014).
Table 3.1 Thermophysical properties of R134a (Lemmon et al., 2013)
Tsat
[0C] ρl
[kg/m3] ρv
[kg/m3] l
v
µl
[µPa s] µv
[µPa s] l
v
σ
[mN/m]
20 1225.90 27.65 44.34 207.75 11.48 18.09 8.71
30 1188.00 37.37 31.79 183.47 11.90 15.41 7.40
35 1168.10 43.22 27.02 172.33 12.12 14.21 6.76
72
Fig. 3.3 Effect of saturation temperature on frictional pressure gradient
0
5
10
15
20
25
30
P
/z)
F [
kP
a/m
]
R134a, G = 50 kg/m2s
Minichannel with fins (dh= 0.64 mm) T
sat [0C]
20 30 35
0
5
10
15
20
25
35
P
/z)
F [
kP
a/m
]
Tsat
[0C]
20 30
Minichannel with fins (dh= 0.64 mm)
R134a, G = 100 kg/m2s
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
Tsat
[0C]
20 30 35
P
/z)
F [
kP
a/m
]
Vapor quality
Minichannel with fins (dh= 0.64 mm)
R134a, G = 200 kg/m2s
73
3.1.3 Effect of channel hydraulic diameter
The comparisons of the frictional pressure gradient were conducted between
rectangular minichannel with fins and without fin of hydraulic diameters of 0.64 mm
and 0.81 mm with same outer dimension and similar tested conditions, as shown in Fig.
3.4.
Fig. 3.4 Comparison of frictional pressure drop between minichannels with fins and
without fins.
0
5
10
15
20
25
30
100 150 200
100 150 200
(P
/z)
F [
kP
a/m
]
Minichannel with finsG [kg/m2s]
G [kg/m2s]Minichannel without fin
Tsat
=30 0C
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
100 150 200
100 150 200
(P
/z)
F [
kP
a/m
]
Vapor quality
G [kg/m2s]Minichannel with fins
G [kg/m2s]Minichannel without fin
Tsat
=35 0C
74
The experimental results exhibited that the frictional pressure drop of the multiport
minichannel with fins is 1.08-1.25 times higher than that of multiport minichannel
without fin for the same tested condition. At low mass velocity, the effect was not
notable. The effect is increasing with increasing the mass velocity. The smaller
hydraulic diameter tube offers higher frictional pressure drop due to the higher wall
shear stress which increases with increasing velocity gradients. The velocity gradiants
decreases with decreasing channel hydraulic diameter. This trend was strongly
supported by Revellin and Thome (2007), Sakamatapan et al. (2014) and Jige et al.
(2016).
3.2 Two-phase frictional pressure drop in circular microfins and
smooth tubes
The adiabatic two-phase frictional pressure drop of R134a in horizontal circular
microfins and smooth tubes are analyzed and discussed in this section. The
experimental study conducted over the mass flux range of 50-200 kg/m2s, vapor quality
range of 0 to 0.9 and at the saturation temperature of 20, 30 and 35 0C, respectively.
3.2.1 Influence of mass flux and vapor quality
Two phase frictional pressure drop at the adiabatic condition for microfin and
smooth tube are stated in Fig. 3.5 (a) and Fig. 3.5 (b). For both tubes, the frictional
pressure drop increases with mass flux and vapor quality. These are general trends of
two-phase frictional pressure drop (Collier and Thome, 1994). The increase of frictional
pressure drop is due to the effects of higher shear stress and momentum that leads to an
increase in wall shear stress as a result frictional pressure drop increases. The frictional
pressure drop mainly depends on the wall shear stress between liquid phase and tube
wall and the interfacial shear stress between liquid and vapor phases. Roughly speaking,
these shear stresses are strongly affected by the velocity gradient of each phase. The
larger bulk velocity of the liquid phase allows the larger velocity gradient of the liquid
phase near the tube wall, which results in the increase of wall shear stress. Similarly,
since the liquid-vapor interface acts like a tube wall to the vapor phase, the increase of
75
velocity difference between the liquid and vapor phases causes the increase of
interfacial shear stress (Kim et al., 2008).
Fig. 3.5 Effects of mass flux and vapor quality on frictional pressure drop: (a) Microfin
tube; (b) Smooth tube.
0 0.2 0.4 0.6 0.8 1.00
4
8
12
16
20
50 100 200
(P
/z)
F [
kPa/
m]
Vapor quality
R134a, Tsat
= 20 0C Microfin tube
G [kg/m2s]
a)
0 0.2 0.4 0.6 0.8 1.00
4
8
12
16
20
(P
/z)
F [
kPa/
m]
Vapor quality
R134a, Tsat
= 20 0C Smooth tube
G [kg/m2s]
50 100 200
b)
76
3.2.2 Influence of microfins
The frictional pressure drop in smooth and microfin tube at similar experimental
condition was compared to identify the effects of internal fins on pressure drop. The
result overlaid in Fig. 3.6, shows that the frictional pressure drops of microfin tube is
higher than those of smooth tube approximately 6% to 29%. This is due to the internal
geometry. Pressure drop penalty factor, the ratio of pressure drop between microfin and
smooth tube at the same condition, are presented in Fig. 3.7. Figure 3.7 shows that the
pressure drop penalty factor increases as vapor quality increases and mass flux has an
insignificant effect.
Fig. 3.6 Comparison of frictional pressure drop between smooth and microfin tubes
3.2.3 Influence of saturation temperature
In order to investigate the influence of saturation temperature on the frictional
pressure drop, experimental investigation was conducted by changing the saturation
temperature from 20 0C to 35 0C at mass flux 200 kg/m2s, as shown in Fig. 3.8. It was
found that the saturation temperature had a significant effect on frictional pressure
gradient which decreased with increasing saturation temperature. The reason is that the
0 0.2 0.4 0.6 0.8 1.00
4
8
12
16
20
Microfin tube
G [kg/m2s] 50 100 200
50 100 200
(P
/z)
F [
kPa/
m]
Vapor quality
Smooth tube
G [kg/m2s]
R134a, Tsat
= 20 0C
77
saturation temperature changes the viscosity as well as shear stress. The physical
explanation of these effects is same as with the multiport minichannels.
Fig. 3.7 Frictional pressure drop penalty factor
Fig. 3.8 Effects of saturation temperature on Frictional pressure drop.
0 0.2 0.4 0.6 0.8 1.01
1.2
1.4
1.6
1.8
2.0
50 100 200
Pre
ssur
e dr
op p
enal
ty f
acto
r
Vapor quality
G [kg/m2s]
0.0 0.2 0.4 0.6 0.8 1.00
4
8
12
16
20
20 30 35
(P
/z)
F [
kP
a/m
]
Vapor quality
Tsat
[0C]Smooth tube (d = 2.14 mm)
G = 200 kg/m2s
78
3.3 Conclusions
An adiabatic two-phase frictional pressure drop charecteristics of R134a in two
rectangular multiport minichannels with fins and without fin and microfin tube were
investigated experimentally for different mass velocity and saturation temperature. The
effects of mass velocity, vapor qualities, saturation temperature and channel geometry
on the frictional pressure drop were analyzed and discussed.
The main conclusions are as follows:
1. The experimental frictional pressure gradiants in both multiport minichannels
and microfin tube increase with mass velocitie and vapor quality and decrease
with saturation temperature.
2. The hydraulic diameter of the multiport minichannel has significant influence on
the frictional pressure gradients which increases with decreasing hydraulic
diameter of the minichannles.
3. The microfin tube has slightly influence on the frictional pressure gradients. The
frictional pressure drop of the microfin tube was higher than those of smooth
tube about 10-15%.
79
References
Collier, J. G., Thome, J. R., 1994. Convective Boiling and Condensation, Third edition,
Oxford University Press, Oxford, UK.
Hwang, Y. W., and Kim, M. S., 2006. The pressure drop in microtubes and the
correlation development, International Journal of Heat and Mass Transfer 49, 1804–
1812.
Jige, D., Inoue, N., Koyama, S., 2016. Condensation of refrigerants in a multiport tube
with rectangular minichannels, International Journal of Refrigeration 67, 202-213.
Kim, Y. J., Jang, J., Hrnjak, P. S., Kim, M. S., 2008. Adiabatic horizontal and vertical
pressure drop of carbon dioxide inside smooth and microfin tubes at low
temperatures, Journal of Heat Transfer 130, 111001-1-111001-10.
Pamitran, A. S., Choi, K. I., Oh, J. T., Hrnjak, P., 2010. Characteristics of two-phase
flow pattern transitions and pressure drop of five refrigerants in horizontal circular
small tubes, International Journal of Refrigeration 33, 578–588.
Park, C. Y., Hrnjak, P. S., 2007. CO2 and R410A flow boiling heat transfer, pressure
drop, and flow pattern at low temperatures in a horizontal smooth tube, International
Journal of Refrigeration 30, 166–178.
Revellin, R., Thome, J. R., 2007. Adiabatic two-phase frictional pressure drops in
microchannels, Experimental Thermal and Fluid Science 31, 673-685.
Sakamatapan, K., and Wongwises, S., 2014. Pressure drop during condensation of
R134a flowing inside a multiport minichannel. International Journal of Heat and
Mass Transfer 75, 31-39.
80
CHAPTER 4
Condensation Heat Transfer
The local heat transfer coefficient has been measured in horizontal rectangular
multiport minichannels and circular tube with and without fins during condensation of
R134a. The experiments have been conducted over the entire range of vapor quality at
mass flux range of 50 to 200 kg/m2s and saturation temperature between 20 to 35 0C.
The effect of different parameters on the condensation heat transfer coefficient has been
explored in this topic.
4.1 Condensation heat transfer in rectangular multiport minichannels
with and without fins
Many researchers’ already stated that the heat transfer mechanism during the
condensation process is strongly dependent on the flow pattern inside the channels.
Several experimental investigations were performed to developed information on the
flow patterns of condensing flow and the operating conditions (Soliman, 1986).
Therefore, to identify the flow pattern the present experimental data were overlaid on
two most widely used existing flow pattern map proposed by Scott (1964) and Taitel
and Dukler (1976) as illustrate in Fig. 4.1 and Fig. 4.2, respectively. Most of the present
experimental data points are lapse in the annular flow, annular-wavy and annular-slug
flow transition zone on modified Baker flow pattern map shown in Fig. 4.1, while few
data obtained at low vapor quality (x < 0.26) points fall into the slug and plug flow
region. In the Taitel and Dukler flow pattern map illustrate in Fig. 4.2, most of the
current data are fall in the annular flow region, although very few data obtained at low
vapor quality (x < 0.19) lapse into the intermittent flow region.
81
Fig. 4.1 Experimental data of condensation heat transfer spread on modified Baker two-
phase flow pattern map (Scott, 1964)
Fig. 4.2 Experimental data of condensation heat transfer overlaid on Taitel and Dukler
(1976) two-phase flow pattern map
10-3 10-2 10-1 100 101 102 103 104100
101
102
103
104
Multiport minichannel
Annular
10-3
10-2
10-1
100
101
Stratified Smooth
Bubbly
IntermittentStratified-Wavy
with fins without fin
Fr G
or
T
K
X
82
4.1.1 Effect of mass velocity and vapor quality
In order to investigate the effect of different parameters on heat transfer coefficient,
the local heat transfer coefficient of R134a in horizontal rectangular minichannels with
and without fins are measured and discussed as an average value over the entire length
of the test section. The experimental results were obtained for different mass fluxes
from 50 to 200 kg/m2s and at saturation temperature of 30 0C and 35 0C. Fig. 4.3 (a) and
Fig. 4.3 (b) illustrate the local heat transfer coefficient variation along the tube with
respect to the vapor quality, (1-x) of R134a in horizontal rectangular multiport
minichannels with and without fins at 35 0C saturation temperature for different mass
flux. For all mass fluxes and both the multiport minichannels with and without fins,
experimental results display that the average heat transfer coefficient decreases as the
condensation progresses.
The heat transfer coefficient decreases much fasters at high vapor quality (x > 0.5)
in both minichannels. The heat transfer coefficient decreases due to the increase of
thermal resistance of condensate and decrease of shear stress of the vapor and liquid
phase. Sakamatapan et al. (2013) observed the similar phenomenon. They explained the
mechanism as the velocity of the vapor and liquid phases is high at high vapor quality.
Therefore, the shear stress at the interface between the vapor and liquid film is higher
than that at low vapor quality. The shear stress is increases due to higher turbulence at
the interface between the vapor and liquid film, which lead to a corresponding increase
in the condensation heat transfer coefficient. Furthermore, as expected, the average heat
transfer coefficient significantly increases with mass flux in both minichannels
illustrates in Fig 4.3. The facts suggest that the condensation heat transfer is dominated
by the force convection as well as the shear stress. This effect is more important at low
vapor qualities. The tested range of vapor quality was 0.1 to 0.9. The vapor quality was
not reached higher than 0.9 for all mass fluxes. From the general theory, it is expected
that the heat transfer coefficient fall after higher vapor quality than 0.9, in that situation
the liquid film almost disappears and the flow is more similar to single vapor flow with
a decrease in heat transfer coefficient (Belchi, 2014).
83
Fig. 4.3 Effects of mass flux and vapor quality on average heat transfer coefficient: (a)
Minichannel with fins; (b) Minichannel without fins
4.1.2 Effect of saturation temperature
The influence of saturation temperature on the average heat transfer coefficient was
investigated by changing the saturation temperature at constant mass flux and heat flux.
Fig. 4.4 depicts the effect of saturation temperature on experimental average heat
transfer coefficient of R134a at mass flux of 150 kg/m2s. The experimental result
indicates that the average heat transfer coefficient is increase with decreasing saturation
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
200
50 100 150
Hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2 K
]
1-x
R134a, Tsat
= 35 0CMinichannel with fins G [kg/m2s]
a)
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
200
G [kg/m2s]Minichannel without fin
Hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2 K
]
1-x
50 100 150
R134a, Tsat
= 35 0C
b)
84
temperature. The reason is that the saturation temperature changes the system pressure
as well as the thermal and transport properties of refrigerant. The viscosity ratio and
density ratio increases (as mentioned in Table 4.1) with decreasing saturation
temperature which increases the shear stress. The surface tension and thermal
conductivity of liquid film also increases with decreasing saturation temperature as
shown in Table 4.1. Therefore, this occurrence makes the heat transfer coefficient
higher.
Fig. 4.4 Effect of saturation temperature on average heat transfer coefficient; (a)
Minichannels with fins; (b) Minichannels without fins.
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
30 35
Hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2 K
]
1-x
R134aG = 150 kg/m2s
Multiport minichannel with finsT
sat [0C]
a)
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
30 35
Hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2K
]
1-x
R134aG = 150 kg/m2s
Multiport minichannel without fin
Tsat
[0C]
b)
85
Table 4.1 Thermophysical properties of R134a (Lemmon et al. 2013)
Tsat
[0C]
ρl
[kg/m3]
ρv
[kg/m3]
l
v
µl
[µPa s]
µv
[µPa s]
l
v
σ
[mN/m]
kl
[W/mK]
30 1188.00 37.37 31.79 183.47 11.90 15.42 7.40 0.079
35 1168.10 43.22 27.02 172.33 12.12 14.21 6.76 0.076
4.1.3 Effect of minichannels diameter
The comparisons of average heat transfer coefficient were conducted between
multiport minichannels with and without fins of hydraulic diameters of 0.64 mm and
0.81 mm with same outer dimension and similar tested condition as depicts in Fig. 4.5.
At saturation temperature of 35 0C and mass flux of 50, 100, 150 and 200 kg/m2s,
respectively, results indicate (in Fig. 4.5) that heat transfer coefficient of rectangular
multiport minichannel with fins is higher than the rectangular multiport minichannel
without fin about average 39% at higher vaper quality (x > 0.3). According to Yang and
Webb (1996), the enhancement is attributed to the effect of surface tension drainage
force. The surface tension force acts to maintain a smaller film thickness on the groove
fin than exists on the surface of the smooth tube. At low vapor quality (x < 0.3), the
heat transfer coefficient for the multiport minichannels with fins is higher than of
multiport minichannel without fin about 10-15%. This trend is also supported by Yang
and Webb (1996).
The tube outer diameter, channel width and channel height in both tube are similar. Due
to the fins inside the channel, the tube hydraulic diameter is reduced. Because of the
fins inside the channel, the actual heat transfer surface area is increased. The
augmentation ratio, the ratio of actual heat transfer surface area between minichannel
with fins and without fin, is the main cause of heat transfer enhancement.
86
Fig. 4.5 Comparison of average heat transfer coefficient between multiport
minichannels with and without fins: (a) G = 50 kg/m2s; (b) G = 100 kg/m2s; (c) G = 150
kg/m2s; (d) G = 200 kg/m2s.
4.2 Condensation heat transfer in circular microfins and smooth tube
4.2.1 Effect of mass fluxes and vapor quality
Fig. 4.6 shows the average condensation heat transfer coefficient as a function of
vapor quality with variation of mass fluxes for the microfin and smooth tubes. As
expected, the heat transfer coefficient is decreased as condensation proceeded. Fig. 4.6
also showed that the heat transfer coefficient was significantly increased with mass
flux. These trends are usual in case of in tube condensation (Collier and Thome, 1994,
Ghiaasiaan, 2008). The heat transfer coefficient decreases because the vapor shear
stresses decreases and the thermal resistance of the condensate increases. If the mass
velocity or vapor quality increases the void fraction in a tube also increases. If the void
fraction increases, more surface will be exposed to vapor and liquid film become
thinner which yielding a high heat transfer coefficient (Collier and Thome, 1994, Kim,
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
with fins without fin
Hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2 K
]
1-x
R134a, Tsat
= 35 0C
G = 50 kg/m2s
Multiport minichannelsa)
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
with fins without fin
Hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2K
]
1-x
R134a, Tsat
= 35 0C
G = 100 kg/m2s
Multiport minichannelb)
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
with fins without fin
Hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2 K
]
1-x
R134a, Tsat
= 35 0C
G = 150 kg/m2s
Multiport minichannelc)
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
with fins without fin
Hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2 K
]
1-x
R134a, Tsat
= 35 0C Multiport minichannel
G = 200 kg/m2s
d)
87
2016). This enhancement is mainly due to the major effect of the contribution of forced
convection condensation heat transfer at the tube wall.
Fig. 4.6 Effects of mass flux and vapor quality on condensation heat transfer coefficient in:
(a) Microfin tube; (b) Smooth tube.
4.2.2 Effect of tube diameter
The comparison of measured heat transfer coefficients between smooth and microfin
tube has been done in this study and overlaid in Fig. 4.7.
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
G = 50 kg/m2s, q = 7 kW/m2
G = 100 kg/m2s, q = 12 kW/m2
G = 200 kg/m2s, q = 16 kW/m2
Hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2 K
]
1-x
Microfin tube (deq
= 2.68 mm)R134a, Tsat
= 30 0Ca)
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30
G = 50 kg/m2s, q = 7 kW/m2
G = 100 kg/m2s, q = 12 kW/m2
G = 200 kg/m2s, q = 16 kW/m2
Hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2 K
]
1-x
Smooth tube (di = 2.14 mm)R134a, T
sat = 30 0C
b)
88
Fig. 4.7 Condensation heat transfer coefficient of microfin tube compared with
condensation heat transfer coefficient of smooth tube.
0
5
10
15
20
25
30
q = 7 kW/m2
Tsat
= 30 0C Microfin tube (d
eq = 2.68 mm)
Smooth tube (di = 2.14 mm)
Hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2 K
]
G = 50 kg/m2s
R134a
0
5
10
15
20
25
Hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2K
] R134aT
sat = 30 0C
G = 100 kg/m2sq = 12 kW/m2
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
Hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2 K
]
1-x
R134aT
sat = 30 0C
G = 200 kg/m2sq = 16 kW/m2
89
It can be seen from Fig. 4.7 that the heat transfer coefficient for the microfin tube are
greater than those of smooth tube in the whole quality range about 2-68%.The reason is
that the surface tension effect on liquid drainage which formed a very thin liquid film on
the surface of microfin. Fig. 4.8 depicts the heat transfer enhancement factors varied with
mass fluxes and vapor quality. The heat transfer enhancement factor is defined as the ratio
of the heat transfer coefficient of the microfin tube to that of smooth tube at the same
condition. The heat transfer enhancement factors significantly increases with increasing
mass fluxes due to the contribution of forced convection condensation heat transfer as
mentioned earlier. With increasing the mass flux the turbulence created by fin grooves also
increased which enhance the heat transfer enhancement factor. This trend is fully
consistent with the Sapali and Patil (2010). In the case of low vapor quality region, the
heat transfer coefficient is almost same in both the smooth and microfin tube.
Fig. 4.8 Condensation heat transfer coefficient enhancement factor.
0 0.2 0.4 0.6 0.8 11
1.2
1.4
1.6
1.8
2.0
50 100 200
Hea
t tr
ansf
er e
nh
ance
men
t fa
cto
r
1-x
G [kg/m2s]
90
4.3 Conclusions
Condensation heat transfer characteristics were experimentally investigated inside
two horizontal rectangular multiport minichannels and microfin tube for different mass
velocity and saturation temperature. The effects of mass flux, vapor quality, saturation
temperature and channel diameter of the tube on heat transfer coefficient were
examined and discussed. Based on the experimental study, the main findings of the
present investigation can be summarized as follows:
1. The average heat transfer coefficient of R134a during condensation tended to
increases with increasing mass flux and vapor quality in both multiport
minichannels and microfin tube.
2. The saturation temperature has significant influence on heat transfer coefficient
which decreases with increasing the saturation temperature. The reason is the
thermal conductivity of liquid film which decreases with increasing saturation
temperature.
3. The heat transfer coefficient of rectangular multiport minichannel with fins is
approximately 10-39% higher than those of rectangular multiport minichannel
without fin for the same operating conditions due to the surface tension force.
4. The higher heat transfer coefficients were obtained in microfin tube then that of
smooth tube about 2-68%.
91
References
Belchi, E. A. L., 2014. Characterization of heat transfer and pressure drop in
condensation processes within minichannel tubes with last generation of
refrigeration fluids, PhD thesis.
Collier, J. G., Thome, J. R., 1994. Convective boiling and condensation, 3rd edn,
Oxford University Press, Oxford.
Ghiaasiaan, S. M., 2008. Two-phase flow, boiling and condensation, Cambridge
University Press, Cambridge.
Kim, N. H., 2016. Condensation heat transfer and pressure drop of R410A in a 7.0 mm
O.D. microfin tube at low mass fluxes, Heat Mass Transfer, doi 10.1007/s00231-
016-1789-2.
Lemmon, E.W., Huber, M.L., McLinden, M.O., 2013. Reference Fluid Thermodynamic
and Transport Properties-REFPROP, Version 9.1, NIST Standard Reference
Database 23, Gaithersburg, April.
Sakamatapan, K., Kaew-On, J., Dalkilic, A. S., Mahian, O., Wongwises, S., 2013.
Condensation heat transfer characteristics of R-134a flowing inside the multiport
minichannels, International Journal of Heat and Mass Transfer 64, 976-985.
Sapali, S. N., Patil, P. A., 2010. Heat transfer during condensation of HFC-134a and
R404A inside of a horizontal smooth and microfin tube, Experimental Thermal and
Fluid Science 34, 1133-1141.
Scott, D. S., 1964. Properties of cocurrent gas-liquid flow, Advances in Chemical
Engineering 4, 199-277.
92
Soliman, H. M., 1986. The mist-annular transition during condensation and its influence
on the heat transfer mechanism, International Journal of Multiphase flow 12, 277-
288.
Taitel, Y., Dukler, A. E., 1976. A model for predicting flow regime horizontal and near
horizontal gas-liquid flow, AIChE Journal 22, 47-55.
Yang, C. Y., Webb, R. L., 1996. Condensation of R12 in small hydraulic diameter
extruded aluminum tubes with and without micro-fins, International Journal of Heat
and Mass Transfer 39, 791-800.
93
CHAPTER 5
Comparison of two-phase frictional pressure drop
Accurate prediction of frictional pressure drop is an essential requirement for the design
of any heat exchanger. In the last sixty seven years, several theoretical models and
empirical correlation have been proposed for the pressure drop prediction. However, in
the following chapter the experimental data of frictional pressure drop for multiport
minichannels and microfins tube were compared against existing models available in
the open literature. The frictional pressure drop of rectangular multiport minichannels is
compared with fifteen models including homogeneous model developed for both
conventional and minichannels. Whereas, the frictional pressure drop of microfins tube
are compared with seven correlations developed for conventional channel smooth and
microfins tube. The 288 experimental data points are used for the comparison. The
criterion used for the evaluation is the mean absolute error (MAE) and average error
(AE), listed in Table 5.2, which are calculated using the following equations:
,pred ,exp
1 ,exp
1 NF F
i F
P PMAE
N P
(5.1)
,pred ,exp
1 ,exp
1 NF F
i F
P PAE
N P
(5.2)
Actually, the average error is used to identify either a correlation has an under-
prediction or over-prediction.
5.1 Models review and comparison of frictional pressure drop in
multiport minichannels with the well-known correlations
94
5.1.1 Models review
First of all, a bibliography research has been made to find the well-known and
renowned correlations available to calculate frictional pressure drop in rectangular
multiport minichannels.
5.1.1.1 Correlations developed for convensional channel
The following correlations were developed specially for frictional pressure drop
prediction in convensional tube.
5.1.1.1.1 Homogeneous model (Thome, 2006)
The homogeneous model assumes that the two phases to flow as a single phase
possessing mean fluid properties. It is charecterized by suitably averaged properties of
the liquid and vapor phase. The homogeneous model is also known as the friction factor
or fog flow model (Collier and Thome, 1994). By considering the homogeneous model,
the frictional pressure drop can be expressed as a function of the two phase friction
factor, tpf as:
22 tp
F h tp
f GP
z d
(5.3)
The two-phase friction factor can be expressed in terms of the two-phase Reynolds
number by the Blasius equation as follows:
0.25
16for 2000
0.079for 2000
tp
tp
tp
tp
tp
ReRe
f
ReRe
(5.4)
Thome (2006) suggested that the homogeneous model is not suitable for mass flux
less than 2000 kg/m2s and at low reduced pressure.
95
5.1.1.1.2 Lockhart and Martinelli correlation (1949)
The frictional pressure drop is typically predicted using separated flow models. The
Lockhart and Martinelli (1949) was proposed the first separated flow model to predict
the frictional pressure drop for isothermal two-phase flow and after that the separated
flow model has been continuously developed by many researchers. The separated flow
model considers the two-phase are artificially flow separately into two streams, namely
liquid and vapor. In this model, each stream is assumed to travel at a mean velocity.
The Lockhart and Martinelli (1949) method is the original method that predicted the
two-phase frictional pressure drop based on a two-phase multiplier for the liquid-phase
or the vapor-phase, respectively (Thome, 2006).
2l
F l
P P
z z
(5.5)
2v
F v
P P
z z
(5.6)
The liquid-phase and vapor-phase pressure gradiants are obtained from
222 1l
l h l
f G xP
z d
(5.7)
2 22 v
v h v
f G xP
z d
(5.8)
The single-phase friction factors of the liquid-phase, lf and vapor-phase, vf are
calculated as follows with their respective physical properties.
0.25
0.079l
l
fRe
(5.9)
0.25
0.079v
v
fRe
(5.10)
The corresponding two-phase multipliers for liquid and vapor phase are obtained
96
2
2
11 for 4000l l
tt tt
CRe
X X (5.11)
2 21 for 4000v tt tt lCX X Re (5.12)
where ttX is the Martinelli parameter in the turbulent flow regimes defined as
0.5 0.10.91 v l
tt
l v
xX
x
(5.13)
The value of C in Eqs. 5.11 and 5.12 mainly depends on the flow regimes. The
appropriate values of C are listed in Table 5.1.
Table 5.1 Appropriate values of C for Lockhart and Martinelli correlation
Liquid Vapor C
Turbulent Turbulent 20
Laminar Turbulent 12
Turbulent Laminar 10
Laminar Laminar 5
5.1.1.1.3 Friedel Correlation (1979)
The Friedel correlation (1979) is one of the most accurate two-phase frictional
pressure drop correlation. The correlation was obtained based on a two-phase multiplier
using a large database of two-phase frictional pressure drop consisted 25000 data points.
The database consists of air-water, air-oil and R12 as working fluids.
2lo
F lo
P P
z z
(5.14)
22 lo
lo h l
f GP
z d
(5.15)
97
0.2240.7822 2
0.045 0.035
3.24 11 l vo
lo
v lo
x x Hfx x
f Fr We
(5.16)
0.91 0.19 0.722
2, , 1h l v v
h tp tp v l l
G dGFr We H
gd
(5.17)
5.1.1.1.4 The Müller-Steinhagen and Heck correlation (1986)
Müller-Steinhagen and Heck (1986) proposed a two-phase frictional pressure drop
correlation by optimizing an empirical interpolation between all vapor flow and all
liquid flow. The authors checked the reliabilities of the correlation against a databank
containing 9300 data points of frictional pressure drop for various working fluids and
flow conditions. The database covered the diameter range of tube from 4 mm to 392
mm and working fluids of air-water, air-oil, hydrocarbon, R11, R12 and R22.
1/3 3(1 )F vo
P PE x x
z z
(5.18)
2lo vo lo
P P PE x
z z z
(5.19)
5.1.1.1.5 The Wang et al. correlation (1997)
Wang et al. (1997) developed a correlation based on a two-phase multiplier by
considering flow pattern for adiabatic frictional pressure drop of R22, R134a and
R401C. The Wang et al. (1997) correlation as follows:
For 200G kg/m2s
2l
F l
P P
z z
(5.20)
2
2
11l
C
X X (5.21)
2.15 5.1
6 0.128 0.9384.566 10 l llo
v v
vC X Re
v
(5.22)
98
For 200G kg/m2s
2v
F v
P P
z z
(5.23)
2 0.62 2.451 9.4 0.564v X X (5.24)
5.1.1.2 Correlations developed for minichannels
The following models were developed specially for friction pressure drop prediction
in minichannels.
5.1.1.2.1 The Mishima and Hibiki correlation (1996)
The authors proposed the correlation based on two-phase multiplier using the
Lockhart and Martinelli model. They modified the Chisholm’s parameter, C as a
dependable function of tube inner diameter.
2l
F l
P P
z z
(5.25)
2
2
11l
C
X X (5.26)
31921(1 )idC e (5.27)
5.1.1.2.2 The Lee and Lee correlation (2001)
The authors proposed a set of correlations to predict the two-phase frictional
pressure drop through horizontal rectangular minichannels. The correlation is the
Lockhart and Martinelli type. They modified the Chisholm’s parameter, C to take
account of the channel hydraulic diameter and the flow rates of the vapor and liquid.
8 1.317 0.719 0.5576.833 10ll loC Re (5.28)
0.4510.408tt loC Re (5.29)
2 0.7266.185 10lt loC Re (5.30)
99
0.1743.627tl loC Re (5.31)
where l lj
and
2l
l hd
(5.32)
5.1.1.2.3 The Koyama et al. correlation (2003)
Koyama et al (2003) developed a simple correlation based on the Mishima and
Hibiki correlation (1995). The authors modified the two-phase multiplier to takeing an
account of the surface tension effects as follows:
2v
F v
P P
z z
(5.33)
0.17
2 0.6 21 13.17 1 Bolv tt tt
v
e X X
(5.34)
2 ( )h l vd gBo
(5.35)
0.5 0.10.91 v l
tt
l v
xX
x
(5.36)
5.1.1.2.4 The Lee and Mudawar correlation (2005)
Lee and Mudawar (2005) proposed a correlation that incorporates the effects of
surface tension and liquid viscosity in the separated flow model as two-phase multiplier
for liquid-phase and vapor-phase. The authors were developed two separate correlations
for C based on the flow states of the liquid and vapor as follows:
For laminar flow of liquid and laminar flow of vapor
0.047 0.602.16vv lo loC Re We (5.37)
For laminar flow of liquid and turbulent flow of vapor
0.25 0.231.45vv lo loC Re We (5.38)
100
5.1.1.2.5 The Hwang and Kim correlation (2006)
Hwang and Kim (2006) developed the two-phase flow frictional pressure drop
correlation in the form of the Lockhart-Martinelli correlation. The authors included the
effect of the Reynolds number, surface tension and tube diameter in thire proposed
correlation. They developed the correlation based on their experimental data of R134a
in three circular minichannels with inner diameters of 0.244, 0.43 and 0.792 mm at
adiabatic condition. The correlation as follows:
2l
F l
P P
z z
(5.39)
2
2
11l
C
X X (5.40)
0.452 0.32 0.820.227 Rel confC X N (5.41)
2
( )conf
l v
dN
g
(5.42)
5.1.1.2.6 The Sun and Mishima correlation (2009)
The authors proposed a model based on 2092 experimental data points of two-phase
frictional pressure drop which were collected from 18 sources. The working fluid
includes R134a, R22, R410A, R407C, R404A, R123, R236ea, R245fa, R507, CO2,
water and air. The data points covered the hydraulic diameter ranges from 0.506 to 12
mm. Sun and Mishima (2009) modified Chisholm correlation which showed best
performance in the turbulent region.
2l
F l
P P
z z
(5.43)
For 2000 and 2000l vRe Re
2
2
11l
C
X X (5.44)
0.15326 1 1 exp
1000 0.27 0.8l
conf
ReC
N
(5.45)
101
For 2000 and 2000l vRe Re
2
1.19 2
11l
C
X X (5.46)
0.4 0.51
1.79 v
l
Re xC
Re x
(5.47)
5.1.1.2.7 The Zhang et al. correlation (2010)
This correlation was proposed by applying the artificial neural network based on
2201 experimental data points of 18 fluids collected from 13 sources. The databank
covered the hydraulic diameter ranges from 0.07 to 6.25 mm. Zhang et al. (2010)
modified the Mishima and Hibiki correlation and proposed the new Chisholm
parameter C for minichannel using the non-dimensional Laplace constant as follows:
2l
F l
P P
z z
(5.48)
2
2
11l
C
X X (5.49)
21 1 exp( 0.142 / )confC N (5.50)
5.1.1.2.8 The Li and Wu correlation (2010)
The authors presented a general correlation for adiabatic two-phase frictional
pressure drop in minichannels based on the collected database having 769 data points.
They collected those data points from the literature for both multi and single channel
configuration covering 12 fluids for a wide range of operational conditions and channel
hydraulic diameter from 0.148 to 3.25 mm. Li and Wu (2010) modified the Chisholm
parameter of two-phase multipliers by introducing the Bond number and the Reynolds
mumber as follows:
2l
F l
P P
z z
(5.51)
102
2
2
11l
C
X X (5.52)
For 1.5Bo
0.4511.9C Bo (5.53)
For 1.5 11Bo
0.560.5109.4 lC BoRe
(5.54)
where, 2
l v hg dBo
(5.55)
5.1.1.2.9 The Kim and Mudawar correlation (2012)
Kim and Mudawar (2012) proposed a universal approach to predict two-phase
frictional pressure drop in single and multiport minichannels having differents
geometrical configurations. They developed Lockhart and Martinelli type correlation
based on 7115 frictional pressure drop data points collected from 36 sources covering
17 working fluids, hydraulic diameters from 0.0695 to 6.22 mm, mass velicities from
4.0 to 8528 kg/m2s and reduced pressure pressures from 0.0052 to 0.91. The Chisholm
parameter, C of various combinations of Reynolds number, Weber number, Suratman
number and density ratio were developed for each of the four combinations of flow
regimes as follows:
2l
F l
P P
z z
(5.56)
where,
2
2
11l
C
X X (5.57)
/
/l
v
P zX
P z
(5.58)
103
222 1l
l l h
f G xP
z d
(5.59)
2 22 v
v v h
f G xP
z d
(5.60)
1
0.25
0.2
16 for 2000
0.079 for 2000 20000
0.046 for 20000
k k
k k k
k k
Re Re
f Re Re
Re Re
(5.61)
5.1.1.2.10 The Jige et al. correlation (2016)
The authors presented a new condensation frictional pressure drop correlation for
multiport tube. They proposed the correlation based on their measured experimental
data of rectangular multiport minichannels having 0.85 mm hydraulic diameter. In this
correlation, they considered the effect of channel geometry using the two-phase
multiplier and frictional pressure drop for a vapor phase with total flow. The correlation
is as follows:
2vo
F vo
P P
z z
(5.62)
where
22 vo
vo h v
f GP
z d
(5.63)
1.25 0.75
2 1.8 1.8 0.68 0.43(1 ) 0.65 (1 )v lo l vvo
l vo v l
fx x x x
f
(5.64)
The values of the friction factor of vapor phase and liquid phase are obtained by
1
0.2
for 1500
0.046for 1500
h
vh
v
vo
h
vh
v
GdC
Gd
fGd
Gd
(5.65)
104
1
0.2
for 1500
0.046for 1500
h
lh
l
lo
h
lh
l
GdC
Gd
fGd
Gd
(5.66)
The value of channel geometry constant, C1 is determined as follows:
1 16 for circular channelsC
2 3 4 51 24 1 1.355 1.947 1.701 0.956 0.254 for rectangular channelsC
5.1.2 Comparison of experimental frictional pressure drop of minichannels
with existing correlations
The present experimental data of frictional pressure drop were compared against the
existing well-known pressure drop correlations proposed by Homogeneous Model
(Thome, 2006), Lockhart and Martinelli (1949), Friedel (1979), Muller-Steinhagen and
Heck (1986), Mishima and Hibiki (1996), Wang et al. (1997), Lee and Lee (2001),
Koyama et al. (2003), Lee and Mudawar (2005), Hwang and Kim (2006), Sun and
Mishima (2009), Li and Wu (2010), Zhang et al.(2010), Kim and Mudawar (2012) and
Jige et al. (2016), as shown in Figs. 5.1(a)-5.1(l). The existing well-known pressure
drop correlations are already discussed above.
The correlation of Friedel (1979) and Muller-Steinhagen and Heck (1986) for
relatively large diameter circular tubes and Lockhart and Martinelli (1949), Sun and
Mishima (2009), Li and Wu (2010), Zhang et al. (2010) and Kim and Mudawar (2012)
for single and multiport minichannels were proposed based on a wide range of
consolidated databases.
105
Fig. 5.1 Comparison of frictional pressure drop with existing; (a) Homogeneous Model;
(b) Lockhart and Martinelli (1949) correlation; (c) Friedel (1979) correlation; (d)
Muller-Steinhagen and Heck (1986) correlation; (e) Mishina and Hibiki (1996); (f)
Wang et al. (1997); (g) Lee and Lee (2001); (h) Koyama et al. (2003); (i) Lee and
Mudawar (2005); (j) Hwang and Kim correlation; (k) Sun and Mishima (2009); (l) Li
and Wu (2010); (m) Zhang et al. (2010); (n) Kim and Mudawar (2012); and (o) Jige et
al. (2016) correlation.
100
101
102
100
101
102
50 100 150 200
(P
/z)
F, P
red
icte
d [
kP
a/m
]
(P/z)F, Experimental [kPa/m]
G [kg/m2s]Minichannel with fins
50 100 150 200
Homogeneous model
+30%
-30%
Minichannel without finG [kg/m2s]
a)
100 101 102
100
101
102
b)
(P
/z)
F, P
redic
ted [
kP
a/m
]
(P/z)F, Experimental [kPa/m]
G [kg/m2s] Minichannel without fin
-30%
+30%
50 100 150 200
G [kg/m2s] Minichannel with fins
Lockhart and Martinelli (1949)
50 100 150 200
106
Fig. 5.1- (continued)
100 101 102
100
101
102
(P
/z)
F, P
red
icte
d [
kP
a/m
]
(P/z)F, Experimental [kPa/m]
Minichannel with finsG [kg/m2s]
50 100 150 200
+30%
-30%
Minichannel without finG [kg/m2s]
50 100 150 200
Friedel (1979)c)
100 101 102
100
101
102
(P
/z)
F, P
redi
cted
[kP
a/m
]
(P/z)F, Experimental [kPa/m]
Minichannel with finsG [kg/m2s]
50 100 150 200
+30%
-30%
Minichannel without fin
50 100 150 200
G [kg/m2s]
Muller and Heck (1986)d)
100 101 102
100
101
102
50 100 150 200
50 100 150 200
(P
/z)
F, P
redic
ted [
kP
a/m
]
(P/z)F, Experimental [kPa/m]
Minichannel with finsG [kg/m2s]
+30%
-30%
Minichannel without finG [kg/m2s]
Mishima and Hibiki (1996)e)
107
Fig. 5.1- (continued)
100 101 102
100
101
102
50 100 150 200
50 100 150 200
(P
/z)
F, P
redic
ted [
kP
a/m
]
(P/z)F, Experimental [kPa/m]
G [kg/m2s]Minichannel with fins +30%
-30%
Minichannel without finG [kg/m2s]
Wang et al. (1997)f)
100
101
102
100
101
102
(P
/z)
F, P
redic
ted
[kP
a/m
]
(P/z)F, Experimental [kPa/m]
Minichannel with finsG [kg/m2s]
50 100 150 200
+30%
-30%
Minichannel without finG [kg/m2s]
50 100 150 200
Lee and Lee (2001)g)
100 101 102
100
101
102
(P
/z)
F,
Pre
dic
ted
[k
Pa/
m]
(P/z)F, Experimental [kPa/m]
Minichannel with finsG [kg/m2s]
50 100 150 200
+30%
-30%
Minichannel without finG [kg/m
2s]
50 100 150 200
Koyama et al. (2003)h)
108
Fig. 5.1- (continued)
100
101
102
100
101
102
(P
/z)
F, P
redic
ted
[kP
a/m
]
(P/z)F, Experimental [kPa/m]
Minichannel with finsG [kg/m2s]
50 100 150 200
Lee and Mudawar (2005)i)
+30%
-30%
50 100 150 200
G [kg/m2s] Minichannel without fin
100
101
102
100
101
102
(P
/z)
F, P
redic
ted
[kP
a/m
]
(P/z)F, Experimental [kPa/m]
Minichannel with finsG [kg/m2s]
50 100 150 200
+30%
-30%
Minichannel without finG [kg/m2s]
50 100 150 200
Hwang and Kim (2006)j)
100 101 102
100
101
102
(P
/z)
F, P
redic
ted [
kP
a/m
]
(P/z)F, Experimental [kPa/m]
G [kg/m2s] Minichannel without fin
50 100 150 200
Sun and Mishima (2009)
-30%
+30% Minichannel with finsG [kg/m2s]
50 100 150 200
k)
109
Fig. 5.1- (continued)
100 101 102
100
101
102
(P
/z)
F, P
redic
ted [
kP
a/m
]
(P/z)F, Experimental [kPa/m]
Li and Wu (2010)
50 100 150 200
G [kg/m2s] Minichannel without fin
-30%
+30%Minichannel with finsG [kg/m2s]
50 100 150 200
l)
100 101 102
100
101
102
Minichannel with fins
(P
/z)
F, P
redic
ted [
kP
a/m
]
G [kg/m2s] 50 100 150 200
+30%
-30%
Minichannel without finG [kg/m2s]
50 100 150 200
Zhang et al. (2010)
(P/z)F, Experimental [kPa/m]
m)
100 101 102
100
101
102
(P
/z)
F, P
redic
ted [
kP
a/m
]
(P/z)F, Experimental [kPa/m]
50 100 150 200
G [kg/m2s]Minichannel with fins +30%
-30%
Minichannel without finG [kg/m2s]
50 100 150 200
Kim and Mudawar (2012)n)
110
Fig. 5.1- (continued)
Lee and Lee (2001) and Hwang and Kim (2006) proposed the correlations based on
the experimental data of adiabatic flow in small diameter rectangular and circular tubes.
Whereas, the Koyama et al. (2003) and Jige et al. (2016) were developed the frictional
pressure drop correlations based on the experimental data on condensation flow in the
rectangular multiport minichannels.
The homogeneous model is enough accurate to predict experimental data of
rectangular multiport minichannels with fins as shown in Fig. 5.1 (a) with mean
absolute error 15.6%. But this model under-predicted the experimental data of
minichannels without fin, especially at mass velocity 50 and 200 kg/m2s.
The Lockhart and Martinelli (1949) correlation showed good prediction for
experimental data of minichannels with fins with 29.9% mean absolute error but
underestimated the experimental data of minichannels without fin with mean absolute
error 15.5%. The predicted results are presented in Fig. 5.1 (b).
The correlation of Friedel (1979) is compared with the present data and the results
are depicted in Fig. 5.1 (c). The correlation was consistently under-predicted the
experimental results of both minichannels with mean absolute error of 43%. The
discrepancy between experimental and predicted data may be due to the important
difference between the diameter considered by the authors and that studied in the
present study.
100 101 102
100
101
102
G [kg/m2s]
Minichannel without fin
50 100 150 200
50 100 150 200
(P
/z)
F, P
redic
ted [
kP
a/m
]
(P/z)F, Experimental [kPa/m]
Jige et al. (2016)
Minichannel with fins +30%
-30%
G [kg/m2s]
o)
111
As seen in Fig. 5.1 (d), the correlation of Muller-Steinhagen and Heck (1986)
correlation consistently over-estimated the present experimental data for both
minichannels with 40.2% mean absolute error. This correlation may be over-estimate
the experimental data because the diameter range considered by the authors. The
authors was developed the correlation for tubes diameter range from 4 -392 mm.
The comparison of present experimental results with the correlation of Mishima and
Hibiki (1996) is depicted in Fig. 5.1 (e). As seen in the figure, the correlation is highly
under-predicted present experimental results. The mean absolute error of prediction is
41.2%. The under-prediction may be because of Chisholm parameter that was
developed by the authors only based on the tube diameter for air-water flows.
As seen in Fig. 5.1 (f), the Wang et al. (1997) correlation is completely failed to
predict the present experimental data for both minichannels with fins and without fin.
The mean absolute error of the prediction is 56.1% as listed in Table 5.2. The
correlation is unable to predict the present experimental results because it was
developed for conventional circular tube.
The results of the comparison with the Lee and Lee (2001) correlation are presented
in Fig. 5.1 (g). The correlation had shown slightly under-prediction at low mass velocity
and slightly over-estimation at high mass velocity with mean absolute error 28.9 %.
Fig. 5.1 (h) presented comparison of present experimental results with the correlation of
Koyama et al. (2003). The correlation predicts the results very well with little under-
estimation at low mass velocity but mean absolute error of the comparison is within
15.4%.
The correlation of Lee and Mudawar (2005) is not able to predict present
experimental data correctly. The results of comparison are depicted in Fig. 5.1 (i). As
seen in figure, the model clearly overestimated and underestimated over the whole
range studied.
As seen in Fig. 5.1 (j) and (k), the Hwang and Kim (2006) and Sun and Mishima
(2009) correlations are predicted the experimental data accurately for high mass
velocity. Both the correlations, can predict experimental data of low mass velocity with
slightly under-estimation. The error of prediction increases with decreasing mass
velocity as show in Fig. 5.1 (j) and (k). The mean absolute errors of the comparison are
25.5% and 22.4%, respectively.
112
The Li and Wu (2010) correlation predicted the experimental data fairly good but
slightly under-predicts few data, especially at low mass flux for both minichannels with
mean absolute error 17.3%. The comparison is depicted in Fig. 5.1 (l).
The comparison of present experimental results with the correlation of Zhang et al.
(2010) is overlaid in Fig. 5.1 (m). The correlation showed good prediction at high mass
velocity for both minichannels but failed to predict the experimental data for low mass
velocity. This correlation predicted the experimental data with mean absolute error of
29.8%.
The correlation of Kim and Mudawar (2012) was compared with the present
experimental data of both minichannels. The predicted results are presented in Fig. 5.1
(n). The correlation greatly under-estimates present experimental data with mean
absolute error of 42.4%.
As seen in Fig. 5.1 (o), the correlation of Jige et al. (2016) accurate enough to
predict the present experimental but showed under-estimation at low frictional pressure
drop values which correspond to low mass velocity and high vapor quality. This
correlation can predict frictional pressure drop data with mean absolute error of 20.6%.
The compared results of each correlation are listed in Table 5.2 in the form of average
error (AE) and mean absolute error (MAE).
113
Table 5.2 Deviations of frictional pressure drop for multiport minichannels
Correlation
Minichannel
with fins
Minichannel
without fin All data
AE
(%)
MAE
(%)
AE
(%)
MAE
(%)
AE
(%)
MAE
(%)
Homogenous model 4.8 15.6 -20.8 22.1 -8.0 18.8
Lockhart and Martinelli (1949) -29.0 29.9 -11.2 15.5 -20.1 22.7
Friedel (1979) -36.6 41.8 -20.1 44.3 -28.3 43.0
Muller-Steinhagen and Heck (1986) 23.4 28.2 51.5 52.3 37.4 40.2
Mishima and Hibiki (1996) -22.4 32.3 -50.1 50.1 -36.2 41.2
Wang et al. (1997) -51.8 51.5 -60.5 60.5 -56.1 56.1
Lee and Lee (2001) 2.0 24.6 25.5 33.1 13.7 28.9
Koyama et al.(2003) -17.6 19.3 -7.9 11.6 -12.7 15.4
Lee and Mudawar (2005) -15.5 26.8 -31.2 35.1 -23.3 30.9
Hwang and Kim (2006) -35.0 35.0 -12.6 15.9 -23.8 25.5
Sun and Mishima (2009) -22.3 24.2 -19.2 20.6 -20.7 22.4
Zhang et al. (2010) 3.0 25.7 -33.9 33.9 -15.1 29.8
Li and Wu (2010) -18.5 21.1 -12.4 13.5 -15.4 17.3
Kim and Mudawar (2012) -50.4 51.7 -33.2 33.2 -41.8 42.4
Jige et al. (2016) 5.8 21.3 0.2 20.0 3.0 20.6
5.2 Models review and comparison of frictional pressure drop in
microfins tube with the well-known correlations
5.2.1 Models review
The experimental frictional pressure drop datapoints were compared with the
following models briefly reviewed here.
5.2.1.1 The Miyara et al. correlation (2000)
114
The authors proposed a frictional pressure drop correlation in the same manner of
Haraguchi et al. (1994) for herringbone microfin tube. The correlation was correlated
with the two-phase multiplier and Lockhart-Martinelli parameter as follows:
2v
F v
P P
z z
(5.67)
where
2 2
0.2
0.092
/v v i i v
P G x
z d Gxd
(5.68)
0.35
1/21.2 1.65 tt
v
i v l v
GX
gd
(5.69)
0.5 0.10.91 v l
tt
l v
xX
x
(5.70)
5.2.1.2 The Koyama and Yonemoto correlation (2006)
Koyama and Yonemoto (2006) developed the Lockhart-Martinelli type frictional
pressure drop correlation based on their experimenta data of 6.51 mm inner diameter
microfin tube, Miyara’s (2003) data and Haraguchi’s data. The correlation is as follows:
2v
F v
P P
z z
(5.71)
where,
2 22 v
v i v
f G xP
z d
(5.72)
0.2
0.046
/v
i v
fGd x
(5.73)
0.05 0.51 1.2v ttFr X (5.74)
i v l v
GFr
gd
(5.75)
115
5.2.1.3 The Müller-Steinhagen and Heck correlation (1986)
The authors developed a two-phase frictional pressure drop correlation for smooth
tube by optimizing an empirical interpolation between all vapor flow and all liquid flow.
The Müller-Steinhagen and Heck (1986) checked the reliabilities of the correlation
against a database containing 9300 data points of frictional pressure drop for various
working fluids and flow conditions. The database covered the diameter range of tube
from 4 mm to 392 mm and working fluids of air-water, air-oil, hydrocarbon, R11, R12
and R22. This correlation is given by:
1/3 3(1 )F vo
P PE x x
z z
(5.76)
where
2lo vo lo
P P PE x
z z z
(5.77)
22 vo
vo h v
f GP
z d
(5.78)
22 lo
lo h l
f GP
z d
(5.79)
5.2.1.4 The Goto et al. correlation (2001)
The correlation was developed by these authors utilizes a single-phase multiplier
based on vapor phase. They used their measured experimental frictional pressure drop
data for condensation and evaporation of R410A and R22 inside a convensional spiral
groove tube having 7.30 mm mean inned diameter. The following equation was
suggested by the authors:
2v
F v
P P
z z
(5.80)
where
22 ( )v
v h v
f GxP
z d
(5.81)
116
0.791 1.64v ttX (5.82)
4 0.53
0.20
2 0.21
3
1.47 10 for 2000 2600
0.046 for 2600 6500
1.23 10 for 6500 12700
9.20 10 for 12700<
v v
v vv
v v
v
Re Re
Re Ref
Re Re
Re
(5.83)
5.2.1.5 The Haraguchi et al. correlation (1994)
They proposed an empirical correlation for the local frictional pressure drop during
condensation of R22, R134a and R123 inside a horizontal smooth tube having 8.4 mm
inner diameter. The proposed the Lockhart-Martinelli type correlation as follows:
2v
F v
P P
z z
(5.84)
Where
2 2
0.2
0.092
/v v i i v
P G x
z d Gxd
(5.85)
0.75
0.35
0.51 0.5
( )v tt
h v l v
GX
gd
(5.86)
5.2.1.6 The Olivier et al. correlation (2004)
Olivier et al. (2004) proposed this correlation by modifiying the Carnavos
correlation (1980) to predict the frictional pressure drop of R22, R407C and R134a in
convensional smooth tube, helical and herringbone microfin tube during condensation.
The frictiona pressure drop was obtained by the product of the liquid-phase pressure
drop and two-phase multiplier as follows:
2l
F lo
P P
z z
(5.87)
where
117
2
1.655
7.2421.376l
ttX (5.88)
22 [ (1 )]lo
lo h l
f G xP
z d
(5.89)
0.5
0.750.2
20.046 1 sec
cosh
lo l
e h
d entf Re
d d
(5.90)
5.2.1.7 The Kedzierski and Goncalves correlation (1999)
The authors suggested using the Pierre’s semi-empirical equation to predict the
pressure drop. They proposed a correlation of friction factor prediction by regression
analysis based on the experimental data of microfin tube. This correlation was
developed as a dependable fuction of fin height, tube diameter and Reynolds number as
follows:
0 2
0i
i
F h
f v vPv v G
z d
(5.91)
Where
0.2111/ 4.16 532 /3 32.275 10 9.33 10 exp0.003
re d
r
ef Re
d
(5.92)
lvxh
g z
(5.93)
5.2.2 Comparison of experimental frictional pressure drop of microfins
tube
In order to validate the experimental procedure, the experimental frictional pressure
drops of the microfin tube were compared with the seven most widely used pressure
drop correlations proposed by Muller and Heck (1986), Haraguchi et al. (1993),
Kedzierski and Goncalves (1999), Miyara et al. (2000), Goto et al. (2001), Olivier et al.
(2004) and Koyama and Yonemoto (2006). The Muller and Heck (1986) correlation
118
was developed for smooth tube and other six correlations were developed for microfin
tube. The compared frictional pressure drop results of adiabatic pressure drop in the
microfin tube are shown in Table 5.3.
At mass flux 50 kg/m2s, the correlation of Haraguchi et al. (1993) and Miyara et al.
(2000) showed fairly good prediction and other correlations were greatly under
predicted. The Goto et al. (2001) correlation can predict the present experimental
friction pressure drop for mass flux 100 and 200 kg/m2s within an acceptable limit of
error as presented in Fig. 5.2 (b) and (c). Except the Kedzierski and Goncalves (1999)
correlation, other correlations can predict the present pressure drop of mass flux 100
kg/m2s within a certain limit of error. At mass flux 200 kg/m2s, all of the correlation,
except Goto et al. (2001) correlation, completely failed to predict the present data. The
average errors and mean absolute errors are listed in table 5.3.
Table 5.3 Average errors and Mean absolute errors of frictional pressure drop of
microfin tube
Correlation AE
(%)
MAE
(%)
Miyara et. al (2000) -27.2 24.7
Koyama and Yonemoto (2006) -20.0 30.4
Muller and Heck (1986) -39.7 44.1
Goto et al. (2001) -24.4 26.1
Haraguchi et al. (1993) -15.8 20.7
Olivier et al. (2004) -39.0 32.4
Kedzierski and Goncalves (1999) -35.2 30.8
119
Fig. 5.2 Frictional pressure drop of the microfin tube compared with existing
correlations: (a) G = 50 kg/m2s; (b) G = 100 kg/m2s; (c) G = 200 kg/m2s.
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30a) Experimental Miyara et al. (2000) Koyama and Yonemoto (2006) Muller and Heck (1986) Goto et al. (2001) Haraguchi et al. (1993) Olivier et al. (2004) Kedzierski and Goncalves (1999)
(P
/z)
F [
kP
a/m
]
Vapor quality
R134a, Tsat
= 20 0CMicrofin tube
G = 50 kg/m2s
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30b) Experimental Miyara et al. (2000) Koyama and Yonemoto (2006) Muller and Heck (1986) Goto et al. (2001) Haraguchi et al. (1993) Olivier et al. (2004) Kedzierski and Goncalves (1999)
(P
/z)
F [
kP
a/m
]
Vapor quality
G = 100 kg/m2sR134a, T
sat = 20 0C
Microfin tube
0 0.2 0.4 0.6 0.8 10
5
10
15
20
25
30 Experimental Miyara et al. (2000) Koyama and Yonemoto (2006) Muller and Heck (1986) Goto et al. (2001) Haraguchi et al. (1993) Olivier et al. (2004) Kedzierski and Goncalves (1999)
(P
/z)
F [
kP
a/m
]
Vapor quality
G = 200 kg/m2sR134a, T
sat = 20 0C
Microfin tubec)
120
5.3 Conclusions
For the comparison of experimental frictional pressure drop data, several of the most
widely used existing frictional pressure drop models are reviewed in this chapter. Some
convensional tubes models and other specially developed for minichchannels are
considered for the comparison of frictional pressure drop in rectangular multiport
minichannels. Five existing correlations those were developed for convensional
microfin tubes are also considered for the prediction of frictional pressure drop in
microfin tube. The experimental frictional pressure gradient was compared with those
reviewed correlations. Some correlations over-predicted, some are under-predicted and
few correlations captured the correct frictional pressure drop within the limits of
experimental error. All of the existing correlations were failed to capture the present
experimental frictional pressure drop with a high degree of accuracy.
121
References
Carnavos, T. C., 1980. Heat transfer performance of internally finned tubes in turbulent
flow, Heat transfer Engineering 1, 32-37.
Collier, J. G., Thome, J. R., 1994. Convective Boiling and Condensation, Third edition,
Oxford University Press, Oxford, UK.
Friedel, L., 1979. Improved friction pressure drop correlations for horizontal and
vertical two-phase pipe flow, in: European Two-phase Group Meeting, Ispra, Italy,
Paper E2.
Goto, M., Inoue, N., Ishiwatari, N., 2001. Condensation and evaporation heat transfer of
R410A inside internally grooved horizontal tubes. International Journal of
Refrigeration 24, 628-638.
Haraguchi H, Koyama S, Fujii T. Condensation of refrigerants HCFC22, HFC134a and
HCFC123 in a horizontal smooth tube (1st report, proposal of empirical expressions
for the local frictional pressure drop). Trans JSME (B) 1994;60(574):239–44 [in
Japanese].
Hwang, Y.W. and Kim, M.S., 2006. The pressure drop in microtubes and the
correlation development, International Journal of Heat and Mass Transfer 49, 1804–
1812.
Jige, D., Inoue, N., Koyama, S., 2016. Condensation of refrigerants in a multiport tube
with rectangular minichannels, International Journal of Refrigeration 67, 202-213.
Kedzierski, M.A., Goncalves, J.M., 1999. Horizontal convective condensation of
alternative refrigerants within a microfin tube, Journal of Enhanced Heat Transfer 6,
161-178.
122
Kim, S.M. and Mudawar, I., 2012. Universal approach to predicting two-phase
frictional pressure drop for adiabatic and condensing mini/micro-channel flows.
International Journal of Heat and Mass Transfer 55, 3246–3261.
Koyama, S., Kuwahara, K., Nakashita, K., 2003. Condensation of refrigerant in a
multiport channel, In: Proceedings of First International Microchannel and
Minichannels, ASME, 193-205.
Koyama, S., Yonemoto, R., 2006. Experimental study on condensation of pure
refrigerants in horizontal microfin tube-proposal of correlations for heat transfer
coefficient and frictional pressure drop, International Refrigeration and Air
Conditioning Conference, Purdue, R133.
Lee, H.J. and Lee, S.Y., 2001. Pressure drop correlations for two-phase flow within
horizontal rectangular channels with small heights, International Journal of
Multiphase Flow 27, 783–796.
Lee, J. and Mudawar, I., 2005. Two-phase flow in high-heat-flux micro-channel heat
sink for refrigeration cooling applications: Part I––pressure drop characteristics,
International Journal of Heat and Mass Transfer 48, 928–940.
Li, W. and Wu, Z., 2010. A general correlation for adiabatic two-phase pressure drop in
micro/mini-channels, International Journal of Heat and Mass Transfer 53, 2732–
2739.
Lockhart, R.W. and Martinelli, R.C., 1949. Proposed correlation of data for isothermal
two-phase, two-component flow in pipes, Chemical Engineering Progress 45, 39–
48.
Mishima, K., Hibiki, T., 1995. Effect of inner diameter on some characteristics of air-
water two-phase flows in capillary tubes, Transection of JSME (B) 61(589), 99–106
[in Japanese].
123
Mishima, M. and Hibiki, T., 1996. Some characteristics of air–water two-phase flow in
small diameter vertical tubes, Internal Journal of Multiphase Flow 22, 703–712.
Miyara, A., Otsubo, Y., Ohtsuka, S., Mizuta, Y., 2003. Effects of fin shape on
condensation in herringbone microfin tubes, International Journal of Refrigeration
26, 417-424.
Miyara, A., Nonaka, K., Taniguchi, M., 2000. Condensation heat transfer and flow
pattern inside a herringbone-type micro-type tube, International Journal of
Refrigeration 23, 141-152.
Müller-Steinhagen, H. and Heck, K., 1986. A simple frictional pressure drop correlation
for two-phase flow in pipes, Chemical Engineering Progress 20, 297–308.
Olivier, J. A., Liebenberg, L., Kedzierski, M. A., Meyer, J. P., 2004. Pressure drop
during condensation inside horizontal smooth, helical microfin, and herringbone
microfin tubes, Journal of Heat Transfer 126, 687-696.
Sun, L. and Mishima, K., 2009. Evaluation analysis of prediction methods for two-
phase flow pressure drop in mini-channels, Internal Journal of Multiphase Flow 35,
47–54.
Thome, J.R., 2006. Engineering Data Book III, Chapter 13th.
Wang, C. C., Chiang, C. S., Lu, D. C., 1997. Visual observation of two-phase flow
pattern of R22, R134a and R407C in a 6.5 mm smooth tube, Experimental Thermal
and Fluid Science 15, 395-405.
Zhang, W., Hibiki, T., Mishima, K., 2010. Correlations of two-phase frictional pressure
drop and void fraction in mini-channel, International Journal of Heat and Mass
Transfer 53, 453–465.
124
CHAPTER 6
Comparison of Condensation Heat transfer
For practical application such as design of compact and high performance heat
exchanger, accurate prediction of heat transfer coefficient is a crucial obligation. There
are several theoretical models and empirical correlations have been proposed by many
researchers in the last decade. However, due to the complexity of two-phase flow, it is
quite difficult to predict the experimental data accurately over a broad range of
operating conditions and parameter. In the following chapter, the experimental heat
transfer coefficients data were compared with ten widely used and renowned
correlations, which suggested for conventional tube, minichannels and microchannels.
The 213 experimental data points are used for the comparison. The criterion used for
the evaluation is the mean absolute error (MAE) and average error (AE), listed in Table
6.1, which are calculated using the following equations:
,pred ,exp
1 ,exp
1 Ntp tp
i tp
h hMAE
N h
(6.1)
,pred ,exp
1 ,exp
1 Ntp tp
i tp
h hAE
N h
(6.2)
Actually, the average error is used to identify either a correlation has an under-
prediction or over-prediction.
6.1 Models review and comparison of heat transfer coefficients in
minichannels with existing correlations
125
6.1.1 Models review
First of all, a bibliography research has been made to find the most widely used and
renowned correlations available to calculate condensation heat transfer coefficient in
rectangular multiport minichannels.
6.1.1.1 Correlations developed for conventional tube
The following correlations were developed specially for the condensation heat
transfer coefficient prediction in conventional tube.
6.1.1.1.1 The Shah correlation (1979)
The author presented a simple dimensionless model to predict the film condensation
heat transfer coefficient based on 474 experimental data points collected from the
literature. The data points includes water, R11, R12, R22, R113, ethanol, benzene,
methanol, toluene and trichloroethylene as working fluids during condensation in
horizontal, vertical and inclined tubes with ranges of diameters from 7 to 40 mm.
0.040.760.8
0.38
3.8 11tp l
r
x xh h x
p
(6.3)
0.8 0.40.023 ll l l
kh Re Pr
d
(6.4)
6.1.1.1.2 The Haraguchi et al. correlation (1994)
Haraguchi et al. (1994) developed an empirical correlation for the heat transfer
coefficient based on the turbulent liquid film theory and Nusselt’s theory. They used
their measured condensation heat transfer coefficients of R134a, R22 and R123 in an 8
mm diameter horizontal conventional smooth circular tube. This model includes the
effects vapor shear stress and gravity forces.
ltp
h
Nukh
d (6.5)
126
2 2FC GCNu Nu Nu (6.6)
where
0.77 0.80.0152 1 0.6 vFC l l
tt
Nu Re PrX
(6.7)
0.25
0.725 l lGC
Ga PrNu H
Ph
(6.8)
0.75
0.351 0.5( )
v tt
h v l v
GX
gd
(6.9)
0.1( ) 10 1 8.9 1H (6.10)
1
( / ) 0.4(1 ) /11 0.4 0.6
1 0.4(1 ) /v l v
l
x xx
x x x
(6.11)
6.1.1.1.3 The Dobson and Chato correlation (1998)
The authors proposed a two-phase heat transfer coefficient correlation in terms of
refrigerants properties and Martinelli parameter. They used experimental heat transfer
coefficient of the refrigerants R134a, R12, R22 and near-azeotropic blends of
R32/R125 in 50/50 percent and 60/40 percent compositions during condensation in
horizontal smooth circular tubes with diameters ranging from 3.14 to 7.04 mm. Donson
and Chato (1998) suggested the following model for annular flow regimes:
0.8 0.4
0.89
2.220.023 1 l
tp l l
tt h
kh Re Pr
X d
(6.12)
6.1.1.2 Correlations developed for minichannels and microchannels
The following models were developed specially for the condensation heat transfer
coefficient prediction in minichannels and microchannels.
6.1.1.2.1 The Wang et al. correlation (2002)
127
Two correlations, each representing the physics of the specific phase distribution
was proposed by these authors. The first one is for the annular flow based on the
frictional multiplier and dimensionless boundary layer temperature. The second one is
for stratified flow. For stratified flow, the film wise condensation and single-phase
forced convective heat transfer models were combined with straightforward void
fraction weighting. They developed this model based on their experimental local
convective heat transfer and flow regime measurements of R134a during condensation
inside a horizontal rectangular multiport minichannels of 1.46 mm hydraulic diameter.
Heat transfer correlation for annular flow regime:
1.6650.6792 0.2208
2
1.376 80.0274 tt
annular l l
tt
XNu Pr Re x
X
(6.13)
Heat transfer correlation for stratified flow regime:
1stratified film convectionNu Nu Nu (6.14)
Where
12/3
11 v
l
x
x
(6.15)
1/43
0.555 lv l l v hfilm
l l sat wall
gh dNu
k T T
(6.16)
0.8 0.40.023convection l lNu Re Pr (6.17)
Heat transfer correlation for combined flow regime:
ltp
h
Nukh
d (6.18)
1annular annular annular stratifiedNu f Nu f Nu (6.19)
Where
128
in transition
annular
in out
x xf
x x
(6.20)
6.1.1.2.2 The Koyama et al. correlation (2003)
The authors proposed this model using the experimental data of R134a during
condensation in two different multiport extruded minichannels having 8 channels with
1.11 mm hydraulic diameter and 19 channels with 0.8 mm hydraulic diameter. They
modified the Haraguchi et al. (1994) correlation by replacing two-phase multiplier with
Mishima and Hibiki (1995) as follows:
ltp
h
Nukh
d (6.21)
2 2FC GCNu Nu Nu (6.4)
where
0.77 0.80.0152 1 0.6 vFC l l
tt
Nu Re PrX
(6.22)
1/4
0.725 l lGC
Ga PrNu H
Ph
(6.23)
0.3192 21 21 1 hdv tt tte X X (6.24)
0.1 4( ) 10 1 1 1.7 10 1loH Re
(6.25)
1
( / ) 0.4(1 ) /11 0.4 0.6
1 0.4(1 ) /v l v
l
x xx
x x x
(6.26)
3 2
2h l
l
gdGa
(6.27)
l sat wi
lv
Cp T TPh
h
(6.28)
1,h h
l lo
l l
G x d GdRe Re
(6.29)
129
6.1.1.2.3 The Park et al. correlation (2011)
The Perk et al. modified the Koyama et al. correlation based on their experimental
data of R1234ze(E), R134a and R236fa during condensation in multiport minichannel
of 1.45 mm hydraulic diameter.
The modified equations are:
1.37 0.70.0055 vFC l l
tt
Nu Pr ReX
(6.30)
0.25
0.850.746(1 ) ( )Bo l l lGC
Ga PrNu e H
Ph
(6.31)
They followed Koyama et al. (2003) for other equations.
6.1.1.2.4 The Bohdal et al. correlation (2012)
The authors proposed this correlation with the use of mathematical statistics
principles. They selected the model’s parameter by quasi-Newton and simplex
methods. To develop the correlation, the authors used their own experimental data of
R134a, R407C and R404A during condensation in 9 circular minichannels with internal
diameters of 0.31, 0.45, 0.64, 0.98, 1.40, 1.60, 1.94, 2.30 and 3.30 mm, respectively.
0.266
0.258 0.495 0.28825.0841
ltp l l r
h
kxh Re Pr p
- x d
(6.32)
6.1.1.2.5 The Kim and Mudawar correlation (2013)
Kim and Mudawar (2013) proposed a universal approach to predict the heat transfer
coefficient during condensation in minichannels based on a consolidated databank
consisting of 4045 data points. They collected those data points from 28 sources. The
databank consists of data points of 17 different working fluids and single and multiport
minichannels covering hydraulic diameters from 0.424 to 6.22 mm.
130
0.69 0.34 0.2
0.50.69 0.34 2 7 0.38 1.39 2 0.2
0.048 / for > 7
(0.048 / ) (3.2 10 ) for 7
l l v tt tttp h
l l l v tt l vo tt
Re Pr X We Xh d
k Re Pr X Re Su We X
(6.33)
where,
0.64 0.3 0.039 0.4
0.79 0.157 2 0.084 0.3 0.039 0.4
2.45 / [ (1 1.09 ) ] for 1250
0.85 [( / ) ( / )] / [ (1 1.09 ) ] for 1250v vo tt l
v tt v l l v vo tt l
Re Su X ReWe
Re X Su X Re
--
-------------------------------------------------------------------------------------------------- (6.34)
2 21v CX X (6.35)
2 2(1 ) /l l v vX f v x f v x (6.36)
1
0.25
1
16 for 2000
0.079 for 2000 20000
0.046 for 20000
p p
p p p
p p
Re Re
f Re Re
Re Re
(6.37)
where the subscript p denotes l or v for liquid-phase and vapor-phase, respectively.
0.03 0.1 0.35
4 0.17 0.5 0.14
0.59 0.19 0.36
5 0.44 0.5 0.48
0.39 ( / ) if 2000and 2000
8.7 10 ( / ) if 2000and 2000
0.0015 ( / ) if 2000and 2000
3.5 10 ( / ) if
lo vo l v l v
lo vo l v l v
lo vo l v l v
lo vo l v
Re Su Re Re
Re Su Re ReC
Re Su Re Re
Re Su Re
2000and 2000l vRe
(6.38)
2
1, , ,hv h h h
vo lo l v
v l l v
Gd xd Gd Gd xSu Re Re Re
(6.39)
6.1.1.2.6 The Shah correlation (2016)
The author presented a correlation for heat transfer during condensation in
horizontal minichannels based on a database contained 1017 data points collected from
31 sources. The collected database covered 13 working fluids and single and multiport
minichannel with different shape of hydraulic diameter ranges from 0.10 to 2.8 mm.
Shah (2016) suggested the following equations:
131
0.62
1.249 1
if 100and 0.98( 0.263)
if 20and 0.95(1.254 2.27 )
if neither of the above conditions is satisfied
l vo v
tp N vo v
l N
h We J Z
h h We J Z
h h
(6.40)
where,
0.3685 0.2363 2.144
0.817 0.11 1.128 1l l vl lo l
v v l
h h x Pr
(6.41)
0.8 0.40.023 llo lo l
h
kh Re Pr
d
(6.42)
31/3
21.32 l l v l
N lo
l
g kh Re
(6.43)
2h
vo
v
G dWe
(6.44)
v
h v l v
xGJ
gd
(6.45)
0.8
0.4 1
1rZ p
x
(6.46)
6.1.1.2.7 The Jige et al. correlation (2016)
This model was developed for predicting heat transfer coefficient during
condensation in rectangular multiport minichannels considering the flow patterns,
effects of vapor shear stress and surface tension. The authors used their own
experimental condensation heat transfer data of refrigerants R134a, R32, R1234ze(E),
and R410A in a horizontal rectangular multiport minichannels with hydraulic diameter
of 0.85 mm. The considered the annular flow regimes for high vapor quality region and
intermittent flow regimes for low vapor quality region.
The heat transfer for intermittent flow was obtained by using the correlation of
forced single-phase liquid flow as follows:
132
2/3
2 3
10002
for 2000
1 12.7 12
8.23(1 1.891 2.220 0.894 ) for 2000
ll l
l
L ll
l
fRe Pr
ReNu f
Pr
Re
(6.47)
The heat transfer for annular flow regimes was obtained by combining the effects of
the vapor shear stress and surface tension using the same function form of the
Haraguchi et al. (1994) correlation, which considered the effects of the vapor shear
stress and gravity.
3 3 1/3, ,( )A A F A SNu Nu Nu (6.48)
where,
0.4 0.3 0.5, 0.6 0.06
1vo l
A F l l l vo
v
Nu Re Pr Re fx
(6.49)
0.25
, 0.51 l h lvA S
l l R wi
d hNu
k T T
(6.50)
Two-phase multiplier:
1.25 0.75
1.8 1.431.8 0.681 0.65 1l lo l vvo
v vo v l
fx x x x
f
(6.51)
Friction factor for vapor-phase:
0.2
if 1500
0.046if 1500
h
vh
v
vo
h
vh
v
Gd
Gd
fGd
Gd
(6.52)
133
Friction factor for liquid-phase:
0.2
if 1500
0.046if 1500
h
lh
l
lo
h
lh
l
Gd
Gd
fGd
Gd
(6.53)
where is the channel geometry constant which was obtained by
2 3 4
16 for Circular channels
24(1 1.355 1.947 1.701 0.956 ) for Rectangular channels
(6.54)
Finally, the heat transfer during condensation in rectangular multiport minichannels was
calculated by:
1tp h
A L
l
h dNu Nu Nu
k (6.55)
Where the void fraction is calculated by the homogeneous model as:
1 v
l
x
x x
(6.56)
6.1.2 Comparison with existing correlations
In the present experimental study, the average heat transfer coefficients in multiport
minichannels were compared against correlations discussed above.
The Shah (1979) correlation greatly over-predicted the experimental data for both
minichannels except few data for x > 0.7 as stated in Fig. 6.1 (a). This is because the
correlation was developed for conventional circular tube. Although, the Haraguchi et al.
(1994) correlation was developed for conventional circular tube but the correlation
predicted present data relatively good for mass fluxes 200 and 150 kg/m2s as shown in
Fig. 6.1 (b) and it failed to captured the data for low mass fluxes. Fig. 6.1 (c) and Fig.
6.1 (d), respectively shown that the correlation of Dobson and Chato (1998) and Wang
134
et al. (2002) consistently underestimated the present experimental data for both test
section. The Dobson and Chato (1998) and Wang et al. (2002) correlations were
proposed for conventional tube and minichannel.
The correlation of Koyama et al. (2003) and Park et al. (2011) predicted better but
slightly under predicted the present experimental data for both test section as depicts in
Fig. 6.1 (e) and 6.1 (f), respectively. They developed their correlations by modifying
Haraguchi et al. (1994) correlation for rectangular minichannels. As stated in Fig. 6.1
(g), the Bohdal et al. (2012) correlation failed to captured the present experimental data
for mass fluxes 50-150 kg/m2s but predicted well data for mass flus 200 kg/m2s.
According to Fig. 6.1 (h)-6.1 (j), the correlation of Kim and Mudawar (2013), Jige
et al. (2016) and Shah (2016) provides comparatively good prediction but the accuracy
slightly deteriorated for few data. A detailed comparison of average error and mean
absolute error are summarized in Table 6.1.
Table 6.1 Deviations of Heat transfer coefficients during condensation
Correlation
Minichannel
with fins
Minichannel
without fin All data
AE
(%)
MAE
(%)
AE
(%)
MAE
(%)
AE
(%)
MAE
(%)
Shah (1979) 63.0 63.1 81.8 81.9 72.4 72.5
Haraguchi et al.
(1994) 11.28 27.56 16.9 30.9 14.0 29.3
Dobson and Chato
(1998) -27.8 30.1 -23.8 26.2 -25.8 28.1
Wang et al. (2002) -44.0 42.8 -51.2 48.5 -47.6 45.6
Koyama et al. (2003) -34.35 34.1 -24.7 27.7 -29.5 30.9
Park et al. (2011) -42.5 40.5 -35.7 35.8 -39.1 38.1
Bohdal et al. (2012) 30.2 40.4 28.0 36.2 29.1 38.3
Kim and Mudawar
(2013) 3.2 30.9 5.0 25.7 4.1 28.3
Shah (2016) -23.1 28.2 2.8 26.0 -10.1 27.1
Jige et al. (2016) -6.23 30.1 -19.0 28.2 -12.6 29.1
135
Fig. 6.1 Comparison of experimental average heat transfer coefficient with existing; a)
Shah (1979); b) Haraguchi et al. (1994); c) Dobson and Chato (1998); d) Wang et al.
(2002); e) Koyama et al. (2003); f) Park et al. (2011); g) Bohdal et al. (2012); h) Kim
and Mudawar (2013); i) Jige et al. (2016); and j) Shah (2016) correlation.
100 101 102
100
101
102
with fins without fin
G [kg/m2s]
Shah (1979)
50 100 150 200
50 100 150 200
Pre
d. hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2 K
]
Expt. heat transfer coefficient [kW/m2K]
Multiport minichannels
-30%+30%
a)
100 101 102
100
101
102b)
50 100 150 200
50 100 150 200
Pre
d. hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2 K
]
Expt. heat transfer coefficient [kW/m2K]
G [kg/m2s]Multiport minichannels with fins without fin
Haraguchi et al. (1994)
-30%+30%
136
Fig. 6.1 – (continued)
100 101 102
100
101
102c)
50 100 150 200
50 100150 200
Pre
d. hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2 K
]
Expt. heat transfer coefficient [kW/m2K]
G [kg/m2s]Multiport minichannels with fins without fin
Dobson and Chato (1998)
-30%+30%
100
101
102
100
101
102
d)
-30%+30%
50 100 150 200
50 100 150 200
Pre
d. hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2 K
]
Expt. heat transfer coefficient [kW/m2K]
Wang et al. (2002)
G [kg/m2s]Multiport minichannels with fins without fin
100
101
102
100
101
102
e)
50 100 150 200
50 100 150 200
Pre
d.
hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2 K
]
Expt. heat transfer coefficient [kW/m2K]
G [kg/m2s]Multiport minichannels with fins without fin
Koyama et al. (2003)
-30%+30%
137
Fig. 6.1 – (continued)
100 101 102
100
101
102f)
50 100 150 200
50 100 150 200
Pre
d. hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2K
]
Expt. heat transfer coefficient [kW/m2K]
Park et al. (2011)
G [kg/m2s]Multiport minichannels with fins without fin
-30%+30%
100
101
102
100
101
102
50 100 150 200
50 100 150 200
50 100 150 200P
red
. h
eat
tran
sfer
co
effi
cien
t [k
W/m
2 K]
Expt. heat transfer coefficient [kW/m2K]
Bohdal et al. (2012)
Multiport minichannels G [kg/m2s]
with fins without fin
-30%+30%
g)
100
101
102
100
101
102
50 100 150 200
50 100 150 200P
red. hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2 K
]
Expt. heat transfer coefficient [kW/m2K]
Kim and Mudawar (2013)
Multiport minichannels G [kg/m2s]
with fins without fin
-30%+30%
h)
138
Fig. 6.1- (continued)
100
101
102
100
101
102
50 100 150 200
50 100 150 200
Pre
d. hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2 K
]
Expt. heat transfer coefficient [kW/m2K]
G [kg/m2s]Multiport minichannels with fins without fin
Jige et al. (2016)
-30%+30%
i)
100
101
102
100
101
102
50 100 150 200
50 100 150 200
Pre
d. h
eat
tran
sfer
coe
ffic
ient
[kW
/m2K
]
Expt. heat transfer coefficient [kW/m2K]
Shah (2016)
Multiport minichannels G [kg/m2s]
with fins without fin
-30%+30%
j)
139
6.2 Comparison of condensation heat transfer coefficients in microfin
tube with existing correlations
The present experimental condensation heat transfer coefficient data on the microfin
tube were compared with five widely used available correlations of Koyama and
Yonemoto, 2006; Kedzierski and Goncalves, 1999; Carnavos, 1980; Cavallini et al.,
1999; and Goto et al, 2003, respectively that were particularly developed for predicting
heat transfer coefficient in microfin tube. The existing condensation heat transfer
correlations are listed in Table 6.2. The compared errors and results of the correlations
are stated in Table 6.3 and Fig. 6.2, respectively.
Table 6.2 Condensation heat transfer correlations for microfin tubes
Author(s) Correlation Remarks
Carnavos
(1980)
0.1 0.5
30.8 0.40.023 sec
h
l
af nl l
nf a
hdNu
k
A ANu Re Pr
A A
dh = 3.91-22.7
mm, air, water,
ethylene glycol-
water, Horizontal
Cavallini et al.
(1999)
tp t
l
h dNu
k
0.260.8 0.34 20.05 eq l W vNu Re Pr Rx Bo Fr
Where
0.5
4 1 l
v
eq
t l
G x x
Red
l Pll
l
CPr
k
2vo
v
r
uFr
gd
8
l rW
eg dBo
n
di = 6.14-15.87
mm, Pure
refrigerant,
azeotropic and
zeotropic
refrigerant
mixtures, 7
working fluids,
Horizontal
microfin tubes,
300 data points
140
Table 6.2 – (continued)
2 1 sin
2
cos 12
cos
r
x
en
d
R
Kedzierski
and
Goncalves
(1999)
ltp
h
Nukh
d
0.235 0.308 2.7084.94 xl l vNu Re Pr S
Where
2 21.16 0.887
10log
x x
cr cr
p p
p p
v lv
v vS
v
1v lv xv x v
d = 3.14-7.04 mm,
R134a, R124, R32,
R410A (R32/R125,
50/50% mass),
Horizontal
microfins tube
Goto et al.
(2003)
ltp
h
Nukh
d
2 2( FC NCNu Nu Nu
Where
0.25
0.25
( )0.725 l
NC
A l
Ga PrHNu
Ph
0.1 0.1
0.70.7431
v lFC v l
tt v
xNu f Re
X x
4 0.53
0.20
3 0.21
3
1.47 10 for 2000 2600
0.046 for 2600 6500
1.23 10 for 6500 12700
9.20 10 for 12700<
v v
v vv
v v
v
Re Re
Re Ref
Re Re
Re
0.791.0 1.64v ttX
dm = 7.18, 7.22,
7.27, 7.30 mm,
R410A, R22,
horizontal,
microfins tubes
141
Table 6.2 – (continued)
Koyama and
Yonemoto
(2006)
ltp
i
Nukh
d
2 2( FC NCNu Nu Nu
0.1
0.5 0.52.121
lFC v v l l
v
xNu f Re Pr
x
0.25
0.5 0.1
( )1.98 l
NC
A l
Ga PrHNu
Bo Ph
Where
l v iP t gdBo
2 3
2l i
l
g dGa
Pl sat wil
lv
C T TPh
h
0.05 0.51 1.2v ttFr X
v l v i
GFr
gd
0.5
0.750.2
0.046
sec
v
af
v
nf
fA
ReA
0.110 1 8.9 1H
di = 6.25-8.37 mm,
11 microfins tubes.
R22, R134a, R123,
142
Table 6.3 Average errors and Mean absolute errors of condensation heat transfer coefficient in microfin tube.
Correlation AE
(%)
MAE
(%)
Carnavos (1980) -85.3 80.8
Cavallini et al. (1999) -26.5 26.9
Kedzierski and Goncalves (1999) -31.8 32.1
Goto et al. (2003) -36.0 34.5
Koyama and Yonemoto (2006) -18.8 24.8
The Carnavos (1980) correlation greatly underestimated the present data as depict in
Fig. 6.2 (a) with mean average error 80%. The correlations of Koyama and Yonemoto
(2006) and Goto et al. (2003) can predict accurately data only for mass flux 100 kg/m2s
and 50 kg/m2s as stated in Fig. 6.2 (e) and (d), respectively. But their correlations
slightly under predicted others data as overlaid in Fig. 6.2 (e) and (d). The Kedzierski
and Goncalves (1999) correlation also slightly underestimated the present experimental
data with mean average error 32.1% as shown in Fig. 6.2 (c).
The Cavallini et al. (1999) correlation showed the best prediction with mean
absolute errors of 26.9%. Cavallini et al. (1999) model can predict present experimental
data accurately for mass flux 100 kg/m2s and 200 kg/m2s but failed to predict data for
mass flux 50 kg/m2s as depicted in Fig. 6.2 (b). Poor prediction by existing correlations
may be attributed due to the lack of low mass flux data in the consideration database
during correlation development.
143
Fig. 6.2 Condensation heat transfer coefficient of microfin tube compared with existing
correlations; (a) Carnavos (1980); (b) Cavallini et al. (1999); (c) Kedzierski and
Goncalves (1999); (d) Goto et al. (2003); (e) Koyama and Yonemoto (2006).
100 101 102
100
101
102
a)
Pre
d. H
eat
tran
sfer
coef
fici
ent
[kW
/m2 K
]
Expt. Heat transfer coefficient [kW/m2K]
G [kg/m2s 50 100 200
+30%
-30%
Carnavos (1980)
100 101 102
100
101
102
b)
Pre
d. H
eat
tran
sfer
coef
fici
ent
[kW
/m2 K
]
Expt. Heat transfer coefficient [kW/m2K]
Cavallini et al. (1999)
50 100 200
G [kg/m2s +30%
-30%
100 101 102
100
101
102
c)
Pre
d. H
eat
tran
sfer
coef
fici
ent
[kW
/m2K
]
Expt. Heat transfer coefficient [kW/m2K]
50 100 200
G [kg/m2s
Kedzierski and Goncalves (1999)
+30%
-30%
100
101
102
100
101
102
d)
Pre
d. H
eat
tran
sfer
coef
fici
ent
[kW
/m2 K
]
Expt. Heat transfer coefficient [kW/m2K]
G [kg/m2s 50 100 200
+30%
-30%
Goto et al. (2003)
100 101 102
100
101
102
50 100 200
Pre
d. H
eat
tran
sfer
coef
fici
ent
[kW
/m2 K
]
Expt. Heat transfer coefficient [kW/m2K]
G [kg/m2s
Koyama and Yonemoto (2006)
+30%
-30%
e)
144
6.3 Conclusions
Ten most widely used well-known correlations that were developed for the
conventional tube and minichannels and five correlations for microfin tubes are
reviewed and compared with experimental heat transfer coefficients, respectively.
Among them, some correlations over-predicted, some are under-predicted and few
correlations captured the correct heat transfer coefficient within the limits of
experimental error. All of the existing correlations were failed to capture the present
experimental heat transfer coefficient within a high degree of accuracy.
145
References
Bohdal, T., Charun, H., Sikora, M., 2012. Heat transfer during condensation of
refrigerants in tubular minichannels, Archives of Thermodynamics 33 (2), 3-22.
Carnavos, T. C., 1980. Heat transfer performance of internally finned tubes in turbulent
flow, Heat transfer Engineering 1, 32-37.
Cavallini, A., Del Col, D., Doretti, L., Longo, G.A., Rossetto, L., 1999. A new
computational procedure for heat transfer and pressure drop during refrigerant
condensation inside enhanced tubes, Journal of Enhanced Heat Transfer 6, 441–456.
Dobson, M. K., Chato, J. C., 1998. Condensation in smooth horizontal tubes, Journal of
Heat Transfer 120, 192-213.
Goto, M., Inoue, N., Yonemoto, R., 2003. Condensation heat transfer of R410A inside
internally grooved horizontal tubes, International Journal of Refrigeration 26, 410–
416.
Haraguchi, H., Koyama, S., Fujii, T., 1994. Condensation of refrigerants HCFC 22,
HFC 134a and HCFC 123 in a horizontal smooth tube (2nd report, proposals of
empirical expressions for the local heat transfer coefficient) Trans. JSME 60, 245-
252 (in Japanese).
Kedzierski, M.A., Goncalves, J.M., 1999. Horizontal convective condensation of
alternative refrigerants within a microfin tube, Journal of Enhanced Heat Transfer 6,
161-178.
Kim, S. M., Mudawar, I., 2013. Universal approach to predicting heat transfer
coefficient for condensing mini/micro-channel flow, International Journal of Heat
and Mass Transfer 56, 238-250.
146
Koyama, S., Kuwahara, K., Nakashita, K., Yamamoto, K., 2003. An experimental study
on condensation of refrigerant R134a in a multi-port extruded tube, International
Journal of Refrigeration 26, 425-432.
Koyama, S., Yonemoto, R., 2006. Experimental study on condensation of pure
refrigerants in horizontal microfin tube-proposal of correlations for heat transfer
coefficient and frictional pressure drop, International Refrigeration and Air
Conditioning Conference, Purdue, R133.
Mishima, K., Hibiki, T., 1995. Effect of inner diameter on some characteristics of air-
water two-phase flows in capillary tubes, Transection of JSME (B) 61(589), 99–106
[in Japanese].
Park, J. E., Farahani, F. V., Consolini, L., Thome, J. R., 2011. Experimental study on
condensation heat transfer in vertical minichannels for new refrigerant R1234ze(E)
versus R134a and R236fa, Experimental Thermal and Fluid Science 35, 442-454.
Shah, M. M., 1979. A general correlation for heat transfer during film condensation
inside tube, International Journal of Heat and Mass Transfer 22, 547–556.
Shah, M. M., 2016. A correlation for heat transfer during condensation in horizontal
mini/micro channels, International Journal of Refrigeration 64, 187–202.
Wang, W. W. W., Radcliff, T. D., Christensen, R. N., 2002. A condensation heat
transfer correlation for millimeter-scale tubing with flow regime transition,
Experimental Thermal and Fluid Science 26, 473-485.
147
CHAPTER 7
Development of New Correlations
For the design of compact and high performance heat exchanger, it is essential to
develop an accurate model for the prediction of frictional pressure drop and heat
transfer coefficients in rectangular multiport minichannels. All of the existing pressure
drop and heat transfer correlations discussed in Chapter 5 and Chapter 6, somehow
shown a slightly over or underestimation of the experimental results. In this chapter the
experimental data are correlated to develop an accurate model for the prediction of two-
phase frictional pressure drop and condensation heat transfer coefficient.
7.1 Development of new pressure drop correlation for minichannels
Adiabatic and diabetic two-phase pressure drop can be predicted based on either the
homogeneous model or the separated flow model. The simplest approach to the
prediction of two-phase flows is homogeneous model, which assume that the phases are
thoroughly mixed and can be treated as a single-phase flow. However, the homogenous
method is not suitable for mass flux less than 2000 kg/m2s and at low reduced pressure
(Thome, 2006). Whereas, in separated flow model the phase is considered to be flowing
separately. The frictional pressure drop in two-phase flows is typically predicted using
separated flow models. The first separated flow model was proposed for isothermal
two-phase flow pressure drop by Lockhart and Martinelli (1949) and then followed by
many others. Chisholm (1967) developed a theoretical basis for the Lockhart-Martinelli
correlation for two-phase flow. Later on, Friedel (1979), Muller-Steinhagen and Heck
(1986), Jung and Radermacher (1989), Wang et al. (1997) proposed a simple model for
two-phase frictional pressure drop prediction in macro-channels. Among them, Friedel
(1979) and Muller-Steinhagen and Heck (1986) correlations were developed using a
large data bank containing 25,000 and 9300 measurements of frictional pressure drop
148
for a variety of fluids and conditions respectively. Those models are widely used in
conventional theory to predict frictional pressure drop in macro-channels, many recent
authors (Choi et al., 2008; Xu et al., 2012) have reported the ability of these correlations
to estimate with reasonable accuracy the frictional pressure drop in mini-channels
(Lopez-Belchi et al., 2014).
In the last few years, many studies have developed pressure drop correlation on
the basis of the Lockhart and Martinelli (1949), Chisholm (1967), Friedel (1979)
correlations. Choi et al. (2008), Pamitran et al.(2010) and Kim and Mudawar (2013)
proposed a new correlation on the basis of the Lockhart-Martinelli method. Mishima
and Hibiki (1996), Yu et al. (2002), Kawahara et al. (2002), Sun and Mishima (2009)
and Zhang et al. (2010) developed pressure drop correlations on the basis of the
Chisholm (1967) correlation. The Chang et al. (2000), Chen et al. (2001), and Zhang
and Webb (2001) developed pressure drop correlation on the basis of the Friedel (1979)
correlation. Revellin and Thome (2007) developed a new homogenous two-phase
frictional pressure drop model with a limited range of application. Most of the
researchers developed their correlation for high mass velocity and minichannels without
fins.
However, in the present analysis separated flow model will be used for the
development of new correlation to predict frictional pressure drop in minichannels. In
the separated flow model empirical correlations two-phase multiplier and single-
phase flow pressure drop are needed.
The two-phase multipliers are defined as:
2 Fl
l
P
z
P
z
(7.1)
2 Fv
v
P
z
P
z
(7.2)
2 Flo
lo
P
z
P
z
(7.3)
149
2 Fvo
vo
P
z
P
z
(7.4)
Hence, the frictional pressure drop can be calculated from two-phase multiplier as
follows:
2
22 1l
l
F l h
f G xP
z d
(7.5)
2
2 2 vv
F v h
f GxP
z d
(7.6)
22 2 lolo
F lo h
f GP
z d
(7.7)
22 2 vovo
F vo h
f GP
z d
(7.8)
Any of the above mentioned separated flow model can be used to predict the two-
phase frictional pressure drop inside minichannels if two-phase multiplier is available.
The present analysis considers the Eq. (7.5) for two-phase frictional pressure drop in
rectangular multiport minichannels. It is necessary to develop a model for determining
the two-phase multiplier. Therefore, a new approach is developed to improve the
accuracy of frictional pressure drop prediction of two-phase flow in rectangular
multiport minichannels with and without fins. The present correlation is developed for
multiport tube with and without fin considering the effect of channel geometry (Jige et
al., 2016), reduced pressure (Kim and Mudawar, 2012; Zhang et al., 2010), Reynolds
number and Weber number based on the Lockhart and Martinelli (1949) model. Lee
and Mudawar (2005) assumed that the added complexity of two-phase flow in a
minichannel is the net result of interactions between inertia, viscous force, and surface
tension. These interactions can be added by Reynolds and Weber number. The reduced
pressure is introduced to consider the variation of fluid properties with saturation
temperature (Kim and Mudawar, 2012).
150
The new two-phase frictional pressure drop correlation for adiabatic flow in rectangular
multiport minichannel with and without fins is as follows:
The two-phase frictional pressure drop was calculated by
2l
F l
P P
Z Z
(7.9)
The two-phase frictional pressure drop multiplier
2
2
11l
tt tt
C
X X (7.10)
The Martinelli parameter, Xtt, can be obtained as:
0.5 0.10.91 v l
tt
l l vv
xP PX
Z Z x
(7.11)
where the Chisholm’s parameter, C is adjusted by least square method with a new
dimensionless parameter based on the present experimental frictional pressure drop data
as
0.31
0.35 0.25 0.09 0.09(1 ) tp tp
c
PC x x Re We
P
(7.12)
Where λ is the constant value depends on the channel geometry (Jige et al., 2016). The
value of λ for circular channel is 16 and for rectangular channels, it’s calculated using
the equation of the Shah and London (1978).
3 52 424 1 1.355 1.947 1.701 0.956 0.254 (7.13)
2h
tp
tp
G dWe
(7.14)
151
htp
tp
GdRe
(7.15)
The two-phase mixture viscosity and density were calculated by the equations of
MacAdames et al. (1942).
1 1
tp v l
x x
(7.16)
1 1
tp v l
x x
(7.17)
However, the newly proposed correlation can predict the present experimental data
well on the whole with an average deviation of -2.3% and mean deviation of 17.4%, as
shown in Fig. 7.1. The proposed correlation can predict 99% of the data point within the
±30% error limits.
Fig. 7.1 Comparison of present experimental frictional pressure drop data with
proposed correlation
100
101
102
100
101
102
(P/z)
F, P
redic
ted [
kP
a/m
]
(P/z)F, Experimental [kPa/m]
G [kg/m2s] 50 100 150 200
Proposed correlation
Minichannel without fin
-30%
+30%Minichannel with finsG [kg/m2s]
50 100 150 200
152
Moreover, the new prediction method has also been validated with the available
data collected from open literature listed in Table 7.1. Figure 7.2 shows a comparison
between the present correlation and frictional pressure drop data of single-channel tube
and multiport tubes (Jige et al., 2016; Revellin and Thome, 2007; Hwang and Kim,
2006; Zhang and Weeb, 2001). The comparison has been done with data of seven
working fluids covering circular and rectangular tube of diameter from 0.244 to 3.25
mm. The proposed correlation will be applicable for mass flux from 50 to 2000 kg/m2s,
vapor quality from 0.03 to 0.98 and reduced pressure from 0.10 to 0.80, respectively.
The newly develop correlation showing good agreement with the present experimental
data and some researcher’s data in the single and multiport tubes with rectangular
minichannels with and without fins and circular channel.
Fig. 7.2 Validation of proposed frictional pressure drop correlation with available
experimental data collected from the open literatures.
100 101 102 103 104
100
101
102
103
104
Present study Jige et al. (2016) Revellin and Thome (2007) Hwang and Kim (2006) Zhang and Wedd (2001)
(P/z)F, P
redic
ted [
kP
a/m
]
(P/z)F, Experimental [kPa/m]
+30%
-30%
153
Table 7.1 Two-phase frictional pressure drop data for proposed correlation validation
Author (s) Channel
geometry* dh
[mm] Fluid (s)
Mass flux [kg/m2s]
Test mode
No. of data point
Jige et al. (2016)
R Multi, H
0.85
R134a, R410A
R1234ze(E) R32,
100-500 Con. 198
Revellin and Thome (2007)
C Single, H
0.509 0.709
R134a, R245fa
1200-2000 A 160
Hwang and Kim (2006)
C Single, H
0.244 0.43 0.792
R134a 140-950 A 80
Zhang and Webb (2001)
C Single/ R Multi,
H
2.13 3.25
R134a, R22, R404A
400-1000 A 65
* C: circular, R: rectangular, H: horizontal; Con.: Condensation; A: Adiabatic
7.2 Development of new heat transfer correlation for minichannels
For practical application such as design of heat exchangers, the experimental data
essential to correlate empirically to determine the heat transfer coefficient. Due to the
variety in operating conditions and complex characteristics of two-phase flow, all the
existing correlations discussed in previous chapter somehow shown a slightly over or
underestimation of the present experimental heat transfer coefficient of condensing
flow. From the present experimental data, the authors discovered that the heat transfer
coefficients were strongly dependent on mass flux, vapor quality, saturation
temperature, and channel geometry. Most of the experimental heat transfer coefficient
data points were laps in the annular flow. Therefore, a new annular flow condensation
heat transfer correlation was developed using the same functional form as the Kim and
Mudawar (2013) to improve the accuracy of the heat transfer coefficient prediction of
two-phase flow in horizontal rectangular multiport minichannels with and without fins.
The reduced pressure and vapor quality were introduced in the present correlation to
consider the variation of fluid properties with saturation temperature. Lee and Mudawar
(2005) assumed that the added complexity of two-phase flow in a minichannel is the net
result of interactions between inertia, viscous force, and surface tension. These
interactions were added by Reynolds and Prandtl number.
154
The following two-phase heat transfer coefficient correlation for condensing flow in
horizontal rectangular multiport minichannel with and without fins is obtained by fitting
the values of exponents:
0.1 0.09
0.11 0.45
1v l
tp l l
cr tt h
kp xh Re Pr
p x X d
(7.18)
where, the two-phase pressure drop multiplier of vapor flow is obtained by
2 21v tt ttCX X (7.19)
The Lockhart- Martinelli parameter, Xtt and Chisholm’s parameter, C is obtained by
following Eq. 7.3-7.4.
However, the newly proposed correlation can predict the present experimental data
well under all operating conditions with an average error of -6.9% and mean average
error 17.4%, as shown in Fig. 7.3. The proposed correlation can predict 99% of the data
point within the ±30% error limits.
Fig. 7.3 Comparison of experimental average heat transfer coefficient with proposed
correlations
100 101 102
100
101
102
50 100 150 200
50 100 150 200
Pre
d. h
eat
tran
sfer
co
effi
cien
t [k
W/m
2 K]
Expt. heat transfer coefficient [kW/m2K]
Proposed correlation
Multiport minichannels G [kg/m2s]
with fins without fin
-30%+30%
155
Furthermore, the newly developed correlation for heat transfer coefficient of
condensing flow has also been validated with the available data listed in Table 6. Those
data was collected from the open literature. In the present study, total 750 condensation
heat transfer data points for minichannels were amassed from seven sources (Agarwal
et al., 2010; Yang and Webb, 1996; Jige et al., 2016; Derby et al., 2012; Webb, 1999;
Kim et al., 2003; Belchi et al., 2015). Figure 7.4 depicts a comparison between the
present correlation and available experimental data. The comparison has been done with
data of seven working fluids covering circular, rectangular, square, triangular and semi-
circular multiport minichannels with and without fins of diameter from 0.424 to 2.637
mm. The proposed correlation has been validated with data for mass flux range of 50
kg/m2s to 8000 kg/m2s, vapor quality range of 0 to 1 and reduced pressure range of
0.10 to 0.80, respectively. The newly proposed correlation showed good agreement
with the present experimental data and some previous condensing flow data of seven
different refrigerants in multiport minichannels with and without fins as presented in
Fig. 7.4.
Fig. 7.4 Validation of proposed condensation heat transfer coefficient correlation with
available experimental data collected from the open literature.
100 101 102
100
101
102
Present studyAgarwal et al. (2010)Jige et al. (2016)Kim et al. (2003)Belchi et al. (2015)Darby et al. (2012)Webb (1999)Yang and Webb (1996)
Pre
d. hea
t tr
ansf
er c
oef
fici
ent
[kW
/m2 K
]
Expt. heat transfer coefficient [kW/m2K]
-30%+30%
156
Table 7.2 Condensation heat transfer coefficient data for the proposed correlation
validation
Author (s) Channel
geometry*
dh
[mm] Fluid (s)
Mass flux
[kg/m2s]
No. of
data
points
Agarwal et al.
(2010)
R Multiport,
WF, H
0.424-
0.839 R134a 300-750 153
Yang and Webb
(1996)
R, Multiport,
WF/F, H
2.637,
1.564 R12 400-1400 35
Jige et al.
(2016)
R Multiport,
WF, H 0.85
R134a,
R1234ze(E)
R32,
100-400 235
Derby et al.
(2012)
S, T, SC,
Multiport,
WF, H
1.0 R134a 75-450 60
Webb
(1999)
R, Multiport,
WF, H 1.33 R134a 255-327 15
Kim et al.
(2003)
R Multiport,
WF/F, H
1.41,
1.56 R22, R410A 200-600 45
Belchi et al.
(2015)
R Multiport,
WF, H 1.16 R32, R410A 100-8000 160
* C: circular, R: rectangular, WF: without fin, F: with fins, S: square, T: triangular, SC:
semi-circular, H: horizontal
157
7.3 Conclusions
For the prediction of frictional pressure drop and condensation heat transfer
coefficient, two new correlations have been proposed in order to predict the
experimental results accurately. The newly proposed frictional pressure drop correlation
predicted the present experimental data well under all operating conditions with an
average error of -2.3% and mean absolute error of 17.4%. The proposed heat transfer
coefficient correlation also showed good prediction under all operation conditions with
an average error of -6.9% and mean absolute error of 17.4%. The proposed correlations
can predict 99% of the present experimental results within the ±30% error limits. The
newly proposed correlations also showed good agreement with some previous frictional
pressure drop and condensing heat transfer coefficients data of different refrigerants in
single and multiport minichannels.
158
References
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condensation heat transfer in non-circular microchannels, International Journal of
Refrigeration 33, 1169-1179.
Belchi, A. L., Gomez, F. I., Cascales, J. R. G., Garcia, F. V., 2015. Heat transfer
coefficient during condensation inside a minichannel multiport tube with R32 and
R410A as working fluids, Science and Technology for the Built Environment 21,
535-544.
Chang, Y.J., Chiang, S.K., Chung, T.W., Wang, C.C., 2000. Two phase frictional
characteristics of R-410A and air–water in a 5 mm smooth tube. ASHRAE
Transactions DA-00-11-3, 792–797.
Chen, I.Y., Yang, K.S., Chang, Y.J., Wang, C.C., 2001. Two-phase pressure drop of
air– water and R-410A in small horizontal tubes, International Journal of
Multiphase Flow 27, 1293–1299.
Chisholm, D., 1967. A theoretical basis for the Lockhart–Martinelli correlation for two-
phase flow, International Journal of Heat and Mass Transfer 10, 1767–1778.
Choi, K.I., Pamitran, A.S., Oh, C.Y., Oh, J.T., 2008. Two-phase pressure drop of R-
410A in horizontal smooth minichannels, International Journal of Refrigeration 31,
119-129.
Derby, M., Lee, H. J., Peles, Y., Jensen, M. K., 2012. Condensation heat transfer in
square, triangular, and semi-circular mini-channels, International Journal of Heat
and Mass Transfer 55, 187-197
Friedel, L., 1979. Improved friction pressure drop correlations for horizontal and
vertical two-phase pipe flow, in: European Two-phase Group Meeting, Ispra, Italy,
Paper E2.
159
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CHAPTER 8
Conclusions and recommendations
8.1 Conclusions
An adiabatic frictional pressure drop and condensation heat transfer characteristics
of R134a flowing inside a rectangular multiport minichannels with fins having 20
channels with a hydraulic diameter of 0.64 mm, rectangular multiport minichannels
without fin having 20 channels with a hydraulic diameter of 0.81 mm and small
diameter microfin tube with an equivalent diameter of 2.68 mm were investigated
experimentally. The effects of mass flux, vapor quality, saturation temperature and
channel geometry of the tube on the frictional pressure drop and condensation heat
transfer were examined and clarified. Based on the experimental study, the main
findings of the present investigation can be summarized as follows:
1. The frictional pressure drop of R134a significantly increases with the mass flux
and vapor quality in both rectangular multiport minichannels and microfin tube.
2. The frictional pressure drop of R134a decreases with saturation temperature.
3. The hydraulic diameter of the minichannel has significant influence on the
frictional pressure gradients which increases with decreasing hydraulic diameter
of the minichannles. The frictional pressure drop of multiport minichannel with
fins was 1.08-1.25 times higher than that of multiport minichannel without fin.
4. The microfin tube has slightly influence on the frictional pressure gradients. The
frictional pressure drop of the microfin tube was higher than those of smooth
tube about 10-15%.
5. The average heat transfer coefficient of R134a during condensation tended to
increases with increasing mass flux and vapor quality in both rectangular
minichannels and microfin tube. The heat transfer coefficient is increases faster
at higher vapor quality (x > 0.5).
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6. The saturation temperature has significant influence on condensation heat
transfer coefficient which decreases with increasing the saturation temperature.
The reason is the thermal conductivity of liquid film which decreases with
increasing saturation temperature.
7. The heat transfer coefficient of rectangular multiport minichannel with fins is
approximately 10-39% higher than those of rectangular multiport minichannel
without fin for the same operating conditions due to the surface tension force.
8. The higher heat transfer coefficients were obtained in microfin tube about 2-
68% than that of smooth tube at the same operating condition.
9. The experimental frictional pressure drops of rectangular multiport
minichannels were compared with fifteen widely used existing well known
correlations that were developed for the conventional and minichannels. Some
correlations over-predicted, some are under-predicted and few correlations
captured the correct frictional pressure drop within the limits of experimental
error.
10. The frictional pressure drops of microfin tube were compared with seven
existing well-known correlations. Among them, the Goto et al. correlation gives
fairly good prediction with 26.1% mean absolute error.
11. The experimental heat transfer coefficients were compared with ten well-known
correlations that were developed for the conventional tube, minichannels and
microchannel. Among them, some correlations over-predicted, some are under-
predicted and few correlations captured the correct heat transfer coefficient
within the limits of experimental error.
12. A new correlation for the prediction of frictional pressure drop and condensation
heat transfer coefficients in rectangular multiport minichannels were proposed
based on the experimental results. Both correlations agreed well with the present
measured data and available data in the open literature.
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8.2 Future works
Some recommendations for future works based on the present work are as follows:
1. Further research is still needed before the fundamentals of condensation heat
transfer in minichannels and small diameter microfin tubes are fully understood.
To achieve that goal, it is needed to expand the present experimental database.
2. Better design tools to correctly predict the frictional pressure drop and
condensation heat transfer coefficients in small diameter microfin tubes still
need to be developed.
3. A new database has been obtained for pressure drop and condensation in
minichannels and microfin tube for high pressure refrigerant R134a. It is
therefore recommended that new condensation heat transfer coefficient and
frictional pressure drop measurement experiments be extended to other medium
pressure and low pressure pure and mixture refrigerant.
4. In the same test section, the research work also can be extended to observe
evaporation characteristics with the same refrigerant.