Ijmet 09 11_008

http://www.iaeme.com/IJMET/index.asp 61 editor@iaeme.com
International Journal of Mechanical Engineering and Technology (IJMET)
Volume 9, Issue 11, November 2018, pp. 61–71, Article ID: IJMET_09_11_008
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJMET&VType=9&IType=11
ISSN Print: 0976-6340 and ISSN Online: 0976-6359
© IAEME Publication Scopus Indexed
THEORETICAL ANALYSIS OF TWO-PHASE
FRICTIONAL PRESSURE DROP DURING
CONDENSING IN HORIZONTAL MINI
CHANNEL
Tejendra Patel
Research scholar, Mechanical Engineering Department, SVNIT, Surat, Gujarat, India.
Ashok Parekh
Associate Professor, Mechanical Engineering Department, SVNIT, Surat, Gujarat, India.
Parbhubhai Tailor
Professor, Mechanical Engineering Department, SVNIT, Surat, Gujarat, India.
ABSTRACT
In the present situation energy saving and environmental friendly devices are the
prerequisite matter. Not only the uses of electronic equipment but also the rates of
miniaturisation of electronics system have also increased. The problem of local heat
accumulation in electronic equipment because of its miniaturization and there is a
possibility of failure of equipment if accumulated heat is not dissipating from it. The
miniature cooling system is one of the solutions to overcome this problem. Two phase
frictional pressure drop and condensing heat transfer are two key parameters to
understand the flow process of heat transfer. So in the present study comparative analysis
of two phase frictional pressure drop has been carried using refrigerants viz. R1234ze,
R1234yf, R290, R134a, R152a, R22 and R410A for the flow through horizontal mini
channel of hydraulic diameter of 1.085 mm,1.116 mm and 0.956 mm. The saturation
temperature has been varied from 30 0
C to 50 0
C and mass flux has been varied from 150
kg/m2
s to 800 kg/m2
s. Results of comparative analysis of frictional pressure drop shows
that Kim and Mudawar [19] correlation has best predictability of experimental data with
an MRD of -7.36 % & MARD of 12.21%. From compiled experimental data of various
researchers new modified correlation has been developed for frictional pressure drop
with MRD-0.000165 % and MARD 10.033 %.
Key words: Condensation, Frictional Pressure drop, MARD, MRD, Mini channel
Cite this Article Tejendra Patel, Ashok Parekh and Parbhubhai Tailor, Theoretical
Analysis of Two-Phase Frictional Pressure Drop during Condensing in Horizontal Mini
Channel, International Journal of Mechanical Engineering and Technology, 9(11), 2018,
pp. 61–71.
http://www.iaeme.com/IJMET/issues.asp?JType=IJMET&VType=9&IType=11

Tejendra Patel, Ashok Parekh and Parbhubhai Tailor
1. INTRODUCTION
At present Heating, Ventilation and Air conditioning (HVAC) industries deals with the
construction and operation of compact refrigeration system or miniature cooling system which
removes heat from limited space where high heat flux generates i.e. electronic circuit of avionics,
rocket engine nozzle, satellite electronics, turbine blade etc.As uses of electronic equipments go
on increasing day by day, there is significant attention of researchers towards the problemof heat
accumulation in an electronic circuit and miniaturization of a system. The miniature cooling
system is the only way to absorb heat by boiling of suitable working fluid and reject the same
heat to air or any secondary cooling medium to condense working fluid. The mini channel heat
exchanger reduces refrigerant charge and hence its mass. Thus condensation study in small-scale
confined space like mini channel channel is important to meet the required cooling load. The
investigation on two phase frictional pressure drop and condensing heat transfer in mini channel
during condensation becomes one of the most researched topics and also there is limited
experimental and numerical work reported in the same.
In the present situation energy saving and environmental friendly devices are the prerequisite
matter. As a consequence of the phase out of CFCs and HCFCs refrigerants due to their negative
influence on the ozone layer, HFCs came into the use but majority of them having high global
warming potential. Hence researchers are working on new HFO (Hydro fluoro olefin) refrigerants
having low GWP. The pioneer work by Sobhan and Garimella [1] focused on characterization of
heat transfer coefficient and pressure drop in era of electronics cooling application. Zhang et al.
[2] carried out research on use of refrigerant in electronic cooling and analysed the refrigerant
side condensing heat transfer coefficient for three different refrigerants R22, R410A and R407C,
flowing through circular tubes of 1.088 and 1.289 mm of hydraulic diameter. The range of mass
fluxes had been taken as 300 to 600 kg/m2
s.Pressure drop inside a horizontal mini-channel of
hydraulic diameter 0.31 mm was investigated by Lazarek and Black [3] with R113 as refrigerant.
Authors introduced Chisholm multiplier ‘C’ to calculate two-phase pressure drop. After
correlating their resultsthe value of C found to be 30. Two-phase pressure drop of H2O and air in
an adiabatic flow through capillary tubes of aluminium and glass of hydraulic diameter ranging
from 1 mm to 4 mm was studied by Mishima and Hibiki [4]. Webb and Kemal[5] studied pressure
drop during condensation in a channel of 0.44 mm hydraulic diameter. Authors first time took
the measurements in small diameter channel and it was found that the pressure drop values
increases with decrease in hydraulic diameter for a fixed value of mass flux. Cavallini et al.[6]
calculated the adiabatic pressure gradient of R134a, R236ea and R410A inside a rectangular
multi-port mini-channel tubes with hydraulic diameter of 1.4 mm. Correlations developed by
Friedel [7], Zhang and Webb [14], Mishima and Hibiki [4] and Müller-Steinhagen and Heck[8]
were used in their study and are in good agreement with experimental data. Pressure drop during
condensation within single circular 0.96 mm diameter mini channel using R1234yf was
investigated by Del Col et al.[9] and then it was compared with R134a results[13]. It was found
that the values of pressure drop using R1234yf was lower than R134a values by 10 to 12 % under
the similar conditions and It was concluded that R1234yf performance is better than R134a.
Bohdal et al.[10]studied pressure drop during condensation of R404A and R134a inside mini-
channel. Authors showed that the pressure drop values can be accurately estimated by correlations
of Friedel [7] and Garimella [12]. Authors also developed a new correlation for pressure drop
calculations. The literature studies reveal that there is no accurate method to predict the two phase
frictional pressure drop. In the present study broad experimental results have been taken from
open literature and these results have been compared with the results of various frictional pressure
drop models. Based on this comparison Kim and Mudawar [19] model having minimum MRD
and MARD have been found. With correction in constants of Kim and Mudawar [19] model, the

Theoretical Analysis of Two-Phase Frictional Pressure Drop during Condensing in Horizontal Mini
Channel
new model with lower value of MRD and MARD has been developed to predict two phase
frictional pressure drop.
2. COMPARATIVE STUDIES OF VARIOUS TWO PHASE FRICTIONAL
PRESSURE DROP MODELS
During condensation process in mini channel the friction is main reason for pressure drop and
term two phase frictional multiplier ( ) is used to find two phase frictional pressure drop. In
present study total 454 experimental results are obtained from research work of Na Liu et al. [15],
A. F.Illan-Gomez at al [17], Alejandro López-Belchí et al. [18] , and Chang-Hyo Son et al. [16].
The experimental results of two phase frictional pressure drop covers horizontal mini channel of
hydraulic diameter 0.952 mm, 1.152 mm, 1mm& 1.034 mm, Saturation temperature such as 30
0
C, 40 0
C, 45 0
C, and 500
C and refrigerants R290, R1234yf, R1234ze, R22, R32, R410A, R134a
and R152a. These experimental results of two phase frictional pressure drop have been compared
with results obtained from various models as shown table 1. To obtain two phase frictional
pressure drop the thermo-physical properties of refrigerants, non-dimensional numbers,
geometrical parameters and constants are evaluated. The MRD (Mean Relative Deviation) and
MARD (Mean Absolute Relative Deviation) have been evaluated for all eight models under
consideration. The eight models under consideration are Del col et al. [82], the Kim & Mudwar
[19], the Mishima & Hibiki [4], the Cavallini et al. [6], Trans et al. [20], Zhang & Web [14],
Friedel et al.[11] and Garimella et al. [12]. The comparison shows that Kim and Mudawar [19]
model has best predictability of experimental data with an MRD of -7.36 % & MARD of 12.21%.
This model is taken as reference model to develop a new correlation. Table 2 shows the sources
of results which are taken from the open literature along with their test condition for this present
study.
Table 1 Asummary of the two-phase frictional pressure gradient correlations using two-phase multiplier.
Authors Remarks Equations
Friedel et
al. [11]
D > 4 mm, air–
water,
refrigerants,
developed
from 25,000
data points
= = +
.
. ∙ .
,
= − + ∙
!" ∙ #$
!$ ∙ #
%
& = '(.)*
∙ 1 − ' (.,,-
, . =
/0
/1
%
(.23
∙ 4
51
50
6
(.32
∙ 41 −
51
50
6,
Cavallini
et al. [6]
D=0.96 mm,
Condensation,
R1234ze, R22,
R32
According to Cavallini et al pressure gradient in mini-channels is
given by
78
79 :;
= ∅0=
, 78
79 0=
,Where,
78
79 0=
=
,>?@AB
CD?
; E0= = 0.046IJ0=
K(.,
Two phase multiplier is given by:
∅0=
,
= L + 3.595&. 1 − P Q
; R = 1.398 UV
L = 1 − ' ,
+ ',
/0
/1
% 41 −
51
50
6
W.X-,
& = '(.2X,X
1 − ' (.-3-
. =
/0
/1
%
3.3W,
4
51
50
6
(.--
41 −
51
50
6
W.X-,
E=Entrainment fraction

P = 0.015 + 0.44 log
D]^
D?
_?`]
a
,
∗ 10-
c ; P < 0.95, P =
0.95 ; P ≥ 0.95, g1
∗
=
Ah
iC1D]jD?KD]k
; dimensionless gas velocity
/1l = /1 m1 +
1 − ' P
'
%n
Garimella
et al.[1]
D=0:5 -
4:91mm,
condensation,
R134a
To calculate total pressure drop through mini-channels, first void
fraction using Baroczy’s correlation is to be calculated:
∈= p1 + 4
1 − '
'
6
(.)-
4
/1
/0
6
(.qX 50
51
%
(.3W
r
K3
Total pressure drop is given by:
4
st
sL
6
:;
=
1
2
Ev
w,
',
/1 ∈,.X
1
x
Where, Ev= interface friction factor, calculated as
Ev
E0
= yz{
IJ0
|
}l
Laminar region IJ0 < 2100 : y = 1.308 ∗ 10KW
; • = 0.427; • =
0.93; ‚ = −0.121
Turbulent region IJ0 > 2100 : y = 25.64;• = 0.532;• =
−0.327; ‚ = 0.121
Surface tension parameter is evaluated as
} =
g050
„
g0 =
A 3Kh
D? 3K∈
; superficial velocity
And X= Martinelli parameter, calculated as
z = m
st sL⁄ 0
st sL⁄ 1
n
3 ,⁄
Mishima
and
Hibiki [4]
D = 1.05 -4.08
mm,
adiabatic, air-
water
4
st
sL
6
†8
= 1 +
‡
z
+
1
z,
; Eˆ‰‰J‚Š•‹Œ•Ž•‰‚ℎ•‹‹JŽ,
‡ = 21 ∙ •1 − J'U ∙ 4−
0.319
x‘
6’ ; x‘“””•, Eˆ‰‚–‰‚•Ž•‰Š••J, ‡
= 21 ∙ 1 − J'U ∙ 4−
0.333
x
6% ; x“””•
Zhang and
Webb [14]
D = 0.06 mm,
water Re
<2000
‡ = 21 ∙ 41 − exp 4−
0.358
‡ˆ‹
66
Tran et al.
[20]
Circular
channels with
D = 2.46 and
2.92 mm,
rectangular
š›œ
,
= 1 + 4.3z:: − 1 “‡ˆ‹ 1 − ' (.*)X
+ '3.)X• 4
st
sL
6
†8
= 4
st
sL
6
›œ
š›œ
,
Zhang and
Webb [14]
D = 3.25 and
6.25 mm,
multiport
extruded Al
channels with
Dh = 2.13 mm,
š›œ
,
= 1 − ' ,
2.87',
4
t•{:
tlVv:
6
K3
, tVž7 = 4
t•{:
tlVv:
6 , 4
st
sL
6
†8
= 4
st
sL
6
›œ
š›œ
,

Channel
adiabatic,
R134a,
R22,R404A
Del Col et
al. [9]
D = 8 mm,
horizontal
tubes, R22,
R134a, R125,
R32, R236ea,
R407C,
R410A
7;
7Ÿ †8 =
78
79 ›œ
š›œ
,
, š›œ
,
= P +
3.,q, ¡¢
Qž£.¤¥¦§ , &¡
= '(.q*)*
, . =
4
D?
D]
6
(.W,)*
∙
_]
_?
K3.33*
∙ 1 −
_]
_?
W.-))
, P = 1 − ' ,
',
∙ 4
D?∙>]
D]∙>¤
6,
E0 = 8 “
*
¨ž?
3,
+ {“2457Ž‹
¨ž?
)
(.2
•3q
+
W)XW(
¨ž?
3q
}K3.X
•3/3,
,
E1 = 8 “
8
IJ1
%
3,
+ {“2457Ž‹ 4
IJ1
7
6
(.2
•3q
+
37530
IJ1
%
3q
}K3.X
•3/3,
RJ =
w,
x
/„
Kim and
Mudawar
[19]
D = 0.0695 -
6.22 mm,
adiabatic,
condensing,
developed
from
database
ɸ›
,
= 1 +
-
®
+
3
®B, ‡ = •IJ0=
|
¯•1=
l
4
D?
D]
6
7
, ¯•1=
l
=
D]aC°
_]
B
a, b, c, and d are constants by Kim and Mudawar.22
Table 2 Details of data source and its experimental parameters
Sr.
No.
DataSources Working Fluid
Parameters Range
(Hydraulic diameter/Saturation temperature/Mass flux/Vapour
quality/cross section of channel)
1
Alejandro López-Belchí et
al.
NaLiu,HangXiao,Junming
Li et al.
R290
1.08mm/40 0
C to 50 0
C/200-800 kg/m2
s/0.1-0.9/circular & Square
single
2
al. and F.Gomez, A. L
opez, J.R.Garcı´a, et al.
R1234yf
1.16 mm/30 0
C to 55 0
C/350-640 kg/m2
s/0.39-0.89/ Square multi-
port
3
NaLiu,Hang
Xiao,JunmingLi, et al.
R1234ze
1.08mm/40 0
C to 50 0
C/200-800 kg/m2
single
4
al., et al.
R134a
1.16 mm/40 0
C to 50 0
C/300-800 kg/m2
single
5
Chang-Hyo Son et al.
Na Liu, Junming Li et al.
2015 et al.
R22
1.152 mm/30 0
C to 50 0
C/200-800 kg/m2
s/0.1-0.9/Circular
0.952 mm/30 0
C to 50 0
C/200-800 kg/m2
s/0.1-0.9/Square
1.304mm/30 0
C to 50 0
C/200-800 kg/m2
s/0.1-0.9/Square
6 Na Liu, Junming Li et al. R32
1.152 mm/30 0
C to 50 0
C/200-800 kg/m2
s/0.1-0.9/Circular
0.952 mm/30 0
C to 50 0
C/200-800 kg/m2
s/0.1-0.9/Square
1.304mm/30 0
C to 50 0
C/200-800 kg/m2
s/0.1-0.9/Square
7
al.
Na Liu, Junming
Li et al.
R152a
1.152 mm/30 0
C to 50 0
C/200-800 kg/m2
s/0.1-0.9/Circular
0.952 mm/30 0
C to 50 0
C/200-800 kg/m2
s/0.1-0.9/Square
1.304mm/30 0
C to 50 0
C/200-800 kg/m2
s/0.1-0.9/Square
±Ix =
3
²
∑
7;/7Ÿ v ^´?K7;/7Ÿ v µ¶·
7;/7Ÿ v µ¶·
²
v¸3 (1)
±yIx =
3
²
∑ ¹
7;/7Ÿ v ^´?K7;/7Ÿ v µ¶·
7;/7Ÿ v µ¶·
¹²
v¸3 (2)

Where, (dp/dz)cal is the calculated value, (dp/dz)exp is the experimental value, and N is the
number of data points.Table 3 Comparison between experimental data and correlation prediction
for flow through mini-channels
S
r.
N
o
.
Data
Source
s
Wo
rkin
g
Flui
d
% Error of Authors models
Cavalli
ni et
al.
Fri
ede
l et
al.
Wh
ang
&
Ki
m
et
al.
Garime
lla et
al.
Del
cole et
al.
Kim &
Mudawar
et al.
Tran
s et
al.
Zh
an
g
&
W
eb
et
al.
New
Corr
elatio
n
1
Na
Liu,
Hang
Xiao,J
unmin
g Li,
2016
R29
0
M
RD
-21.54
-
21.
30
54.
70
-50.44 -15.11 -8.33
-
65.3
15
-
52.
29
-0.61
M
AR
D
22.027
23.
046
9
55.
67
-50.44 17.75 10.7087
81.2
1
63.
00
9.054
2
F.Gom
ez, A.
L
opez,
J.R.
Garcı´
a,(201
5)
R12
34y
f
M
RD
-12.34
-
46.
92
77.
58
-38.08 -12.22 13.93 -5.47
-
38.
08
2
24.90
M
AR
D
20.58
46.
92
108
.07
6
67.09 20.58 41.04
140.
9
67.
09
3
48.86
3
Na
Liu,
Hang
Xiao,J
unmin
g Li,
2016
R12
34z
e
M
RD
-2.08
-
29.
864
40.
06
61.83 -12.86 -13.608
-
83.7
7
-
47.
24
-7.95
M
AR
D
8.70
30.
23
40.
065
61.83 22.30 21.94
83.7
7
66.
48
9
19.64
4
Na
Liu,
Junmi
ng Li
et al.
2015
# 1
SQUA
RE
R22
M
RD
-14.40
-
11.
877
178
.22
-34.65 -15.29 -7.41
-
76.9
16
-
51.
08
8
1.03
M
AR
D
15.78
23.
092
178
.22
39.083 18.96 8.39
79.0
56
63.
66
6.329
5
Na
Liu,
Junmi
ng Li
R32
M
RD
-34.63
-
9.3
61
157
.72
-40.68 -39.78 -9.313
-
29.4
2
-
48.
50
8
-
0.981

Channel
et al.
2015
1 #
Square
M
AR
D
35.53
22.
908
6
157
.72
41.13 40.36 10.734
98.5
4
71.
50
8
8.239
6
Na Liu
&
Junmi
ng
Li et
al.
2015
R15
2a
M
RD
6.369
-
28.
175
31.
23
-
60.521
-
13.975
-9.207
84.2
73
-
49.
67
3
-1.32
M
AR
D
13.428
29.
725
31.
31
-
60.521
18.058 9.207
85.9
82
70.
28
5
3.22
7
Alejan
dro
López-
Belchí
et
al.,201
6
R13
4a
M
RD
38.568
5.4
01
222
.60
-1.59 36.589 35.35
-
76.1
6
-
31.
72
5
-
27.68
M
AR
D
83.731
62.
381
241
.43
83.854 79.99 88.287
85.9
6
86.
23
2
55.31
2
8
Alejan
dro
López-
Belchí
et
al.,201
6
R41
0A
M
RD
35.986
-
10.
849
215
.68
5
-
41.274
-
38.440
-9.899
-
68.9
45
-
66.
58
0
-
2.091
M
AR
D
35.986
18.
399
215
.68
5
41.274 38.440 10.699
72.3
59
68.
06
7
6.393
Average
M
RD
-
20.901
-
17.
945
120
.01
3
-43.54 -26.03 -7.73
-
55.5
9
-
50.
85
1
-
0.000
165
M
AR
D
24.73
24.
737
121
.97
46.58 29.41 12.33
89.2
46
67.
45
4
10.08
33
3. RESULT AND DISCUSSION
Comparative assessment of eight available different Frictional pressure gradient models has been
carried out and evaluated Mean Relative Deviation (MAD) and MARD (Mean Absolute Relative
Deviation) of each correlation. Finally doing so the correlation which is having minimum error
based on new constant value which deals concern fluid properties and non-dimensional number.
Table 3 indicates the MAD and MARD of all eight models under consideration in the present
study. After comparison it has been found in fig that in case of frictional pressure gradient for
refrigerant flow through horizontal mini-channels, the Kim & Mudawar et al. model has the
considerable predictability of experimental data with an MRD of -7.73 % & MARD of 12.33%.
There are also Cavallini et al. and Freidel et al. models showing good agreement with MARD of
24.11% & 24.74% respectively. It shows good integrity of Kim & Mudawar et al. model with
experimental data compared to other model whereas Cavallini et al. and Freidel et al. correlations
are showing comparatively less integrity than the Kim & Mudawar et al. Among all correlation
except these three Kim & Mudawar et al., Cavallini et al. and Freidel et al correlation other are
under predicting the experimental frictional pressure gradient data. Whang & Kim et al.
correlation is over predicting the experimental data. Now based on above comparison model with
low MRD and MARD has been taken as reference and develop new model by taking new constant
value and ratio of non-dimensional number which are concern to physical properties of working

fluid and geometrical parameters of flow condition. The new value of constant has been decided
by trial and error method incorporated with what if analysis goal seek tool of ms office excel.
(a) (b)
© (d)
(e) (F)

Channel
(g) (h)
Fig. 1 Comparison of Result of experimental Frictional Pressure Gradient with predicted Frictional
Pressure Gradient of (a) Wang & Kim et al. (b) Frediel et al. (c) Zhang & Webb et al. (d) Trans et al. (e)
Del cole et al. (f) Garimella (g) Kim & Mudwar et al. (h) Cavallini et al model.
So finally new modified correlation has been developed with minimum MRD -0.000165 %
and MARD 10.08 % by introducing some new constants and non-dimensional number in existing
low MARD correlation. New modified correlation,
ɸ²žº
,
= 1 +
-
®
+
3
®B
, ‡²žº = 0.3572IJ0=
(.(X(,3
¯•1=
(.(22
&(.(,X
.(.(3X
, ¯•1=
l
=
D]aC°
_]
B ,
7;
7Ÿ †8 =
78
79 ›
š›
,
(3)
Figure 2 Comparison of Result of experimental Frictional Pressure Gradient with predicted Frictional
Pressure Gradient of New model.
New developed correlation is suitable for refrigerants R290, R1234yf, R1234ze, R22, R410A
and R32 for the saturation temperature range 30 to 50 0
C. It is also applicable for hydraulic
diameter range from 0.952 mm to 1.150 mm horizontal mini channel. Fig 1 shows the comparison

made between literature experimental data [15, 16, 17, and 18] and all eight Frictional pressure
gradient model or correlation along with new developed correlation and showing the integrity of
experimental data with model. It can be seen from the table 3 and Fig. 1 except kim & Mudawar,
Freidel et al. and cavallini et al. model all correlation not fairly match and not fit under the ±30
% deviation with the experimental data [15,16,17,18]. Fig. 2 shows good integrity between
predicted data and experimental data [15, 16, 17, and 18] within ±15 % deviation.
4. CONCLUSION
Comparative analysis has been carried out for condensing frictional pressure drop by taking
experimental resuts of the various researches [15, 16, 17, and 18] and total eight models have
been reviewed. Kim and Mudawar model is showing good agreement with MRD of -7.73 %&
MARD of 12.33%.There are also Cavallini et al. and Freidel et al models showing agreement
with MRD of -24.73 % &24.13% respectively. From compiled experimental results of various
researchers new modified model has been developed for frictional pressure drop with MRD-
0.000165 % and MARD 10.033 %.
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