Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: P3.17 - Two-phase Flow Pressure Change across Sudden Expansions in Small Rectangular Channels
ALL VOLUMES CITATION THUMBNAILS PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00102023/00517
 Material Information
Title: P3.17 - Two-phase Flow Pressure Change across Sudden Expansions in Small Rectangular Channels Fluidized and Circulating Fluidized Beds
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Chen, I.Y.
Tseng, C.-Y.
Wang, C.-C.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: two-phase flow
pressure change
sudden expansion
 Notes
Abstract: In this study, the authors first give a short overview on the single-phase flow across sudden expansion, followed by a thorough review of the relevant literature for two-phase flow across sudden expansion, and examine the applicability of the existing correlations. Also, 282 data available from 5 publications are collected. None of the existing correlations can accurately predict the entire database. Most of the correlations highly over predict the data with a mini test section which has a Bond number being less than 0.1 in which the effect of surface tension dominates. Also, some of the correlations significantly under predict the data for very large test sections. Among the models/correlations being examined, the homogeneous model shows a poor predictive ability (a standard deviation of 143%) than the others, but it is handy for the engineering application. Hence by taking account the influences of Bond number, Weber number, Froude number, liquid Reynolds number, gas quality and area ratio into account, a modified homogeneous model is proposed that considerably improves the predictive ability over existing correlations with a mean deviation of 23% and a standard deviation of 29% to all the data with wider ranges for application.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
 Record Information
Bibliographic ID: UF00102023
Volume ID: VID00517
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: P317-Chen-ICMF2010.pdf

Full Text


Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010



Two-phase flow pressure change across sudden expansion in small channels


Ing Youn Chena, Chih-Yung Tsengb, Chi-Chuan Wange

aMechanical Engineering Department, National Yunlin University of Science and Technology, Yunlin, Taiwan 640

bEnergy & Environment Research Laboratories, Industrial Technology Research Institute, Hsinchu, Taiwan 310
'Department of Mechanical Engineering, National Chiao Tung University, Hsinchu, Taiwan, 300


Keywords: Two-phase flow, Pressure change, Sudden expansion




Abstract

In this study, the authors first give a short overview on the single-phase flow across sudden expansion, followed by a
thorough review of the relevant literature for two-phase flow across sudden expansion, and examine the applicability of the
existing correlations. Also, 282 data available from 5 publications are collected. None of the existing correlations can
accurately predict the entire database. Most of the correlations highly over predict the data with a mini test section which has
a Bond number being less than 0.1 in which the effect of surface tension dominates. Also, some of the correlations
significantly under predict the data for very large test sections. Among the models/correlations being examined, the
homogeneous model shows a poor predictive ability (a standard deviation of 143%) than the others, but it is handy for the
engineering application. Hence by taking account the influences of Bond number, Weber number, Froude number, liquid
Reynolds number, gas quality and area ratio into account, a modified homogeneous model is proposed that considerably
improves the predictive ability over existing correlations with a mean deviation of 23% and a standard deviation of 29% to all
the data with wider ranges for application.


Introduction

The flow of two-phase mixtures across sudden expansions
and contractions is relevant in many applications such as
chemical reactors, power generation units, oil wells and
petrochemical plants. It is well known that the gas-liquid
interactions in sudden flow area changes such as pipeline
connections and heat exchangers are a complex function of
the flow rates of the two phases, their physical properties
and pipe geometry. As the two-phase mixture flows
through the sudden area changes, the flow might form a
separation region at the sharp corner leads to an
appreciable pressure loss due to irreversibility. Two-phase
flow studies in constant area pipes have been widely
studied in the literature, however, frictional performance
arisen from singularities such as expansion and contraction
are among the least studies of two-phase system (Chalfi, et
al., 2008). Recently, the authors had investigated the
two-phase flow pressure change across sudden
contractions with small channels. A correlation was
proposed that considerably improves the predictive ability
(with a mean deviation of 30%) over existing correlations
with their 156 data and 357 available literature data (Chen
et al., 2009).
Though, there are several correlations for the two-phase
flow across sudden expansions available in the literature.
Most of the correlations can only predict their own
database but failed to predict the data from the others.
Therefore, a short overview on the single-phase flow
across sudden expansion is firstly given, followed by a


thorough review of the relevant literature for two-phase
flow across sudden expansions. From the available data
collected in the literature, the correlations/models are
tested to see their applicability. Finally, a correlation with
all the significant parameters for the two-phase flow across
sudden expansions is proposed with an acceptable
accuracy for the engineering application.


Review of Literature

Single-phase pressure change across sudden expansion

For single-phase flow, this pressure change across the
sudden expansion was estimated by Delhaye (1981) as a
simple correlation from a simplified momentum balance
equation.

SG20,1 A A
eP = 1


Where p is the fluid density, and mass flux, G, is calculated
based on the smaller cross sectional area of the inlet tube,
and oA is the passage cross section area ratio (oA < 1).
Figure 1 shows a typical change of static pressure along
the axis for flow across the expansion. Due to the
deceleration of the flow in the transitional region, the static
pressure initially increases at the expansion area. After the
pressure reaches the maximum, the pressure gradient
merges with the downstream pressure gradient line. The






Paper No


pressure change at the sudden expansion is defined as the
pressure difference for upstream and downstream fully
developed pressure gradient lines extended to the
expansion position, i.e., APEX, aS shown in Figure 1.


Flow path

Figure 1: Idealized pressure variations across sudden
expansion

Two-phase pressure change across sudden expansion

Romie (1958), Richardson (1958), Lottes (1961), Mendler
(1963), and McGee (1966) were firstly to investigate
two-phase flow through sudden expansions. This study was
continuously investigated by Chisholm and Sutherland
(1969), Delhave (1981), Wadle (1980), Schmidt and
Friedel (1996), Attou et al. (1997), Attou and Bolle (1997),
Abdelall et al. (2005), and Chalfi et al. (2008). In the
majority of the previous studies, the void fraction (u), area
ratio (GA) and gas quality (x), as well as the densities of gas
and liquid (pL PG) WeTC USed to estimate the pressure
recovery across the sudden area expansion. The pressure
change equations were obtained from the mass and
momentum balances without considering the structure of
the flow and the frictional effect on the pipe wall. Ahmed
et al. (2007) had shown that the pressure recovery is
dependent on both the wall shear stress in the developing
region immediately downstream of the expansion and the
wall pressure on the downstream face of the expansion in
the flow developing region. The upstream and downstream
void fractions were estimated using the appropriate
correlations on the local flow pattern. Recently, Ahmed et
al. (2008) also correlated the length of the developing
regime to the area ratio and the upstream liquid Reynolds
number. However, Ahmed et al. model (2007) is
unpractical for the engineering application.
For allowing a relative velocity between the phases, Romie
(1958) derived an expression for sudden enlargement from
the momentum balance.


AP= (1 xy x
G'P (1 -a, (1-a ) P


Where the subscript 1 denotes upstream of expansion, and
2 represents downstream of expansion. If the void fraction
remains unchanged, Eq. (2) is simplified by Delhave (1981)
as:
GCr4a(1-cA)r (1-x)2 (pL /G X2 (3)


McGee (1966) measured pressure drops for steam-water


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

mixtures flowing through sudden expansions. His test
conditions are summarized in Table 1. The predicted
pressure change by Romie's Eq. (2) using the measured
upstream and downstream void fractions compared fairly
well with the data. The agreement with the predictions and
his 64 point data was in the order of + 40%. Neglecting
the density change and replacing a; and at by their average
value, the predictions of Eq. (3) did not affect the results
significantly with a 39% standard deviation as shown in
Table 2. Considering a homogeneous flow from
momentum balance, Eq. (3) is reduced to:

AP =Gaq(-7 )(1- x)P Px(4


The data of McGee (1966) predicted by the
homogeneous model were significantly higher than the
data with a standard deviation of 138% as shown in Table
2. Attou et al. (1997) and Abdelall et al. (2005) had
pointed out that the homogeneous model tends to
significantly overestimate the experimental results due to
the assumption of no slip between the phases.
Richardson (1958) simplified the energy balance model
and assumed that the pressure recovery is proportional to
the kinetic energies of the phases:

G2(1-0 ~A) 0- (1- x)2(
hP,= 2 PL 1 I

Lottes (1961) ignored the gas mass flow rate and assumed
that all losses of dynamic pressure head occur in the liquid
phase only to derive the two-phase pressure change.
Assuming a remains unchanged, his equation is simplified
to:

AP = G-cr (1- ) (6)


Mendler (1963) measured pressure drops for steam-water
mixtures flowing through sudden expansions. His test
conditions are listed in Table 1. His dada predicted by
homogeneous model and the simplified Romie's equation,
Eq. (3) were fairly as 65% and 36%, respectively, shown
in Table 2. Chisholm and Sutherland (1969) developed a
heterogeneous model based on the momentum balance.
Their model was compared with the air-water bubbly flow
data (a < 0.35). Their predictions remained reasonably
good agreement with data, but were slightly under
estimated by Attou et al. (1997). The underestimation of
the Chisholm model was also observed by Wadle (1980).
Wadle assumed the liquid is decelerated much less than the
gas when it passes through the expansion due to its higher
inertia. The pressure recovery at the sudden expansion is
caused by the bulk deceleration effect and a formula was
proposed from his test data to describe the pressure
recovery in an abrupt diffuser. The model includes an
artificial constant K in connection with different working
fluids (K = 0.667 for steam-water, K = 0.83 for air-water).

G K(1-o, ) (1X2 7
AP (1 ) x (7)
2 p,

Attou et al. (1997) had mentioned that Wadle's model


a (2













































































Greek letters
D correction factors given in Eq. (12)
a mean void fraction


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

flow area expansion and contraction using air and water.
Their new data failed within an even lower all liquid
Reynolds number (Reno < 500) than that of Abdelall et al.'s
data (2578 < Reno < 3530). The Zivi slip flow model along
with the Armand-type void fraction, a = 0.5JG JL + G)
fairly under predicted their 24 data up to about 30%, where
Jis the superficial velocity.
From the foregoing review of the two-phase pressure
change across the sudden contraction, the void fraction is
utilized for predictions except the homogeneous model,
Wadle (1980) and Chisholm & Sutherland (1980)
correlations. The void fraction may vary in the short length
of the sudden expansion due to the flow separation,
velocity and geometry changes.
MOst of the pressure change correlations based on the inlet
conditions to give a constant void fraction from
measurements or predictions from conventional
correlations, or by the individually developed empirical
correlations. Some of the investigations included the
upstream and downstream void fractions from the
measurements by Schmidt and Friedel (1996), Abdelall et
al. (2005) and Ahmed et al. (2007). Ahmed et al. (2007)
also predict the flow patterns at the upstream and
downstream, then using the appropriate correlations to
predict the corresponding void fractions. Recently, Dalkilic,
et al. (2008) had surveyed the void fraction correlations
and a summary of 35 correlations was given in a table. The
predictions of correlations had compared with data, and
Thom's void fraction correlation (1964) was found as one
of the bests in their study. Hence the void fraction
correlation proposed by Thom (1964) is implemented for
those correlations in need of void fraction.
Most of the proposed correlations/models are only
applicable to their own database. Also, some of the
correlations are not handy for the engineering application.
The objective of this study is therefore to provide a
simplified and reliable correlation with meaningful
physical parameters from the large literature database to
predict the two-phase pressure change at sudden
expansions.

Nomenclature


Paper No


widely overestimates their air-water bubbly flow data (a <
0.35). Owen et al. (1992) had also observed that, with K =
0.22 (very different from 0.667), Wadle's model agreed
quite well with their measurements. The difference of the
K values was speculated by the difference of the expansion
geometries and flow conditions with a lower mass flow
rate. The parameter, K, is an empirical constant, an
adequate modeling is needed. Attou and Bolle (1997)
simplified the jet line emerging from a sudden expansion
as a straight line, and applied the momentum balance
within the boundary of the conical jet, they obtained a
correlation for the two-phase flow pressure recovery from
a sudden expansion:

AP, = G a,(1- OA)[
Where 0 = 2/(apG) + 1-X2(1 aL], a = 3/[1 + 0-4 +
0-4] and r is a correction factor related to the plwsical
properties of the mixture. For a gas quality x = 0, Eq. (8)
can be reduced to Eq. (1). The best fitting to the correction
factor is r = 1 for steam-water mixture and r = -1.4 for
air-water mixture. The mean quadratic errors for Eq. (8)
are about 23.4%. The correlation is particularly good for
small mass velocities, but it is inapplicable to high quality
flows (x > 0.2).
Based on the momentum and mass transfer balance,
Schmidt and Friedel (1996) developed a new pressure drop
model for sudden expansion which incorporates all of the
relevant boundary conditions. Assuming constant
properties, their developed model predicts several
experimental data sets from 8 test sections with several
conventional inlet (17.2~44.2 mm) and outlet (44.2~72.2
mm) diameters. The average of the logarithmic ratios of
measured and predicted values is less than -3%, the scatter
equals to 61%. The water-air data for the test sections with
area ratio of 0.0568 and 0.0937 conducted at 250C and 5
bar shown in Fig. 4.1 of Schmidt and Friedel (1996) are
listed in Table 1. Though, small error may be included in
the data reading, the data sets are still applicable in this
study.
Recently, Abdelall et al. (2005) investigated air-water
pressure drops caused by abrupt flow area expansions in
two small tubes. The tube diameters were 1.6 and 0.84 mm
with a sudden area change ratio of 0.276. Their
measurements indicated the occurrence of significant
velocity slip. With the assumption of an ideal annular flow
regime in association with the velocity slip ratio given by
Zivi (1964):


(9)


Bo
d
g
Fr
G
K
P
dPe
r
Re
S
uG
us
x
Fe


Bond number defined Eq. (10)
internal diameter of circular tube, m
gravity, m-s2
Froude number defined in Eq. (10)
total mass flux, kg-m -s-
loss coefficient
pressure, Pa
preSsure change across the sudden expansion, Pa
correction factor given in Eq. (8)
Reynolds number, pud p
ship ratio,
actual gas velocity, m-s'
actual liquid velocity, m-s'
gas quality
Weber number defined in Eq. (10)


21G _1 L _p pL
S
21L Gl G x~,P


where uG and uL are the actual gas and liquid velocities of
gas and liquid phases, respectively. The predictions of
Abdelall et al.'s slip flow model are slightly higher than the
experimental data, but the homogeneous model, Eq. (4)
significantly over predicts their data. The error margins for
the predictions of the homogeneous model and Abdelall et
al.'s slip flow model to their 14 data were not reported in
their study.
Based on the same test facility of Abdelall et al. (2005),
Chalfi et al. (2008) recently reported more data for
single-phase and two-phase flow pressure drops caused by






7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

for the models/correlations had being examined; the results
are shown in Table 2. None of the existing correlations can
accurately predict the entire database. Most of the
correlations highly over predict the data with a mini test
section which has a Bond number being less than 0.1 in
which the effect of surface tension dominates. Also, some
Of the correlations significantly under predict the Schmidt
& Friedel data (1996) with very large test sections.
Delhaye (1981) correlation seems to have the best
predictions to the data with a standard deviation of 54%,
but it over predicts the Abdelall et al. data (2005) (139%
standard deviation) and under predicts the Schmidt &
Friedel data (1996) (59% standard deviation), followed by
Richardson (1958) whose standard deviation is 63%, but it
significantly under predicts the Schmidt & Friedel (1996)
data (82% standard deviation). Attou and Bolle (1997)
correlation is with a standard deviation of 66%, but it also
significantly under predicts the Schmidt & Friedel data
(1996) (83% standard deviation). The above four
correlations all utilized the void fraction for the prediction.
Currently, there are so many correlations available in the
literature, which one shows the best predictive ability still
requires further examination. Yet the void fraction is not a
constant in the short path of the sudden expansion
Therefore, exploitation of the void fraction raises
additional uncertainty and inconvenience from the
engineer's perspective. In addition, the correlations of
Attou and Bolle (1997) and Wadle (1980) include an
artificial correction factor which is varied for different
two-phase flow mixtures.
The highly over predictions by the existing correlations to
the Abdelall et al. data (2005) could be attributed to the
very small outlet section (d,,= 0.84 mm, dout = 1.6 mm). In
addition, the significantly under predictions for most of the
correlations to the Schmidt & Friedel (1996) data could be
due to the very large test sections (d, = 17.2 mm, dout =
72.2 mm and d,, = 19.0 mm, dout = 56.0 mm). For
obtaining a better predictive ability for mini test sections,
one should also take into account the influence of surface
tension force (Tripplet et al., 1999). The balance of
buoyancy force and surface tension force can be
represented by Bond number (Bo). Considering the effects
of total mass flux and gas quality to the surface tension,
Schmidt and Friedel (1996) had proposed a Weber number
(We) to correlate the two-phase pressure change across
sudden expansions. The Froude number (Fr) which has the
ratio between the mixture inertia and the buoyancy force
was utilized by Friedel (1979) for the two-phase frictional
pressure drop correlation in conventional straight tubes. In
addition, the liquid Reynold number, Reco = Gd/pt, was
USed as a significant parameter for correlating the
developing length downstream of a sudden expansion by
Ahmed et al. (2008).


Paper No


p density, kg- m-3
Ap density difference between liquid and gas, kg- m-3
0- surface tension, N-m-1
oA CTOss-sectional area expansion ratio, O < aA< A
6 function of the area ratio defined in Eq. (8)
pu viscosity, N-s-m

Subsripts
G gas phase
in sudden expansion inlet
L, liquid phase
LO all hiquid flow
m two-phase mixture
out sudden expansion outlet

Results and Discussion

To test the validity of the foregoing described
models/correlations from the existing literatures, 90 data
from Mendler (1963), 64 data from McGee (1966), 90 data
from Schmidt & Friedel (1996), 14 data from Abdellal et al.
(2005) and 24 data from Chalfi et al. (2008) are collected
and their test conditions, as well as the ranges of the
significant parameters are also listed in Table 1. The data
are compared with the previously described
correlations/models of Delhaye (1981) for Eq. (3),
Homogeneous model for Eq. (4), Richardson (1958) for Eq.
(5), Chisholm and Sutherland (1969), Wadle (1980) for Eq.
(7), Schmidt and Friedel (1996), Attou and Bolle (1997)
for Eq. (8) and Abdelall et al. (2005). Table 2 shows the
standard deviations of the comparison results for each data
set and the total 282 data. The standard deviations of the
relevant predictions to the total data are 54%, 143%, 63%,
74%, 92%, 69%, 66%, 230%, respectively. None of them
can accurately predict the entire database.
10 .
t Abddellal (25 Ot Dat~ao4 **
O Chalfi (2008, 24 Data)
:0 Standard Deviation= 657%
V Scmidt r(19961,90 Dat )
Standard Deviation= 31%




S101 Totaldtandardeviation=143%




Total Data= 282

lo '" n l 0. 1 .. .. ,.


Apgd 2
Bo =, We
G


lo~ lo lo~ loo
ape (Experiment Data,kPa)


lo~ 10


G 2d
Fr
op ,,


G 2
p gd


Figure 2: Comparison of Homogeneous predictions, Eq.
(3), with data.

Figure 2 is the comparison of Homogeneous predictions
with data which has a poor agreement with a standard
deviation of 143% to all the data. The predictive capability


Though, homogeneous model shows a little poor than the
others, but it is handy to use. Hence by taking account the


where pm =[ (1 x) _-Px






Paper No


forgoing parameters in Eq. (10), into the original
homogeneous model, Eq. (4), the proposed modified
Homogeneous model takes the form as:

Modzfy iromogen~eous 1 23


WeBo 1-x03
st = ( >2 x "
Reo x

2? = 0.2 x ( ~r)"


1
FrOX


02 = 0.4x( x 03'+0.3xel6/Resl '
3 x


0.4x(P L 02
G


This proposed modified homogeneous correlation
considerably improves the predictive ability over existing
correlations with a mean deviation of 23% and a standard
deviation of 29% to all the data as shown in Figure 3. The
standard deviations for the predictions of the
Homogeneous model to the data sets of Abdellal et al.
(2005), Chalfi et al. (2008), Mendler (1963), McGee (1966)
and Schmidt & Friedel (1996) are greatly improved by the
modified Homogeneous model, from 468%, 207%, 65%,
138% and 31% to 26%, 32%, 31%, 34% and 24%,
respectively. In summary, the proposed correlation shows a
very good accuracy against the existing data and is capable
of handling the effects of gas quality, area ratio, mixture
inertia, surface tension and buoyancy force, and is valid for
much wider ranges of: 506 < G < 562 gm2S 002
< 0.99, 0.057 < GA < 0.607, 0.84 < d,,, < 19 mm, 0.095 <
Bo < 92, 1.03E+1 < Fr < 9.19E+5, 1.0E+2 < We < 8.3E+4,
and 4.35E+2 < ReLo < 4.95E+05. '

los
a Abdellal (2005, 14 Data) +50% .
: tandar d(D~e~v t nna26%
102 -Standard Deviation= 32%-0%
y ta~ndr rD vato a)
33 Mcgee (1966, 64 Data)

: Standard Deviation= 24%
S10a _


S10 -


10 2Total Standard Deviation = 29% .
Total Data= 282

103
103 102 101 100 101 102 10"
aPe (Experiment Data,kPa)

Figure 3: Comparison of the data with modified
Homogeneous model, Eq.(12).

Conclusions

In this study, the authors present a thorough review of the
relevant literature for two-phase flow across sudden
expansions, and examine the applicability of the existing
correlations. Also, 282 data available from 5 publications
are collected. None of the existing eight correlations can
accurately predict the entire database. Most of the


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

correlations highly over predict the data with a mini test
section which has a Bond number being less than 0.1 in
which the effect of surface tension dominates. Some of the
correlations significantly under predict the data with very
large test sections. The significant parameters of Bond
number, Weber number, Froude number, and liquid
Reynolds number to the frictional two-phase pressure
change across sudden area expansions are discussed.
Among the models/correlations being examined, the
homogeneous model though shows a poor predictive
ability than the others, but it is handy for the engineering
application. Hence by taking account the influences of
Bond number, Weber number, Froude number, liquid
Reynolds number, gas quality and area ratio into the
original homogeneous model for correlating with the data,
a modified homogeneous correlation is proposed that
considerably improves the predictive ability over existing
correlations with a mean deviation of 23% and a standard
deviation of 29% to all the data with wider ranges for
application.

Acknowledgements

The supports from the Energy Bureau and Department of
Industrial Technology of the Ministry of Economic Affairs
and National Science Committee (NSC
97-2221-E-224-054) of Taiwan are greatly appreciated.

References

Abdelall, E.F., Hahm, G., Ghiaasiaan, S.M., Abdel-Khalik,
S.L., Jeter, S.S., Yoda, M. & Sadowski, D.L. Pressure drop
caused by abrupt flow area changes in small channels. Exp.
Thermal Fluid Sci., 29, 425-434 (2005).
Ahmed, W.H., Ching, C.Y. & Shoukri, M. Pressure
recovery of two-phase flow across sudden expansions. Int.
J. Multiphase Flow, Vol. 33, 575-594 (2007).
Ahmed, W.H., Ching, C.Y. & Shoukri, M. Development of
two-phase flow downstream of a horizontal sudden
expansion. Int. J. Heat and Fluid Flow, Vol. 29, 194-206
(2008).
Attou, A., Giot, M. & Seynhaeve, J.M. Modelling of
steady-state two-phase bubbly flow through a sudden
enlargement. Int. J. Heat Mass Transfer, Vol. 40 (14),
3375-3385 (1977).
Attou, A. & Bolle, L. A new correlation for the two-phase
pressure recovery downstream from a sudden enlargement.
Chem. Eng. Technol, Vol. 20, 419-423 (1997).
Chalfi, T.Y, Toufik, Y. & Ghiaasiaan, S.M. Pressure drop
CRUSed by flow area changes in capillaries under low flow
conditions, Int. J. Multiphase Flow, Vol. 34, 2-12 (2008).
Chen, I.Y., Tseng, C.Y., Lin, Y.T. & Wang, C.C. Two-phase
flow pressure change subject to sudden contraction in
small rectangular channels, Int. J. Multiphase Flow, Vol.
35 (3), 297-306 (2008).
Chisholm, D. & Sutherland, L.A. Prediction of pressure
gradients in pipeline system during two-phase flow. Proc.
Inst. Mech. Eng., Vol. 184 (Pt. 3C), 24-32 (1969).
Dalkilic, A.S., Laohalertdecha S. & Wongwises, S. Effect
of void fraction models on the two-phase friction factor of
R134a during condensation in vertical downward flow in a
smooth tube. Int. Comm. Heat and Mass Transfer, Vol. 35
921-927 (2008).


































Table 1. Available data for two-phase pressure change across sudden expansions
Schmidt &
Abdellal et al. Chalfi et al. Mendler (1963) McGee (1966)
Resarcers (2()(5) 1 tube (2()(8) 1 tube 3 tubes 3 tubes Friedel (1996)
2 tubes

G (kg/n~s) 3()74 -4212 5()6 -664 692 -5642 544 -248() 1()(() 3()()

1 ().()(2- ).()13 ).()285-().182 ).()32- ().469 ().()(1 .3()4 ().)1 .99
~Air-Water Air-Water Steanl-Water Stean1-Water Air-Water
Working fluid
25 oC 25 oC 194-252 oC 141-195oC 25 oC
din (nm) ().84 ().84 9.55, 12.9, 17.63 8.64, 11.68 17.2, 19
().145,().264 ().332, ().546,
CT ().276 ().276 '(.()568, ).()937
().493 ().6()7

Bo =~ gd (.()95 ).()95 19,8 -92.1 13.5-3().7 4() 48.8

G2
Fr = 935() -167()()( 264()(-91 9()() 25.7 376()( 1().3-957()( 39.5 172()()(


G~d
We = 312 -133() 1()) 594 1()2() 455()( 185-155()( 716 -836()

Gd
ReLo -258()- 453() 435 -571 9)2()()- 495()()( 336()(-1 37()() 19()(()- 63()()(

AP, (kPa) ).726 -4.62 ().8()1 -3.71 ().575 -15.6 ).()69 -14.4 ().2 -36.()
Data Points 14 24 9() 64 9()

Table 2. The standard deviations for the pndctions of existing com relations to the data
Abdellal Schmidt
Chalfi et Mendler McGee Total
Data et al. & Friedel
al., 1 tube 3 tubes 3 tubes 282
Correlations 1 tube 2 tube
(2008) (1961) (1966) Points
(2005) (1996)
Delhaye (1981) 139% 28% 36% 39% 59% 54%
Homognous 468% 207% 65% 138% 31% 143%
Richardson (1958) 57% 51% 54% 44% 82% 63%
Chisholm & Sutherland (1969) 250% 77% 37% 56% 49% 74%
Wadle (1989) 178% 46% 52% 66% 123% 92%
Schmit & Friedel (1996) 259% 28% 43% 47% 41% 69%
Attou & Bolle (1997) 93% 53% 54% 52% 83% 66%
Abdelall et al. (2005) 133% 46% 169% 80% 360% 230%


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

two-component flow. Rept. ANL-5949 (1958).
Romie, F. Private Communication to P. Lottes, American
Standard Co., (see Lottes, 1961) (1958).
Schmidt, J. & Friedel, L. Two-phase flow pressure change
across sudden expansions in duct areas. Chem. Eng.
Commun, Vol. 141-142, 175-190 (1966).
Tripplet, K.A., Ghiasiaan, S. M., Abdel-Khlik, S.L.,
LeMouel, A. & McCord, B.N. Gas-liquid two-phase flow
in microchannels, Part II: Void fraction and pressure drop.
Int. J. Multiphase Flow, Vol. 25, 395-410 (1999).
Thom, J.R.S. Prediction of pressure drop during forced
circulation boiling of water. Int. J. Heat and Mass Transfer,
Vol. 7, 709-724 (1964).
Wadle, M. A new formula for the pressure recovery in an
abrupt diffuser. Int. J. Multiphase Flow, Vol. 15 (2),
241-256 (1989).
Zivi, S.M. Estimation of steady state steam void-fraction
by means of principle of minimum entropy production.
ASME Trans. C, Vol. 86, 237-252 (1964).


Paper No


Delhaye, J.M. Singular pressure drops, In: Bergles, A.E.
(Ed.), Two-phase and heat transfer in the power and
process industries. chapter 3, Hemisphere, Washington, DC
(1981).
Friedel, L. Improved friction pressure drop correlations for
horizontal and vertical two-phase pipe flow. European
Two-phase Group Meeting, Ispra, Italy, Paper E2 (1979).
Lottes, P.A. Expansion losses in two-phase flow. Nucl. Sci.
Eng., Vol. 9, 26-31 (1961).
McGee, J.W. Two-phase flow through abrupt expansions
and contractions. Ph.D Thesis, University of North
Carolina at Raleigh, U.S.A (1966).
Mendler, O.J. Sudden expansion losses in single and
two-phase flow. Ph.D. thesis, University of Pittsburgh,
Pennsylvania, U.S.A (1963).
Owen, I., Abdou-Ghani, A. & Amini, A.M. Diffusing a
homogenized two-phase flow. Int. J. Multiphase Flow, Vol.
18, 531-540 (1992).

Richardson, B. Some problems in horizontal two-phase,




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - Version 2.9.7 - mvs