Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 16.2.3 - Experimental validation of the model for calculating the drag reduction during gas/power-law fluid flow
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 Material Information
Title: 16.2.3 - Experimental validation of the model for calculating the drag reduction during gas/power-law fluid flow Non-Newtonian Multiphase Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Xu, J.
Wu, Y.-X.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: drag reduction
gas-liquid flow
non-Newtonian fluids
horizontal pipes
 Notes
Abstract: The drag reduction by gas injection for power-law fluid flow in stratified and slug flow regimes has been studied. The methods for predicting of the maximum drag reduction ratio in stratified flow and slug flow regimes were presented. The results show that the drag reduction should occur over the large range of the liquid holdup when the flow behaviour index remains at the low value. Furthermore, for turbulent gas-laminar liquid stratified flow, the drag reduction by gas injection for Newtonian fluid is more effective than the drag reduction of shear-shinning fluid when the dimensionless liquid height remains in the area of high value. The pressure gradient model for a gas/Newtonian liquid slug flow is extended to liquids possessing the Ostwald--de Waele power law model for calculating the drag reduction ratio. The proposed models were validated against 340 experimental data point over a wide range of operating conditions, fluid characteristics and pipe diameters. The drag reduction ratio predicted is well inside the 20% deviation region for 80% of the experimental data. These results substantiate the general validity of the model presented for gas/non-Newtonian two-phase slug flows.
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
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Volume ID: VID00396
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Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010



Experimental validation of the model for calculating the drag reduction ratio during
gas/power-law fluid flow


Jing-yu Xu and Ying-xiang Wu


Key Laboratory for Hydrodynamics and Ocean Engineering, Institute of Mechanics, Chinese Academy of Sciences
Bei si huan xi road No15, beijing 100190, China

xujingyu@imech.ac.cn


Keywords: Drag reduction; gas-liquid flow; non-Newtonian fluids; horizontal pipes


Abstract

The drag reduction by gas injection for power-law fluid flow in stratified and slug flow regimes has been studied. The
methods for predicting of the maximum drag reduction ratio in stratified flow and slug flow regimes were presented. The
results show that the drag reduction should occur over the large range of the liquid holdup when the flow behaviour index
remains at the low value. Furthermore, for turbulent gas-laminar liquid stratified flow, the drag reduction by gas injection for
Newtonian fluid is more effective than the drag reduction of shear-shinning fluid when the dimensionless liquid height
remains in the area of high value. The pressure gradient model for a gas/Newtonian liquid slug flow is extended to liquids
possessing the Ostwald--de Waele power law model for calculating the drag reduction ratio. The proposed models were
validated against 340 experimental data point over a wide range of operating conditions, fluid characteristics and pipe
diameters. The drag reduction ratio predicted is well inside the 20% deviation region for 80% of the experimental data. These
results substantiate the general validity of the model presented for gas/non-Newtonian two-phase slug flows.

Symbols
Subscripts
Notation


A cross-sectional area
D pipe diameter
f friction factor
g acceleration of gravity
G the mass flux
h fluid level
AP pressure drop
11 liquid film zone of length
s1 liquid slug zone of length
1, slug unit of length
mi fluid consistency coefficient
nl flow behaviour index
Re Reynolds number
S pipe perimeter
u mean velocity
ud drift velocity

Greek letters

a liquid holdup
E absolute pipe roughness
/eff effitive viscosity
T shear stress
p density
FA drag reduction ratio
(12 dimensionless pressure drop
X2 Lockhart-Matinelli parameter


2
m


m/S2
kg/m2 sec
m
Pa/m
m
m
m
Pa sn


m
m/s
m/s


m
Pa s
Pa
kg/m3


gas phase
interface
liquid phase
two-phase
superficial liquid phase
superficial gas phase
liquid slug
slug unit
mixture velocities of the superficial gas
and liquid phases


Introduction

In the last decades some work has been carried out to study
on drag reduction in gas-liquid systems. The significant
achievement is that the injection of gas into non-Newtonian
liquids, especially for power-law (shear thinning) liquids, at
a given liquid flow rate will result in the reduction of
pressure drop. The earliest studies concerning this
phenomenon were carried out by Ward and Dallavalle
(1954), who injected air into clay suspensions flowing in
the laminar regime. The drag reduction ratio can be defined
as:
0 A- = 1-0AP
AP, (1)
where D A is the drag reduction ratio, D12 is the
dimensionless pressure drop, AP is the pressure drop and
the subscripts tp, and sl refer to the two-phase and the





Paper No


superficial liquid phase, respectively. Here (D>0 meant
that two-phase pressure drop is smaller than that of the
liquid phase flowing on its own at the same flow rate. Thus
the drag reduction occurs.

Most of models traditionally depended on flow pattern to
predict the drag reduction in horizontal pipes. For stratified
flow the Heywood and Charles (1979) extended the model
of Taitel and Dukler (1976) for gas/Newtonian liquid
stratified flow to liquids obeying the Ostwald-de Waele
power law model, and defined conditions for drag
reduction of the liquid flow by the presence of the gas.
They found that drag reduction occurred over the largest
ranges of liquid and gas flow rates at the lowest nl values
provided that liquid flow remains laminar. However,
Heywood-Charles model did not carry out experiments to
test their model.

Considering the slug flow regime, Farooqi et al. (1980)
described the theological behaviour of the suspensions as
the Bingham plastic model, and extended the Ducker and
Hubbard model (1975) to allow for non-Newtonian
behaviour of the suspensions for predicting the extent of
drag reduction in the slug flow regime. The results showed
that the drag reduction effect became progressively more
marked as both the yield stress and plastic viscosity
parameters increased with increasing suspension
concentration. By analyzing the experimental data of
Farooqi and Chhabra (1982b), Dziubinski (1995) presented
a general expression of drag ratio for two-phase pressure
drop of gas/non-Newtonian fluid based on the concept of
loss coefficient during the intermittent flow. Bishop and
Deshpande (1986) studied the power-law (shear thinning)
non-Newtonian liquid-gas uniform stratified flow. They
found that the Heywood-Charles model was valid for
predicting the pressure drop and liquid holdup for a
uniform stratified flow, and two-phase drag reduction,
which was predicted by the Heywood-Charles model, did
not occur because there was a transition to semi-slug flow
before the model criteria were reached. Ruiz-Viera, et al.
(2006) experimentally observed the drag reduction
phenomenon using different geometries with both smooth
and rough surfaces during slug flow of a lubricating
grease/air mixture. The experimental data showed that drag
reduction appeared to be dramatic by injecting relatively
low flow rates of air, even more as liquid flow rate
decreases, although it was dampened by increasing the
volumetric flow rate of air. In addiction to these, Xu J-y et
al. (2007) studied the co-current flow characteristics of air/
power-law fluid systems in inclined smooth pipes using
transparent tubes of 20, 40 and 60 mm in diameter. In their
works, the Heywood-Charles model (1979) was modified
for horizontal flow to accommodate stratified flow in
inclined pipes, taking into account the average void
fraction and pressure drop of the mixture flow of a
gas/non-Newtonian liquid. However they only presented
the criterion equation to determine whether drag reduction
existed in stratified gas/non-Newtonian liquid flow, the
drag reduction was not studied in detail using the equation
suggested.

Literature survey show that although some studies have
been done on the drag reduction for gas-liquid two-phase


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

flow, few attempts have been made to study the drag
reduction characteristic in horizontal pipes under different
flow regimes. In the chemical process industries,
non-Newtonian liquids, especially pseudoplastic
(po\ic1-LiUv) liquids, are encountered frequently. Several
industrial applications utilize these liquid-gas mixtures
flowing through horizontal tubes. Therefore, there is a need
to understand in depth the hydrodynamics and transport
behavior of non-Newtonian liquid-gas systems. The
purpose of this work was to study the characteristic of drag
reduction in horizontal pipes, especially for flowing in a
commercial pipe. The proposed models of the drag
reduction ratio were tested extensively against a large set of
available experimental data for air/non-Newtonian fluid
systems flowing in smooth and commercial pipes in this
work and for others system reported in the literature.

Experimental Facility

The experiments reported below were carried out on the
multiphase flow facilities at Institute of Mechanics,
Chinese Academy of Sciences. The details of the flow-loop
can be found in the previous works (Xu et al. 2009). Air
came from a compressor pump via gas mass flow-meter.
Polymer solutions used as the liquid phases were conveyed
from liquid phase tank into the pipeline. Liquid phase and
gas phase were fed into the pipeline via a T-junction. The
volumetric flow rates of all phases could be regulated
independently and were measured by thermal mass flow
meter for air phase and electromagnetic flow-meter for
polymer solutions. The multiphase flow pipeline was
manufactured of perspex tubing with an internal diameter
of 50mm through which the flow could be observed. The
total length of this pipeline between the entrance and the
separation unit was approximately 30m. The pipeline
consists of two horizontal legs with a leg length of 10m and
14m, respectively, connected by a horizontal U-turn. The
sampling frequency of the pressure was 500 Hz. Flow
patterns were recorded using a high-speed video camera,
and the flow patterns for each test condition were recorded
and could be observed later in slow motion.

Four different concentrations CMC (carboxymethyl
cellulose) solutions used as non-Newtonian fluid. Solutions
were prepared by adding small quantities of dry polymer
powders accompanied by gentle stirring to prevent the
formation of lumps. The density of each solution was
measured using a constant volume density bottle. The CMC
rheology experiments are measured with a ThermoHaake
RS300 rheometer. A double gap cylinder sensor system
with an outside gap of 0.30 mm and an inside gap of 0.25
mm was used. As expected, CMC solutions in this study
were shear-thinning fluids whose rheology can be
described by Ostwald--de Waele power law model.


= m )nl (2)

Numerical Scheme

Stratified flow in horizontal pipes

Assuming a fully developed stratified flow, the integral






Paper No


forms of the momentum equations for the two fluids are
written for the liquid and gas phase as follows:

dp dh_, Ad(G,u,)_
-A(-L ), iS, + S, +A4pg- -A- =0
dx dx dx (3)

dp dh d(GgUg) )
-A,( ) -Sp zSg + +A g -A = =
dx dx dx (4)

Eliminating the pressure drop by combining equations (3)
and (4), and ignoring the acceleration terms, yields a
relation can be used to calculate the liquid holdup by
solving for the liquid height:


S SI 1 1 h,/D Ia
F= ,-- -+ fS (--+ -)- pgD-
SA A1 A1 A 8ac &x


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


( ) -=2f pu -+ 4 ( S + S )
dxt D 1,r-D2 1 2 2 (10)


where the following relations have been used in a
commercial pipe (Taitel and Bamea, 1990):


S=0.001375[l+(2x104 o +- 1)]
D, Rek (11)


The dimensionless pressure drop can be expressed in a slug
flow:


o 2 f


where


By designating the dimensionless quantities by a tilde (~), a
general dimensionless expression given in the case of a
uniform film thickness for stratified flow:
x j, 2 f it2 2, SI2
X i- (q.-).-q.- (+)=0
A, i i -9 -, a A, A


2 f u2


(13)


n4 f lPg2 fp 2 2
2 2
2 f pPu,
D (14


Once a solution has been obtained for h, by equation (6),
the dimensionless pressure drop can be given respectively
as:


2 -+ S -- )
d o D' g X2 Dm
g (7)


where Os and Of are the dimensionless pressure drop in
the liquid slug and in the film zone respectively. Thus
the drag reduction ratio in slug flow can be expressed as:


qA =1-(qs+q )


Results and Discussion


Thus the drag reduction ratio can be expressed as:


A 1 =I-K'


where


K= S{1
.{i


[ +(1-q.- ) 1-q. +
A u A A


2.2 Slug flow in horizontal pipes


In the slug unit of length, l,, consists of two separate
sections: the liquid slug zone of length 1, and the film zone
of length l. Assuming that the film contains no entrained
gas bubbles and a uniform film along the film zones, the
average pressure gradient in a slug unit is obtained by
performing a momentum balance over a global control
volume of the slug unit:


The drag reduction ratio, ( A, as predicted from the
equation (8) is presented in Fig.1 for various ni values
corresponding to power-law flow behaviour in stratified
horizontal flow. It can be seen that over the range
(8) 0.1 0.1, but for a high value of a the reverse is true. The
drag reduction occurs over the greatest range of a at the
lowest n, values. However, Fig.1 also reveals the
interesting result that the maximum drag reduction ratio
occurs at the highest n, value plotted for a constant liquid
holdup, a namely that the drag reduction by gas injection
(9) for Newtonian fluid in a laminar flow is more effective
than the drag reduction of shear-shinning fluid when the
dimensionless liquid height remains in the area of high
value.


In this work, provided that q and n, are known, the effect of
variation in h on the drag reduction ratio can be
calculated using the equation (8). When the drag reduction
ratio reach the maximum value, h may be obtained by the
differentiation of equation as:


S=0
9h


(14)






Paper No


where ,A is only the function of h. Thus the maximum
drag reduction ratio can be obtained by the equation (16).

In order to validate the method of stratified flow presented
by this work, the experimental data of Bishop and
Deshpande (1986) were compared with the results
predicted from the equations (7) as shown in Figs.2. The
results of this comparison indicate good agreement for the
dimensionless pressure drop. In their work two-phase drag
reduction can not be achieved in stratified flow of
non-Newtonian liquid-gas mixtures. They hypothesized
that the drag reduction was restricted to those situations
where streamline flow patterns existed at the head of an
elongated bubble so that the drag reduction could not exist
in stratified liquid-gas flow. However, in the present work,
it can be seen in Fig. 1 that the drag reduction should occur
over the large range of the liquid holdup when ni remains at
the low value. Thus the reason that the drag reduction was
not observed may be due to the fact that the flow behavior
index of non-Newtonian material in their experiments is not
enough low so that The pressure drop was reduced below
the value for which the liquid flows alone at the same
liquid flowrate (n1 > 0.68 in Bishop and Deshpande' work,
1986)

For calculating the pressure drop of gas/Newtonian fluid in
a horizontal slug flow, we carried out a series of
experiments to study the drag reduction and further
modified the model suggested by Xu J-y et al. (2007, 2009)
to study the drag reduction ratio by considering the
Ostwald--de Waele power law model. In addition, we used
a large set of available experimental data over a wide range
of operating conditions and pipe diameters in the literature
to validate the developed model.

Fig.3 illustrates the effects of liquid flow rate on the drag
reduction ratio for air/CMC solution flow. At lower gas
flow rate within the range of 1.25 m3/h eQ, < 10.0 m3/h,
q, increases monotonically with the gas flow rate
increasing. However, the drag reduction ratio tends to
reach constant values when gas flow rate is further
increased. The reason can be explained by the fact that,
supposing the no slip velocity between the gas and liquid
phases and the homogeneous flow, the Reynolds number of
two-phase can be obtained via equation (11):

Du p.
Re, "
pl/ (17)

where D. =D 8 1N" IK(u, +u ) -1 (n1 1) is defined as the
"effective viscosity". It can be observed from equation (17)
that, for a fluid of given rheology (coefficient nl and mi),
increasing the superficial gas velocity will reduce the
effective viscosity so that the frictional pressure gradient is
decreased. However the gas will always disturb the flow
and there will be additional pressure losses in the mixture
of two phase flow so that two-phase pressure gradient is
augmented. Therefore, the drag reduction ratio, q), might
show different tendencies when the gas flow rate increasing,
as shown in Fig.3.


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


To calculate exactly the drag reduction ratio, the pressure
gradient of two-phase flow calculated has to be validated
firstly. Fig.4 displays that the model predictions were tested
against the data of Farooqi and Richardson (1982b) for air
and kaolin suspensions flowing in a pipe of 0.0417 m in
diameter. A very good agreement was obtained between the
theoretical and experimental pressure gradients in the
superficial gas velocity range of 0-1.0 m/s. The data in the
high gas velocity range of 1.0-6.5 m/s were over-predicted
by the model presented in this work. However in the whole
range both the theoretical curves and the experimental data
for the two-phase pressure drop exhibit the same trend. At
low superficial gas velocities the pressure drop decreases as
Usg is increased. It reaches to a minimum value at the
critical velocity for the transition from laminar to turbulent
flow (Farooqi and Richardson, 1982b). Past this velocity,
the pressure gradient increases steadily. Furthermore,
increasing the superficial liquid velocity at any given usg
results in higher theoretical as well as experimental
pressure drop over the entire range of the tested data air
and kaolin suspensions flow. Fig.5 compares the predicted
pressure gradient with experimental data of Chhabra et al.
(1984) and the present work for air/CMC solutions flowing
in a pipe of 0.0417 m I.D. and of 0.05 m I.D. respectively.
An excellent agreement was obtained between theory and
data. The pressure gradient predicted by the model for
gas/power-law fluid slug flow, as well as the experimental
data, indicate that the drag reduction by gas injection is
more prominent with low superficial gas velocities, as
shown in Figures.

Finally, the proposed method for slug slow has been
checked by plotting the experimental values of the drag
reduction ratio vs. the predicted ones calculated from (15).
As Fig.6 shows, the use of equation (15) allows a good
prediction of the drag reduction ratio for the
gas/non-Newtonian power-law fluid mixture flow. eighty
percent of the experimental values are well inside the 20%
deviation region using 340 experimental data point
collected from different references (Chhabra et al. 1983;
Chhabra et al. 1984; Farooqi and Richardson 1982b;
Ruiz-Viera et al. 2006), including the smooth and rough
pipes.

Conclusions

An experimental and theoretical study of a
gas/non-Newtonian fluid flow through the horizontal pipe
has been conducted. Special attention was given to study
the drag reduction ratio by gas injection for power-law
fluid flow in stratified and slug flow regimes. The method
for predicting of the maximum drag reduction ratio in
stratified flow regime was presented by modifying the
model suggested by Xu et al. The results show that, for
turbulent gas-laminar liquid stratified flow, the drag
reduction by gas injection for Newtonian fluid is more
effective than the drag reduction of shear-shinning fluid
when the dimensionless liquid height remains in the area
of high value. Furthermore, the drag reduction should
occur over the large range of the liquid holdup when the
flow behaviour index remains at the low value. The
method for predicting the gas-liquid stratified was






Paper No


validated by the experimental data of Bishop and
Deshpande, and results of this comparison indicate good
agreement for the dimensionless pressure drop. The
pressure gradient model for a gas/Newtonian liquid slug
flow is extended to liquids possessing the Ostwald--de
Waele power law model for calculating the drag reduction
ratio. The proposed models were validated against a large
set of available experimental data over a wide range of
operating conditions, fluid characteristics and pipe
diameters. A very good agreement was obtained between
the predicted and experimental results. The drag reduction
ratio predicted is well inside the 20% deviation region for
80% of the experimental data. These results substantiate
the general validity of the model presented for
gas/non-Newtonian two-phase slug flow

Acknowledgements

The authors are grateful to the financial support provided
by the National Natural Science Foundation of China (No.
10902114)

References

Bendiksen, K. An experimental investigation of the motion
of long bubbles in inclined tubes. International Journal of
Multiphase Flow 10, 467-483, 1984.

Bishop, A.A., Deshpande,S.D. Non-Newtonian liquid-air
stratified flow through horizontal tubes-II. International
Journal of Multiphase Flow 12, 977-996, 1986.

Chhabra, R.P, Farooqi, S.I., Richardson, J.F. Isothermal
two-phase of air and aqueous polymer solutions in a
smooth horizontal pipe. Chemical Engineering Research
and Design 62, 22-31,1984.

Duker, A.E., Hubbard, M.G. A model for gas-liquid slug
flow in horizontal and near horizontal tubes, Ind. Eng.
Chem. Fundam. 14 337-34, 1976.

Dziubinski, M. A general correlation for the two-phase
pressure drop in intermittent flow of gas and
non-Newtonian liquid mixtures in a pipe. Chemical
Engineering Research and Design 73, 528-533, 1995.

Farooqi, S.I., Richardson, J.F. Horizontal flow of air and
liquid (Newtonian and non-Newtonian) in a smooth pipe.
Part II: Average pressure drop. Transactions of the Institute
of Chemical Engineers 60, 323-333, 1982b.

Farooqi, S.I., Heywood, N.I., Richardson, J.F. Drag
reduction by air injection for suspension flow in a
horizontal pipeline. Transactions of the Institute of
Chemical Engineers 58, 16-27, 1980.

Heywood, N., Charles, M.E. The stratified flow of gas and
non-Newtonian liquid in horizontal pipes. International
Journal of Multiphase Flow 5, 341-352, 1979.

Lockhart, R.W, Martinelli, R.C. Proposed correlation of
data for isothermal two-phase, two-component flow in
pipes. Chemical Engineering and Processing 45, 39-48,


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

1949.

Ruiz-Viera, M.J., Delgado, M.A., France, J.M., Sanchez,
M.C., Gallegos, C. On the drag reduction for the two-phase
horizontal pipe flow of highly viscous non-Newtonian
liquid/air mixtures: Case of lubricating grease.
International Journal of Multiphase Flow 32, 232-247,
2006.

Taitel, Y., Barnea, D. A consistent approach for calculating
pressure drop in inclined slug flow. Chemical Engineering
Science 45, 1199-1206, 1990.

Tailer, Y., Dukler, A.E. A model for prediction flow regime
transition in horizontal and near horizontal gas-liquid.
A.I.C.H.E. Journal 22, 47-55, 1976.

Ward, H.C., Dallavalle, J.M. Co-current
turbulent-turbulent flow of air and water-clay suspensions
in horizontal pipes. Chemical Engineering Progress 10,
1-14, 1954.

Xu, J-y, Wu, Y-x, Shi, Z-h, Lao, L-y, Li, D-h. Studies on
two-phase co-current air/non-Newtonian shear-thinning
fluid flows in inclined smooth pipes. International Journal
of Multiphase flow 33: 948-969, 2007.

Xu, J.-y., Wu, Y.-x. Li, H., Guo, J. and Chang, Y. Study of
drag reduction by gas injection for power-law fluid flow in
horizontal stratified and slug flow regimes. Chemical
Engineering Journal 147, 235-244, 2009.






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


Fig.1 the effect of the flow behavior index on the drag
reduction ratio, o2, in horizontal stratified flow


10-







1







0.1-


Fig.2 Comparison of the theoretical predictions obtained
for the dimensionless pressure drop with experimental data
in this work and those in Bishop and Deshpande' work in
horizontal stratified flow regime




air/CMC-4 flow in this work







L !l .... .... ( (m /h)
S.1 -
-i 1.25
S0 2.50
0o) A 3.75
o- Predicted V 5.00
d 7.50

0 5 10 15 20
Gas flowrate, Qg (m2/h)
Fig.3 Effects of fluid flow rate on the drag reduction ratio
for air/CMC slug flow.


Fig. 4 Comparison of the predicted pressure gradient with
the data of Farooqi and Richardson for air and kaolin
suspensions slug flowing in a pipe of 0.0417 m in diameter
(the flow behaviour index, nl=0.175)


101









10


Ug (m/s)


101









10


0 1 2 3 4


U (m/s)
sg


Paper No


0.5


0.0


-0.5


-1.0


Experimental data by Farooqi and Richardson 1982b


0 0.244
0 0.488
A 0.976


ug (m/s)


--- Predicted by the model (n =0.85)
* Experimental data, Bishop and Deshpande (1986)

n =0.952
g 0.765 0.595 0.535





-0- Predicted by the model, U =0.1769 m/s
Experimental data in this work


Sair/CMC-3 flow in this work




U1l (m/s)
O 0.1769
A 0.3539
A A <1 0.5308
A 0.7077
0 1.0616
0 -Predicted
I AZ






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


Usg (m/s)

Fig. 5 Comparison of the predicted pressure gradient with
experimental data of Chhabra et al. and the present work
for air/CMC solutions flowing in a pipe of 0.0417 m I.D.
and of 0.05 m I.D. respectively (a the flow index, n=0.535;
b the flow index, n=0.595; c the flow index, n=0.58)



1.0 a +30

0.8 -20%





0.2 >



0.0

0.0 0.2 0.4 0.6 0.8 1.0
Experimental, *A
Fig. 6 Compared between experimental and theoretical
obtained values of the drag reduction ratio, for
gas/non-Newtonian fluid flow studied in this work and for
others systems reported in the literature.


Paper No


C Experimental data by Chhabra et al. 1984
CVCMC, conc 1.25%



SPredicted

'u"s (m/s)
5 0.244
-o E 0 0.490
A 0.732
0.976




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