Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 16.6.3 - Droplet Entrainment in Churn Flow
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 Material Information
Title: 16.6.3 - Droplet Entrainment in Churn Flow Fluid Structure Interactions
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Ahmad, M.
Peng, D.J.
Hale, C.P.
Walker, S.P.
Hewitt, G.F.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: entrainment
churn flow
axial view photography
 Notes
Abstract: Churn flow is an important intermediate flow regime between slug and annular flow. In the Taylor bubbles which are characteristic of slug flow, there is a falling film at the tube wall with an upwards gas flow in the core. The transition from slug flow to churn flow occurs when the conditions in the Taylor bubbles occurring in slug flow are such as to promote flooding (Jayanti and Hewitt, 1992). Churn flow is a region in which there are large interfacial waves travelling upwards with falling film regions between the waves; the transition to annular flow occurs when the (film) flow becomes continuously upwards. In both churn flow and annular flow, a (sometimes large) proportion of the liquid flow is in the form of entrained droplets in the gas core. In annular flow systems with evaporation, the entrainment of droplets from the film surface plus the evaporation of the film may not be sufficiently offset by droplet deposition and film dryout occurs. Dryout can be predicted provided expressions can be invoked for local entrainment, deposition and evaporation rates and these expressions integrated to establish the conditions under which the film flow rate becomes zero (Hewitt and Govan, 1990). This integration procedure needs a boundary value for entrained droplet flow rate at the onset of annular flow (i.e. at the transition between churn flow and annular flow) and the predictions obtained for dryout may be sensitive to this boundary value for short tubes. Some data and a correlation for the entrained fraction at the onset of annular flow were obtained by Barbosa et al. (2002) but this correlation applies only to adiabatic and equilibrium conditions. The work described in this paper is focused on the question of droplet entrainment in churn flow and the development of a methodology for predicting the entrained fraction at the onset of annular flow for diabatic (i.e. non-equilibrium) systems. New expressions are given which allow the integration procedure to be extended to cover both churn flow and annular flow. New experiments were also conducted on the churn-annular region using the axial view photography technique. This allowed the entrainment processes to be visualized starting at the onset of churn flow and passing into the annular flow regime.
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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Bibliographic ID: UF00102023
Volume ID: VID00408
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: 1663-Ahmad-ICMF2010.pdf

Full Text

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


Droplet Entrainment in Churn Flow


MasroorAhmad*, Deng J. Pengt, Colin P. Halet, Simon P. Walker* and Geoffrey F. Hewittt

Department of Mechanical Engineering, Imperial College London, SW7 2AZ, UK
t Department of Chemical Engineering, Imperial College London, SW7 2AZ, UK

m.ahmad06@imperial.ac.uk and g.hewitt@imperial.ac.uk


Keywords: entrainment, churn flow, axial view photography




Abstract

Chum flow is an important intermediate flow regime between slug and annular flow. In the Taylor bubbles which are
characteristic of slug flow, there is a falling film at the tube wall with an upwards gas flow in the core. The transition from slug
flow to chum flow occurs when the conditions in the Taylor bubbles occurring in slug flow are such as to promote flooding
(Jayanti and Hewitt, 1992). Chum flow is a region in which there are large interfacial waves travelling upwards with falling
film regions between the waves; the transition to annular flow occurs when the (film) flow becomes continuously upwards. In
both chum flow and annular flow, a (sometimes large) proportion of the liquid flow is in the form of entrained droplets in the
gas core. In annular flow systems with evaporation, the entrainment of droplets from the film surface plus the evaporation of
the film may not be sufficiently offset by droplet deposition and film dryout occurs. Dryout can be predicted provided
expressions can be invoked for local entrainment, deposition and evaporation rates and these expressions integrated to
establish the conditions under which the film flow rate becomes zero (Hewitt and Govan, 1990). This integration procedure
needs a boundary value for entrained droplet flow rate at the onset of annular flow (i.e. at the transition between churn flow
and annular flow) and the predictions obtained for dryout may be sensitive to this boundary value for short tubes. Some data
and a correlation for the entrained fraction at the onset of annular flow were obtained by Barbosa et al. (2002) but this
correlation applies only to adiabatic and equilibrium conditions. The work described in this paper is focused on the question of
droplet entrainment in churn flow and the development of a methodology for predicting the entrained fraction at the onset of
annular flow for diabetic (i.e. non-equilibrium) systems. New expressions are given which allow the integration procedure to
be extended to cover both chum flow and annular flow. New experiments were also conducted on the churn-annular region
using the axial view photography technique. This allowed the entrainment processes to be visualized starting at the onset of
chum flow and passing into the annular flow regime.


Introduction

In gas-liquid mixture flows in vertical pipes, the phases
distribute themselves in a variety of spatial and temporal
distributions, referred to as flow regimes or flow patterns. A
wide variety of names have been given to these phase
distributions; a reasonably well accepted set of descriptions
for vertical upflow is as follows: bubbly flow, slug flow,
chur flow and annular flow. These flow regimes and
corresponding transitions between them are of immense
importance in predicting the transition of a regime of high
heat transfer coefficient to one of greatly reduced heat
transfer coefficient; this transition is referred to by a
number of names, including dryout, critical heat flux (CHF)
and boiling crisis. The accurate prediction of this transition
is of great importance not only in design and safe operation
of nuclear power plants but also many other types of
industrial heat transfer equipment.
Annular film dryout is arguably the most important
mechanism for the onset of reduced heat transfer coefficient.
In annular flows, liquid is lost from the film as a result of
droplet entrainment and evaporation, and it is gained by the


film by droplet deposition rate, which leads to liquid film
dryout. In the annular flow model, the equations for
entrainment, deposition and evaporation are integrated from
the onset of annular flow (i.e. from the chur-annular
transition); when the film flow rate is predicted to be zero,
then dryout is predicted to occur. However, this integration
process requires an initial value for entrained fraction (IEF)
at the chur flow-annular flow transition; the IEF could, in
principle vary between zero and unity. It was observed that
dryout prediction may be a strong function of IEF at the
onset of annular flow especially at high liquid mass fluxes.
In order to solve the problem of IEF at the chur-annular
transition, an understanding of droplet entrainment in chur
flow is vital.
As noted by Barbosa et al, (2001b), the word 'CHURN' is
used by different research groups to describe different flow
types. Thus, Zuber & Findley (1965) describes
churn-turbulent flow as a type of bubble flow whereas Taitel
et.al (1980) considered it to be a developing slug flow.
However, the most widely accepted definition of churn flow
is that of Hewitt & Hall Taylor (1970) who considered it to
be an intermediate regime between slug and annular flow.






Paper No


Chum flow occurs due to break down of slug flow due to
flooding of the liquid film in the Taylor bubble (Jayanti and
Hewitt, 1992; McQuillan, 1985). It is characterized by large
interfacial waves with flow reversal between the waves. The
highly oscillatory liquid film in chum flow is accompanied
a continuous gas core containing considerable amount of
entrained liquid. Ultimately as the gas flow rises the
periodic downward flow of liquid film ceases and gives rise
to a unidirectional annular flow. This flow reversal point is
described in terms of dimensionless superficial gas velocity
by (Hewitt and Wallis, 1963; Wallis, 1969) as:


UGS UGS PG
gd(pL PG)


Although extensive data for pressure gradient and liquid
holdup are available for chum flow and the corresponding
transition regions (McQuillan, 1985; Govan, 1991; Barbosa,
2001a), experimental data regarding film thickness and
droplet entrainment behaviour is quite scarce. This might be
due to the reason that conventional measurement techniques
for film thickness and entrained liquid flow in annular flow
could not be applied to chum flow due to its chaotic nature.
Wallis et.al (1962) carried out entrained fraction
measurements in the chum and churn-annular transition
region by using a 12.7 mm internal diameter vertical tube
fitted with single axially located sampling probe. The results,
shown in Figure 1, indicated a considerable amount of
liquid entrained as droplets in churn flow; the entrained
fraction passes through a minimum around the
chur-annular transition.


0
30

-



20


1: 0
z
I-
z
_o
_a


DIMENSIONLESS SUPERFICIAL GAS VELOCITY
0.0 2.0 4.0 6.0
I I


0
O


* OE


%, a
** **

0 "

So


0
Superficial liquid
velocity [mIs]
0 0.042 (upflow)
o 0.042 (downflow)
0.084 (upflow)
O 0.084 (downflow)
0.147 (upflow)
[] 0.168 (downflow)


0.0 20.0 40.0 60.0
SUPERFICIAL GAS VELOCITY [m/sl


Figure 1: Variation of entrained fraction with gas velocity
(Wallis, 1962).

Recently, similar sorts of experiments encompassing a wider
range of liquid flow rates and pressure, were carried out by
Barbosa et.al (2002) using an isokinetic probe technique in
a 31.8mm internal diameter and 10.8 meter long vertical
tube facility. The results are presented in Figure 2 & 3 and
show that the liquid entrained fraction decreases with
increasing gas velocity in chur flow, passes through a
minimum around the transition to annular flow and


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

increases again in the annular flow region. It is also worth
noting that entrained fraction in these regions is a function
of liquid mass flux and extrapolation of these results reveals
a very high proportion of liquid entrained as droplets at the
onset of churn flow. Barbosa et al (2002) proposed the,
following correlation for IEF at onset of annular flow:



E.0 (in %)= 0.95+342.55 PL- d
PGGG (97


e 40
z


2
I-



LaJ

Z


t io
I--


0.40 0.80 1.20
DIMENSIONLESS GAS VELOCITY


Figure 2: Liquid entrained fraction as a function of the total
liquid mass flux: p = 2 bara (Barbosa, 2002).


0.40 0.80 1.20 1.60
DIMENSIONLESS GAS VELOCITY


Figure 3: Liquid entrained fraction as a function of the total
liquid mass flux: p = 3.6 bara (Barbosa, 2002).

This paper addresses the problem of IEF at onset of annular
flow in the context of dryout predictions using an annular
flow dryout model. Firstly, pictures of churn flow and the
corresponding transitions, obtained by an axial view
photography method, were analyzed. On the basis of visual
observation and the available (Barbosa et al, 2002) data, a
new methodology for entrainment rate calculation in chur
flow is proposed. Also, the annular flow dryout model is





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


extended to chur flow i.e. the integration process is made
to start from onset of chur flow; this leads to better
prediction of dryout data.

Nomenclature

C concentration of droplets (kg m 3)
D deposition rate (kg m-2 sec 1)
d diameter (m)
E entrainment rate (kg m2 sec 1)
Ef entrained fraction (-)
G mass flux (kg m2 sec'1)
g gravitational constant (m sec 2)
kD deposition coefficient (m sec ')
p pressure (bar)
q heat flux (W m 2)
UGS superficial gas velocity (m sec ')
ULS superficial liquid velocity (m sec ')
UG dimensionless superficial gas velocity

Greek letters

P density (kg m 3)
C7 surface tension (kg sec 2)
Yr viscosity (kg m1 sec'1)


Figure 4: Schematic diagram of LOTUS air water facility


Subscripts


L
LE
LF
LFC
G


liquid
entrained liquid
liquid Film
critical liquid film


Reflect mirow


Experimental Facility

In view of importance of flow regimes and corresponding
transitions between these flow regimes in prediction of the
dryout position and post-dryout behaviour, axial view
photography experiments have been carried out on the
LOTUS (LOng TUbe System) facility at Imperial College
London.
The LOTUS system is a vertical air-water two phase facility
with a test section consisting of a 10.41m long vertical
acrylic (PerspexTM) tube with an internal diameter of
0.032m. Water is supplied from a separation vessel by two
pumps with 1.5kw and 8.0kw power. Air is taken from the
Imperial College site mains supply and the air-water
mixture leaving the test section is separated using a cyclone,
with the air being discharged to atmosphere and the water
being returned to the separation vessel. An axial viewer was
fitted to the top of the test section; essentially, this consists
of a high speed video camera (Olympus i-SPEED 3) which
is focused at an illuminated plane at a distance of 470 mm
from the end of the tube. The water flow is diverted away
from the camera window using an arrangement of air jets.
The camera can then capture events occurring at the tube
cross section in the illuminated plane. The principle of this
method is described, for instance, by Hewitt and Whalley
(1980). The schematic diagram of LOTUS facility and axial
view photography setup is shown in Figure 4 & 5. The test
conditions were adjusted to cover the churn and annular
flow regions and the transition between them.


Visualize position


3rd floor
///////////


Figure 5: Axial view photography setup at LOTUS


Results and Discussion

IEF Problem:

The problem of initial entrained fraction (IEF) input for the
annular flow dryout model at high mass fluxes is a long
standing one. Information on the amount of entrained liquid
at the transition from chur to annular flow boundary is
essential as it is the starting point of integration of
entrainment/deposition processes in a heated channel. In
order to demonstrate the problem, the annular film dryout
model (as described by Hewitt and Govan, 1990 and


Paper No






Paper No


embodied in the Imperial College computer code GRAMP)
is applied to the uniform and non-uniform heated tube
dryout data of Bennett et al. (1966) and Keeys et al. (1971).
The results, as indicated in Figure 6&7, confirmed that at
medium to high liquid mass fluxes, dryout location is a
strong function of IEF at onset of annular flow. The analysis
also revealed that high IEF values, normally in range of
0.65-0.95, are required to predict the dryout data at these
high liquid flow rates.


48-
46- A
44-
42- *
S40-
38-
36-
34-
U % (Run 5358_G=380 kg/m2 /sec)
32 -* % (Run 5273_G=1020 kg/m2/sec)
30- % (Run 5374_G=3850 kg/m2/sec)
00 02 04 06 08 10
Initial Entrained Fraction (-)


Figure 6: IEF effect on the dryout predictions in uniformly
heated tubes dryout data


E
0

C3
-J


28-

26-

24.

22-

20-
Keeys-141kw_G=720 kg/m2/sec
18 Keeys-191kw_G=2000 kg/m2/sec


00 02 04 06
Initial Entrained Fraction


08 10


Figure 7: IEF effect on the dryout predictions in
non-uniformly heated tubes dryout data

The same phenomena could be demonstrated by
investigating the effect of IEF on dryout qualities, as
illustrated in Figure 8&9. At low liquid flow rates, the IEF
effect is minimal but at high flow rates dryout quality
increases considerably with increasing IEF at onset of
annular flow.
Also, in the present study, the only available IEF correlation
of Barbosa et.al (2002) was employed initially in the
annular flow dryout model to predict the dryout data. The
correlation yielded IEF values of 0.2 to 0.3 at the onset of
annular flow and these values were much lower than the
entrained fractions required to fit the dryout data for
medium and high mass fluxes using the annular flow dryout
model. A major problem with the Barbosa et al (2002)


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

model is that it is essentially for near-equilibrium flows.
However, in heated channels, the flows will not be in
equilibrium. A "memory" of the high entrained fractions at
the onset of chum flow will persist since the entrained
fraction does not immediately relax to the equilibrium
values as the churn flow regime is traversed along the
channel as a result of the increase in quality due to
evaporation. What are needed, therefore, are local values of
entrainment rate and deposition rate in chum flow so that
the same type of integration can be carried out in chum flow
as is done in the annular flow model for annular flow.


)- -Dryout Point- .: -







S - - IEF =0.9
-" ---. IEF = 0.7
S- -..... IEF = 0.5
.-----IEF =0.3
.. ...... IEF = 0.1
S Onset of annular Flow

-005 000 005 010 015 020 025 030 035 040
Quality


Figure 8: IEF effect on the dryout quality predictions at
high liquid mass fluxes (G = 3850 kg m-2 sec-1)


10

08

*5 06
u-
-0
04

02

00


00 02 04 06 08 10
Quality


Figure 9: IEF effect on the dryout quality predictions at low
liquid mass fluxes (G = 380 kg m-2 sec-1)

Experimental Results:

In view of role of droplet entrainment behaviour in churn
and chum-annular transition region, axial view photography
experiments were carried out at LOTUS facility. The visual
evidence, as shown in Figure 10, also supported the
experimental data of Barbosa et.al (2002) i.e. the amount of
liquid entrained is high as the (chaotic) chum flow regime is
entered and it passes through a minimum around the
churn-annular transition, leading to an increase in entrained
fraction with increasing gas velocity in annular flow.






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

predictions. In the absence of detailed data, it was assumed
that the droplet deposition rate in churn flow could be
predicted from a model identical to that used for annular
flow. Specifically, the model suggested by Hewitt and
Govan (1990) (given in Annex-A) is used. Thus, in
equilibrium chum flow, it is assumed that:


Echurn = Dchurn = (kD )annular C (3)


For the equilibrium chum flow data, (such as that of
Barbosa et al, 2002), the value of C (the concentration of
drops in the gas core in kg/m3, calculated on the assumption
of a homogeneous core flow) is known and (kD) .annular can be
calculated from the equations given in Annex-A, Thus,
Echurn can be calculated. Since C is higher in chum flow
a) than would be expected in annular flow (and increases with
decreasing gas flow rate) it follows that Echurn follows a
similar trend (Figure 11 a,b,c). A simple correlation which
gives an approximate representation of the data calculated


churn = -8.73U + 9.73

Eannular,local (4)

where Eannuar,loca1 is the value of entraimnent rate for annular
flow calculated for annular flow from the relationships
given in Annex-A and for the local values of gas and liquid
flow rates. Thus, Equation 4 is a representation of the
enhancement of entrainment rate above that for annular
flow in the chum flow region. The enhancement factor
becomes unity at UG=1.

036
0 34 --- GL=22 kg/m2/sec (a)
032. GL=48 kg/m2/sec
S030. GL=126kg/m2/se
S028. --GL=218 kg/m2/se
024 GL=331 kg/m /se
E 022
0207
018-
016-'
014.
E 012-
a 010-*
0 08
0 06
002
000
02 04 06 08 10 12 14 16 18
UG (-)


040
(b)
035 -

030

E 025
2(c) 020
Figure 10: Axial view photography experiments undertaken
at superficial liquid velocity ULS = 0.165 m/s in (a) Chum 01 GL23kg/
E GL=23 kg/m2 /sec
Flow (UG = 0.461), (b) Chum-to-Annular Flow transition I 010 GL=48 kg/m2/sec
(UC = 0.968) and (c) Annular Flow (U = 1.066) 005 GL=128 kg/m /sec
S05- GL=215 kg/m2/sec
GL=330 kg/m /sec
Entrainment Rate in Churn Flow: 000o 2 0304 06 0708091011121314151617
UG (-)
In order to predict the IEF at the onset of annular flow, it is
necessary to have a model for the chum flow region. Even
an approximate model would in principle allow the IEF to
be predicted accurately enough to give better dryout






Paper No


(c)
u b -) GL=23 kg/m2/sec
045-- GL=48 kg/m2/sec
040- GL= 128 kg/m2/sec
0 35 ---GL=214kg/m2/sec
.3\ GL=302 kg/m2/sec
0 30 -
0 25-
020- \v -
015 \
0 10 \
005-
0 00 -
04 06 08 10 12 14 16
UG (-)


u 1. -
036
0 34-
S032-
E 030-
0 28-
026-
5 024-
022-
L 020-
018-
016-


06 07 08 09 10 11 12 13 14 15
UG (-)


Figure 11: Entrainment rate variation in chum and annular
flow (a) p = 2 bar (b) p = 3.5 bar (c) p = 5 bar (d) Liquid
Mass Flux = 215 kg m2 sec1

The application of this methodology supported the idea,
depending upon different flow conditions, that the variation
of entrained droplet flow with length in heated tubes ceases
to follow the equilibrium curve; rather, the departure from
equilibrium leads to maintenance of high values of
entrained fraction at start of annular flow as indicated in
Figure 12.


Dryout Point


S .... ......
S... .... . ",
S-


- - q = 5 94E05 W/m'
.* q = 7 2E05 W/m2
- - q = 8 8E05 W/m2
-..... q = 1 OE06 W/m2
- - q = 1 2E06 W/m2


Onset of Churn Flow

1v


00 02 04 06 08 10
Quality


Figure 12: Churn flow methodology (G = 654 kg m2 sec-1)

In order to complete the proposed dryout model, an initial
value of entrained fraction at the start of chum flow is still
required. In order to test the proposed methodology,
predictions were made of dryout data for uniformly and


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

non-uniformly heated tube (Bennett, 1966; Keeys, 1971)
with IEF at the start of chum flow chosen to be 0.9. The
predictions, as indicated in Figure 13, of dryout data are
encouraging i.e. within 20%.


Measured Dryout Location


Figure 13: Prediction of dryout data
(IEF for chum flow = 0.9)

Work is continuing on searching for an improved correlation
for the IEF in chum flow. However, the approximate
approach taken has already yielded much more realistic
results, particularly for high mass fluxes.

Conclusions

In the present study, the behaviour of droplet entrainment in
churn flow is analysed with particular reference to the
prediction of the value of entrained fraction at the start of
annular flow. For this purpose, new equation for
entrainment rate in chum flow is proposed, which allows
the dryout model to start integration of entrainment and
deposition processes from the start of chum flow rather than
the start of annular flow. The prediction of dryout location,
for both uniform and non-uniform heated tubes cases, by
employing the new proposed methodology led to improved
results i.e. within 20%.

Acknowledgements

This work was carried out as part of the TSEC programme
KNOO, and we are grateful to the EPSRC for funding under
Grant EP/C549465/1. One author (M. Ahmad) would like to
acknowledge the Higher Education Commission (HEC) of
Pakistan and Pakistan Institute of Engineering & Applied
Sciences (PIEAS) for funding his PhD studies at Imperial
College London.

References

Barbosa J.R., Govan A.H., Hewitt G.F., Visualisation and
modelling studies of chum flow in vertical pipe, Int. J.
Multiphase Flow, Vol. 27, Issue 12, pp. 2105-2127, (2001a)

Barbosa J.R., Hewitt, G.F., Konig G. and Richardson S.M.,
Liquid entrainment, droplet concentration and pressure
gradient at the onset of annular flow in a vertical pipe, Int. J.
Multiphase Flow, Vol. 28, pp943-961, (2002)

Barbosa, J.R., Richardson, S., Hewitt, G.F, Churn flow:


(d) P= 2 bar
P= 3 5 bar
P= 5 bar





Paper No


myth, magic and mystery. In: 39th European Two-Phase
Flow Group Meeting, Aveiro, Portugal, 18-20 June, (200 lb)

Bennett A.W., Hewitt G.F, Kearsey H.A., Keeys, R.K.F,
Heat transfer to steam water mixtures flowing in uniformly
heated tubes in which the critical heat flux has been
exceeded. AERE-R-5373, (1966).

Govan, A.H., Hewitt, G.F., Richter, H.J., Scott, A., Flooding
and churn flow in vertical pipes. Int. J. Multiphase Flow 17,
27-44 (1991)

Hewitt G.F, Flow regimes: Transitions and flow behaviour.
Multiphase Science and Technology, 15:131-143 (2003)

Hewitt G.F and Govan A.H., Phenomena and prediction in
annular two-phase flow: Invited Lecture, Symposium on
Advances in Gas-Liquid Flows, Dallas, November, 1990 (at
Winter Annual Meeting of ASME) ASME Volume
Reference FED-Vol. 99, HTD Vol. 155 pp 41-56, (1990)

Govan A.H. and Hewitt G.F, Phenomenological modelling
of non-equilibrium flows with phase change. Int. J. Heat
Mass Transfer, 33:229-42 (1990)

Hewitt, G.F, Hall-Taylor, N.S., Annular Gas-Liquid Flow.
Pergamon Press, Oxford (1970)

Hewitt G. F. and Jayanti S., Prediction of the slug-to-churn
flow transition in vertical two-phase flow, Int. J. Multiphase
Flow, Vol. 18, pp 847-860, (1992)

Hewitt, G.F, Wallis, G.B., Flooding and associated
phenomena in falling film in a vertical tube. In: Proceedings
of Multi-Phase Flow Symposium, Philadelphia, PA, 17-22
November, pp. 62-74 (1963)

Hewitt, G.F, and Whalley, PB., Advanced optical
instrumentation methods. Int. J. Multiphase Flow, Vol. 6,
No. 12 p136-156. (1980)

Keeys, R.F.K., Ralph, J.C., & Roberts, D.N., Post burnout
heat transfer in high pressure steam-water mixtures in a tube
with cosine heat flux distribution, AERER6411 (1971).


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

Annex-A

Hewitt and Govan droplet entrainment and
deposition correlation

A method for calculating the entrainment and deposition
rates has been proposed by Hewitt & Govan (1990). These
are as follows.

0- ;if GLF 0 316
E= 5.75x10 -5GG L(GLF -GLF)2 if GL >GLF,


(A-l)
where GLFC is a critical liquid film mass flux given by,


GLC L =exp 5.8504+0.4249 PLG
d )l AL PG U


The droplets deposition rate is expressed as,

D= kC


where C is the concentration of droplets in the core,

GLE
0 __ LE
GG + GLE
+
PG PL

and the droplet deposition transfer coefficient, kd,
by,


(A-2)


(A-3)


(A-4)
is given


0.185 r ;if C < 0.3
PGd PG

0.083 0 ;if -2 0.3
SpGd ) pG


McQuillan, K.W., Whalley, P.B., Hewitt, G.F., Flooding in (A-5)
vertical two-phase flow. Int. J. Multiphase Flow 11,
741-760 (1985)

Taitel, Y, Barnea, D., Dukler, A.E., Modelling flow pattern
transitions for steady upward gas-liquid flow in vertical
tubes. A1ChE J. 26, 345-354 (1980)

Wallis, G.B., The onset of droplet entrainment in annular
gas-liquid flows. General Electric Report No. 62GL127
(1962)

Wallis, G.B., One-Dimensional Two-Phase Flow.
McGraw-Hill, New York (1969)

Zuber, N., Findlay, J.A., Average volumetric concentration
in two-phase flow systems. J. Heat Transfer 87, 453-468
(1965)




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