Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 5.6.2 - Flow Regime Transition Criteria for Two-Phase Flow in a Vertical Annulus
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 Material Information
Title: 5.6.2 - Flow Regime Transition Criteria for Two-Phase Flow in a Vertical Annulus Multiphase Flows with Heat and Mass Transfer
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Julia, J.E.
Hibiki, T.
Ishii, M.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: two-phase flow
flow regime
annulus
transition model
 Notes
Abstract: In this work, a new flow regime transition model is proposed for two-phase flows in a vertical annulus. Following previous works, the flow regimes considered are Bubbly (B), Cap-Slug (CS), Churn (C) and Annular (A), (Julia et al., 2009). Cap-slug flow regime will be considered since in the annulus it is not possible to distinguish between cap and partial-slug bubbles. The B to CS transition is modelled using the maximum bubble package criteria proposed by Mishima and Ishii (1984) and modified by Hibiki and Mishima (2001) for rectangular flow channels. The CS to C transition is modelled using the maximum bubble package criteria. However, this transition considers the coalescence of cap and spherical bubbles in order to take into account the flow channel geometry. Finally, the C to A transition is modelled assuming two different mechanisms, (a) flow reversal in the liquid film section along large bubbles; (b) destruction on liquid slugs or large waves by entrainment or deformation (Mishima and Ishii, 1984; Hibiki and Mishima 2001). In this flow regime transition the annulus flow channel is considered as a rectangular flow channel with no side walls. In all the modelled transitions the drift-flux model is used to obtain the final correlations (Ozar et al., 2008). The prediction accuracy of the newly developed model has been checked against air-water datasets (Kelessidis and Dukler, 1989; Caetano et al., 1992; Das et al., 1999a; Julia et al., 2009), as well as boiling and condensation flow regime maps (Hernandez et al., 2010). In all the cases, the new developed model shows better predicting capabilities than the existing correlations most used in literature (Kelessidis and Dukler, 1989; Das et al., 1999b; Sun et al., 2004).
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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Resource Identifier: 562-Julia-ICMF2010.pdf

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


Flow Regime Transition Criteria for Two-Phase Flow in a Vertical Annulus

J. E. Julia*, T. Hibikit and M. Ishiit

Departamento de Ingenieria Mechnica y Construcci6n, Universitat Jaume I. Campus de Riu Sec, 12071 Castellon, Spain

t School of Nuclear Engineering, Purdue University, 400 Central Dr., West Lafayette, IN 47907-2017, USA
bolivar@emc.uji.es, hibiki@purdue.edu, ishii@purdue.edu

Keywords: two-phase flow, flow regime, annulus, transition model


Abstract

In this work, a new flow regime transition model is proposed for two-phase flows in a vertical annulus. Following previous
works, the flow regimes considered are Bubbly (B), Cap-Slug (CS), Chum (C) and Annular (A), (Julia et al., 2009). Cap-slug
flow regime will be considered since in the annulus it is not possible to distinguish between cap and partial-slug bubbles. The B
to CS transition is modelled using the maximum bubble package criteria proposed by Mishima and Ishii (1984) and modified by
Hibiki and Mishima (2001) for rectangular flow channels. The CS to C transition is modelled using the maximum bubble
package criteria. However, this transition considers the coalescence of cap and spherical bubbles in order to take into account
the flow channel geometry. Finally, the C to A transition is modelled assuming two different mechanisms, (a) flow reversal in
the liquid film section along large bubbles; (b) destruction on liquid slugs or large waves by entrainment or deformation
(Mishima and Ishii, 1984; Hibiki and Mishima 2001). In this flow regime transition the annulus flow channel is considered as a
rectangular flow channel with no side walls. In all the modelled transitions the drift-flux model is used to obtain the final
correlations (Ozar et al., 2008). The prediction accuracy of the newly developed model has been checked against air-water
datasets (Kelessidis and Dukler, 1989; Caetano et al., 1992; Das et al., 1999a; Julia et al., 2009), as well as boiling and
condensation flow regime maps (Hernandez et al., 2010). In all the cases, the new developed model shows better predicting
capabilities than the existing correlations most used in literature (Kelessidis and Dukler, 1989; Das et al., 1999b; Sun et al.,
2004).


Introduction

Multiphase flows are encountered in a wide range of
important industrial applications. In particular, gas-liquid
two-phase flows can be observed in boilers, core and steam
generators in nuclear reactors, petroleum transportation,
electronic cooling and various types of chemical reactors.
Two phases can flow according to several topological
configurations called flow patterns or flow regimes, which
are determined by the dynamic interfacial structure between
both phases. The flow regime depends on a variety of
parameters such as gas and liquid flow velocities, physical
properties of phases and the flow channel size and geometry.
The correct identification of the flow regimes and the
prediction of the transition boundaries are particularly
indispensable because they have a profound influence on all
the two-phase transport processes. Various models have been
developed to predict the transition criteria between the flow
regimes. The majority of the studies in this field have been
confined to circular flow geometry (Taitel et al., 1980;
Mishima and Ishii, 1984), although the transition criteria
have been extended to mini-channel systems (Hibiki and
Mishima, 2001; Mishima and Hibiki, 1996). In all the cases,
consistent experimental flow regime maps are needed to
understand the physical phenomena involved in the flow
regime transitions as well as to validate the models.

Many researchers have been working on developing
objective flow regime identification methodologies. Most
flow regime identification approaches have two steps in


common: the first step consists of developing an
experimental methodology for measuring certain parameters
that are intrinsic to the flow and are also suitable flow regime
indicators (Flow Regime Indicator). In the second step, a
non-linear mapping is performed to obtain an objective
identification of the flow regimes in accordance with these
indicators (Flow Regime Classifier). In the first flow
regime identification works the flow regime mapping were
carried out directly by the researcher using the visual
information as flow regime indicator (Bergles et al. 1968,
Weisman et al., 1979). This methodology provides highly
subjective identification results. Progress in flow regime
classifiers was introduced when some statistical parameters
of the void fraction (q signals were introduced as flow
regime indicators (Jones and Zuber 1975; Tutu, 1982 ; G.
Matsui, 1984). Thus some rules regarding statistical
parameters of the Probability Distribution Function (PDF)
were used to perform the classification. However, these
rules were decided based on the researcher's knowledge, so
the objectivity of the classification is not guaranteed. A
significant advance in the objective flow regime
identification was achieved by the use of ANN (Cai et al.,
1994; Mi et al. 1998; 2001). Using Kohonen
Self-Organizing Neural Networks (SONN) it was possible to
identify the flow regimes more objectively. In the last
decade, some improvements in the flow regime identification
methodology have been made. Lee et al. (2008) used the
Cumulative PDF (CPDF) of the impedance void meter
signals as the flow regime indicator. The CPDF is a more






Paper No


stable parameter than the PDF because it is an integral
parameter. Hernandez et al. (2006) developed different
neural network strategies to improve the flow regime
identification results. Different types of neural networks,
including PNN, Probabilistic Neural Networks, training
strategies and flow regime indicators based on the CPDF
were tested in their work. In order to minimize the effect of
the fuzzy flow regime transition boundaries on the
identification results, a committee of neural networks was
assembled. Recently, Julia et al. (2008) used bubble chord
length distributions obtained from conductivity probes as
flow regime indicators. Bubble chord length represents the
interfacial area or bubble size. Thus, the flow regimes are
defined as time-averaged bubble chord length patterns and
they are considered as local parameters (LFR).

Most of the studies on flow regime identification have
concentrated on gas-liquid two-phase flows in tubes due to
the simple geometry and many practical applications.
However, in many of the chemical and nuclear systems more
complex geometries exist. The annulus channel is often
utilized to simulate some phenomena encountered in the
complex geometries such as sub-channel of a rod bundle in a
nuclear reactor core; yet, it is simple enough to perform
fundamental studies. Sadatomi and Sato (1982) and
Furukawa and Sekoguchi (1986) studied the flow regimes of
gas-liquid two-phase flows in non-circular flow ducts,
including concentric annulus. Kelessidis and Dukler (1989)
and Das et al. (1999a; 1999b) investigated the flow patterns
in vertical upward flow for concentric and eccentric annulus
channels. They also developed flow regime transition criteria
based on phenomenological models and compared with their
experimental findings. Sun et al. (21"'4) investigated the
cap-bubbly to slug flow regime transition criteria in an
annulus and suggested a model for the transition criteria by
modifying the study of Mishima and Ishii (1984). Finally, in
the last years new experimental flow regime maps are
available (Jeong et al, 2008; Julia et al., 2009). In these
works, the cap-slug (CS) flow regime is considered. Cap
bubbles observed in round tubes cannot exist in the annulus if
the annulus gap size is smaller than the distorted bubble limit
(or minimum cap bubble limit). Thus, a growing bubble is
radially confined by the inner and outer walls before it
reaches the maximum distorted bubble limit. If the bubble
grows further, it becomes a cap bubble squeezed between the
inner and outer walls. Typical large bullet-shaped bubbles
(slug or Taylor bubbles) which have diameters close to the
pipe diameter and occupy almost the whole cross section are
not present in the annulus. In most cases, slug bubbles in the
annulus are wrapped around the inner tube, but cannot cover
it completely due to the long periphery in this flow channel.
As a result, cap and slug bubbles are not distinguishable in
this test section and an intermediate flow regime between cap
bubbly and slug flows, which are usually observed in round
pipes, exists in the annulus.

The objective of this work is to propose a new flow regime
transition model for annular flow channel geometry. The
base of the model is the Mishima-Ishii model (1984) and its
modification for rectangular flow channel, Hibiki-Mishima
model, (2001). In addition, the flow regime transition model
for large diameter pipe (Schlegel et al., 2009) will be
considered for the cap-slug to chum flow regime transition.


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

The new transition model will provide prediction accuracy
for every flow regime transition, at least, as high as the best
available in literature. In addition, the final equations for
every flow regime transition are easy to be implemented,
especially in the case of the cap-slug to chur flow regime
transition.

Nomenclature

Co Distribution parameter
DH Hydraulic diameter
DI Internal annulus diameter
D2 External annulus diameter
Db Bubble diameter
f Friction factor
g Gravity acceleration
jf Superficial liquid velocity
jg Superficial gas velocity
IE Entrance Length
s Channel gap size
URC Bubble rise velocity
Vg1 Drift velocity
z Axial position in the flow direction
Greek symbols
a Void fraction
als Void fraction in the liquid slug
amax Critical void fraction for B to CS flow regime transition
Wf Fluid viscosity
p Fluid density
C Surface tension
Mathematical symbols

< > Area average

Acronyms


CPDF
GFR
LFR
PDF
SONN


Cumulative Probability Distribution Function
Global Flow Regime
Local Flow Regime
Probability Distribution Function
Self-Organized Neural Network


Literature Survey

Flow regime definitions in annulus

Figure 1 shows typical flow patterns observed in the annulus
test section with the inner and outer diameters of 19.1 and
38.1 mm, respectively. Vertical upward two-phase flows in
a vertical annulus are usually classified into four basic flow
regimes (Kelessidis and Dukler, 1989; Das et al., 1999a). In
what follows, the characteristics of each flow regime are
described.

Bubbly flow
The liquid phase is continuous and small dispersed bubbles
flow in the liquid. No major difference from the bubbly flow
in round tubes can be found (Fig. la).






Paper No


Cap-Slug flow
The number density of small bubbles increases and bigger
bubbles are formed due to bubble coalescence. The cap
bubbles, which can be observed in round tubes, can not exist
in the annulus if the annulus gap size is smaller than the
distorted bubble limit (or minimum cap bubble limit), e.g.,
10.9 mm for air-water flow under atmospheric pressure at
250C. Thus, a growing bubble is radially confined by the
inner and outer walls before it reaches the maximum
distorted bubble. If the bubble grows further, it becomes a
cap bubble squeezed between the inner and outer walls. Also,
typical large bullet-shaped bubbles (Taylor bubbles), which
are observed in round tubes, have diameters close to the pipe
diameter and they occupy almost the whole cross section.
Such Taylor bubbles occupying almost the whole annulus
cross section are observed only for stagnant liquid conditions.
In most cases, Taylor bubbles in the annulus are wrapped
around the inner tube, but can not cover it completely due to
the long periphery in this flow channel. As a result, the cap
and slug bubbles are not distinguishable in this test section
and an intermediate flow regime between the cap bubbly and
slug flows observed in round pipes exists in the annulus.
Therefore, the "cap-slug flow" expression has been chosen
for this flow regime (Fig. lb). It should be noted that some
scientists use the expression ilug flo for this flow regime.

Chum-Turbulent flow
By increasing the gas flow rate, a breakdown in the partial
length Taylor bubbles leads to an unstable flow regime, and
the continuity of the liquid slug is repeatedly destroyed. This
liquid accumulates, forms a bridge and is again lifted by the
gas. This oscillatory or alternating direction of the liquid
motion is typical in the chum-turbulent flow. No major
difference between the chum-turbulent flow in round pipe
and annulus is observed (Fig. Ic).

Annular flow
The gas phase flows in the center of the gap and the liquid
phase flows along the walls as a film. Generally, part of the
liquid phase is entrained as small droplets in the gas core. No
major difference between the annular flow in round pipe and
annulus is observed (Fig Id).


o 0
o o
o 0
oo
o o
oo o
oo 0
o

___ 0


oo oo oO

( 0
0


0 0
Sooo o


0 0
o ::00

K H

00 00
o 0 ooo :


a) b) c) d)
Figure 1. Flow regimes definition: a) bubbly flow, b)
cap-slug flow, c) chum flow and d) annular flow


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

Existing models of flow regime transition criteria in
an annulus channel
Five models of flow regime transition criteria have been
chosen and compared with the model obtained in this work.
Three of the models, Kelessidis and Dukler (1989), Das et al.
(1999b) and Sun et al. (2i 1i4) were developed for air-water
adiabatic upward flows in a vertical annulus. In addition, the
models developed by Mishima and Ishii (1984) and Hibiki
and Mishima (2001) for vertical upward two-phase flow in
round tubes and narrow channels, respectively, have been
selected, since they has been successfully applied to several
flow configurations.

Kelessidis and Dukler Model (1989)
Kelessidis and Dukler proposed a flow regime map model
based on the phenomenological model of Taitel et al. (1980)
and on their experimental observations. The assumed flow
regime transition criteria in the model are summarized as
follows:

- Transition from bubbly to slug flow is governed by the
bubble packing. For low liquid velocity conditions the
transition occurs when the area-averaged void fraction, ,
reaches 0.25. For high liquid velocity conditions flow
regime remains bubbly flow due to bubble breakup caused by
strong turbulence force even at > 0.25 and the void
fraction at the finely-dispersed bubbly to slug flow transition
is set at
=0.52. The transition from bubbly to dispersed
bubbly is given by a maximum stable bubble diameter
criterion derived by a force balance between the surface
tension and turbulent fluctuations.

- Slug to chum turbulent flow transition is governed by stable
liquid slug length criteria similar to that proposed by Taitel et
al. (1980) in round pipes. It is proposed that the stability of
the liquid slug in an annulus is associated with the liquid
falling as a film around the slug bubble. It is postulated that
the liquid slug is stable if it is long enough such that the liquid
jet around the slug bubble is absorbed by the liquid slug and
the velocity of the liquid jet slows down to that of the
surrounding. The fact that the Taylor bubbles in the annulus
can not cover the flow channel completely is not considered
in the model. It should be noted here that axial coordinate
dependence is considered in the flow regime transition
boundary criterion.

- Chum-turbulent to annular flow transition occurs when the
void fractions of chur-turbulent flow and the void fraction
for annular flow are equal. The void fraction for the annular
flow can be obtained based on geometric considerations and
a force balance between interfacial shear, gravity and axial
pressure drop. The void fraction of chur-turbulent flow is
estimated based on the ratio of superficial gas velocity and
bubble rise velocity.

Das et al. Model (1999b)
They developed a phenomenological model of the flow
regime boundaries as functions of the annulus dimensions,
physical properties and the velocities of the two phases. The
assumed flow regime transition criteria in the model are
summarized as follows:

- The transition from bubbly to slug flow is postulated to





Paper No


occur due to an onset of asymmetric phase distribution from
the symmetry prevailing in bubbly flow. This asymmetry
persists in the entire range of slug flow and occurs due to the
typical shape of cap and Taylor bubbles. Experimental
observation (Das et al., 1999a) revealed that the coalescence
of cap bubbles rather than the spherical ones played a major
role in this flow regime transition. Consequently, it is
assumed that the slug flow appears when the elongated
bubbles formed from the coalescence of cap bubbles have
attained the nose dimensions of the Taylor bubble. This
approach provides a transition void fraction,
=0.2, lower
than the maximum bubble packing criterion followed by
several authors (Taitel et al., 1980; Mishima and Ishii, 1984).
However, for high liquid flow rate (dispersed bubbly flow)
this criterion is replaced by the one given by Kelessidis and
Dukler (1989).

- The slug to chum-turbulent flow regime transition results
from the collapse of the Taylor bubbles. Experimental results
showed that the flooding in the Taylor bubble region would
be the main mechanism underlying the flow regime transition.
Wallis flooding correlation is used for the basis of the
governing equation of this phenomenon (Wallis, 1969). The
fact that the Taylor bubbles in the annulus cannot cover the
flow channel completely is not considered in the model.

- No criterion is given for the transition from chum-turbulent
to annular flow.

Sun et al. Model (2004)
In this work, only the cap-bubbly to slug flow regime
transition is considered. The developed model is based on
the mean void fraction in the liquid slug and considers that
the Taylor bubbles are not axis-symmetric in the annulus. In
this model, some experimental data input such as the
averaged void fraction in the liquid slug in the flow regime
transition is needed.

Mishima and Ishii Model (1984)
Mishima and Ishii considered different mechanisms for the
flow regime transition criteria between bubbly to slug, slug to
chum-turbulent and chum-turbulent to annular flow. These
criteria were compared to experimental data under
steady-state and fully-developed flow conditions by using
relative velocity correlations and can be summarized as;

- The transition criteria between bubbly to slug flow is based
on the maximum bubble packing before significant
coalescence occurs, which is estimated as
= 0.3. No
finely-dispersed bubbly flow regime is considered.

- Slug to chum-turbulent flow transition occurs when the
mean void fraction over the entire flow channel exceeds that
over the Taylor bubble section. Under this condition, the
liquid slugs become unstable to sustain its individual identity
due to the strong wake effect.

- The criteria for chum-turbulent to annular flow transition
are modelled by postulating two different mechanisms.
They are flow reversal in the liquid film section along large
bubbles and destruction of liquid slugs or large waves by
entrainment or deformation. The second criterion from the
onset of entrainment is applicable to predict the occurrence of
the annular-mist flow or to predict the chum-to-annular flow


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

transition in a large diameter tube.
Hibiki and Mishima Model (2001)
This model was developed for rectangular narrow channels
and its basic assumptions are those found in Mishima and
Ishii model (1984).

- The transition criteria between bubbly to slug flow is based
on the maximum bubble packing before significant
coalescence occurs. This value depends on the ratio
between the bubble diameter and the gas p size.

- Slug to chum-turbulent flow transition occurs when the
mean void fraction over the entire flow channel exceeds that
over the Taylor bubble section. Under this condition, the
liquid slugs become unstable to sustain its individual identity
due to the strong wake effect. Two different set of equations
are obtained depending in the gap size.

- The criteria for chum-turbulent to annular flow transition
are modelled by postulating two different mechanisms.
They are flow reversal in the liquid film section along large
bubbles and destruction of liquid slugs or large waves by
entrainment or deformation. The second criterion from the
onset of entrainment is applicable to predict the occurrence
of the annular-mist flow for the case of a large gap size.

Table 1 provides the flow regime transition criteria for the
models mentioned in the previous paragraphs.

Existing flow regime maps in an annulus channel

Kelessidis and Dukler (1989)
Kelessidis and Dukler investigated vertical upward
gas-liquid flow in concentric and eccentric annuli with inner
and outer diameters of 5.08 and 7.62 cm, respectively. The
flow regime indicator was a set of some characteristic
parameters of the PDF obtained from the voltage signal of
two conductivity probes. The flow regime mapping was
performed by applying some rules to the flow regime
indicator measurements following the methodology
developed by Bamea et al. (1980). The flow regime maps
were obtained for two axial locations (z/DH=160 and 200
approximately) and 85 flow conditions within a range of
0.05m/s < < 20 m/s and 0.01 m/s < < 2 m/s where
and are the superficial gas and liquid velocities,
respectively.

Das et al (1999a)
Das et al. (1999a) carried out experiments on air-water
upward flow through three concentric annulus geometries
with inner and outer diameters of 2.54, 1.27, 1.27cm and 5.08,
3.81, 2.54 cm respectively. The flow regime indicator was a
set of some characteristic parameters of the PDF obtained
from the voltage signal of two parallel type conductivity
probes. The flow regime mapping was performed by
applying some rules to the flow regime indicator set. The
flow regime maps were obtained for two axial locations,
entrance and developed flow regions, but no quantitative
information about its location was available. More than 150
flow conditions within a range of 0.04 m/s < < 9 m/s and
0.08 m/s < < 2.8 m/s were obtained.

Caetano et al. (1992)
In this work, air-water and air-kerosene experiments were





Paper No


performed in upward flow through concentric and eccentric
annulus geometries with inner and outer diameters of 4.22
and 7.62 cm, respectively. The flow regime identification
was performed directly by visual observation. More than
140 flow conditions within a range of 0.02 m/s < < 25
m/s and 0.002 m/s < < 3 m/s were obtained.

Julia et al. (2009)
Julia et al. (2009) carried out experiments on air-water
upward flow through a concentric annulus with inner and
outer diameter of 1.91 and 3.81 cm respectively. The flow
regime indicator was a set of some characteristic parameters
of the CPDF of the area-averaged void fraction signals
obtained from impedance meters. The flow regime mapping
was performed by applying a SONN. The flow regime maps
were obtained for three axial locations (z/DH=52, 149 and
230). 72 flow conditions for every axial location within a
range of 0.01 m/s < < 39 m/s and 0.2 m/s < < 3.5
m/s were obtained.

Table 1. Flow regime transition criteria of the selected models.


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

Hernandez et al. (2010)
Hernandez et al. (2010) carried out experiments on boiling
upward flow through a concentric annulus with inner and
outer diameter of 1.91 and 3.81 cm respectively. The flow
regime indicator was a set of some characteristic parameters
of the CPDF of the bubble chord length obtained from
conductivity probes. The flow regime mapping was
performed by applying a SONN. The flow regime maps were
obtained for five axial locations (z/DH=52, 108, 149, 189 and
230). The first three axial locations correspond to the heated
section of the channel and the latter two to the unheated
section. 42 flow conditions for every axial location within a
range of 0.002 m/s < < 1.7 m/s and 0.23 m/s < < 2.5
m/s were obtained.

Table 2 summarizes the flow regime maps in annular flow
channel geometry available in literature.


Transition Model Physical phenomena Criteria
Mishima-shi Coalescence of small
Mishima-Ishii 0.3
bubbles

forjf<1.80m/s
Coalescence of small 0.25
Kelessidis-Dukler
bubbles forjf> 1.80m/s (dispersed bubbly)
0.52

Das et al. Onset of asymmetric phase 0.2
distribution
B-CS
16 (1-ac) r
ac = a +-
Sun et al. Coalescence of cap bubbles "" 5n D2 (1 + D, ) gAp
Where aCl is determined experimentally
m, = 0.2 for s < Db
Coalescence of small
Hibiki-Mishima bubbles modified in order to 0 = + 0.15 for Db < s < 3D
consider channel geometry
_, = 0.3for s > 3D

Stable liquid slug
(a)max =1-0.813
(mean a over the entire flow (
channel exceeds that over the (Co j .30.75
Mishima-shi Taylor bubble section)- 1) (Ap
Not channel geometry 1+0.75 3(ApgD/pf)
considered
Stable liquid slug length
CS-CT (liquid jet around slug 22.96 C J
Kelessidis-Dukler bubble) = 22.96C
Not channel geometry H RC
considered
Collapse of Taylor bubbles
(flooding in the Taylor
Das et al. bubble region) Uc = 1.2j + 0.323g(D1 +D2)
Not channel geometry
considered





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


g = @(()-0.11)


- Flow reversal in the liquid
film section along large
bubbles
- Destruction of liquid slugs
or large waves by
entrainment or deformation


il K ) 2
Pg 2


N0.2 for


2 N 2 (Ap)N 0.4
S 3[(1-0.11Co)/C]


pG /(gAp)]1/2

churn annular
Jg
Kelessidis-Dukler a chu= aC .hum Cj +

alar =f (Ap,g, ,DH,C ,D,,D2)


- Flow reversal in the liquid
film section along large
bubbles (modified for
rectangular channel)
- Destruction of liquid slugs
or large waves by
entrainment or deformation


J 3ApgD ((oc)
S 2Pg


,> ggAp N -0.2
J F) 2 N 0


Table 2. Summary of the flow regime maps in annular flow channel geometry available in literature.


Work Flow Gometry Working range Flow Identification
type Regimes Identicator Classifier
Concentric
Kelessidis Eccentric PDF of
K Adiabatic <20m/s <2m/s B, S, C, A conductivity Researcher rules
-Dukler 5.08 cm i.d. probes
7.62 cm o.d.

concentric 2.54, PDF of
1.27, 1.27cm i. d
Das et al. Adiabatic 1.27, 1.27m i. <9m/s <2.8m/s B, S, C conductivity Researcher rules
and 5.08, 3.81, 2.54
probes
cm o.d..

Concentric
Caetano et Eccentric Visual
Adiabatic <25m/s <3m/s B, S, C, A Researcher
al. 4.22 cm i.d. observation
7.62 cm o.d.
Concentric CPDF of
Julia et al Adiabatic 1.91 cm i.d. <39m/s <3.5m/s B, CS, C, A impedance SONN
3.81 cm o.d. meter
Concentric CPDF of
Hemandez Boiling 1.91 cm i.d. <1.7m/s <2.5m/s B, CS, C conductivity SONN

3.81 cm o.d. probes


Paper No


Mishima-Ishii


CT-A


Hibiki-Mishima


-0.11)





Paper No


Flow Regime Transition Model

In this section, the proposed flow regime transition model
will be developed. In order to check the suitability of the
options considered the experimental flow regime map of
Julia et al. (2009) will be used.

Bubbly to Cap-Slug Transition
All the models considered in Table 1 use the maximum
bubble package criterion for this flow regime transition.
However, the way of obtaining the Gaax value differs in each
model. Figure 1 shows the flow regime transition
boundaries given by the available models compared with the
experimental data of Julia et al. (2009).

For the comparisons Sun et al. model provides Gaax =0.191.
For the calculation experimental data ca,=0.15 is used (Sun et
al., 2004). Hibiki-Mishima model (2001) provides
Cmax=0.24 with Db 5mm. Bubble diameter data at the flow
regime boundary flow conditions is obtained from
experimental data (Jeong et al., 2008).

In all the models, the distribution parameter obtained for
annular flow channel geometry and given in Ozar et al.
(2008) and the drift velocity given by Ishii (1977) for bubbly
flow are used:


C = 1.1-0.1 P (1)
VPf


K "J1/4
Vg '2Apga (1- (Y
V [ _1- ))1,71


101






E 100
.._-t


(2)


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


regime transition. However, cap and slug bubbles can not
be distinguished in the annulus. Consequently, it can be
used for the bubbly to cap-slug flow regime transition.

Kelessidis and Dukler (1989) and Das et al. (1999b) models
present high discrepancies forjf 21.8 m/s. In these models
the dispersed-bubbly flow is considered.

In the present work the criterion provided by Hibiki and
Mishima (2001) for rectangular ducts will be used. This
model provides accurate results for all the jf range. In
addition, its formulation is simpler than the one of Sun et al.
model (2-" 4).

Cap-Slug to Churn Transition
In this flow regime transition the existing models provides
quite different predictions. The physical phenomena
involved in the flow regime transition criteria are different in
all the models. Most of the models do not consider the flow
channel geometry.

In this work, a new transition criteria is proposed based on
the model of Schlegel et al. (2009) for the cap-bubbly to
chum flow regime transition in large diameter pipes.This
means that for the cap-slug to chur flow regime transition
the (extended) annulus can be compared with a large
diameter pipe. This can be explained since slug bubbles
covering almost the flow channel can not exist in both
channel geometries. Consequently, the flow regime
transition is produced by the coalescence of cap-slug bubbles
(adding the coalescence of small bubbles). Thus, the
classical flow regime transition models developed for pipes
(except large diameter pipes) can not be applied to the
annulus in the cap-slug to chum flow regime transition.

The new criterion considers the maximum packing of cap
bubbles. The criterion can be obtained in the following
way:

The cap bubble is considered as spherical for simplicity. The
void fraction of cap bubbles at the transition is estimated to be
=0.20. This value is obtained from the Hibiki-Mishima
model considering that Db>S. Following the same criteria,
the void fraction of the mixture of small bubbles (Db< liquid at the transition is considered as 0.3. The volume of
small bubbles and liquid, Vm, is given by,


V, =(1- (a2))V


jg [m/s]
Figure 1. Comparison of models with experimental data for
the B to CS transition.

All the available models provide accurate results, at least for
low superficial liquid velocity values. Mishima-Ishii (1984)
and Sun et al. (21" '4) models show better agreement for high
and low superficial liquid velocity values, respectively.
Hibiki-Mishima (2001) model provides good results in all the
liquid velocity range.

Sun et al. model (2" 14) was proposed for the cap to slug flow


where V is the volume of the lattice as can be seen in Figure
2.


Figure 2. Lattice for the CS to C transition






Paper No


The void fraction of small bubble in the lattice is estimated


((ml l V1 V1
Vm V(-(,
(2,,~~ = =V1-( 2,))


where Vmi is the volume of small bubbles in the tetrahedral
lattice. The void fraction of small bubbles is given by,


(I)= = )(1- (2))


The void fraction at the transition is given by,

(a) = (a,)+(a,2) ( l )(1-(a,))+(a,)= 0.44 (6)

The distribution parameter given in equation (1) and drift
velocity given in Ishii (1977) are used to obtain thejf-jg flow
map.
1/4

Apgcf (7)

Figure 3 shows the flow regime transition boundaries given
by the available models as well as the new model compared
with the experimental data of Julia et al. (2009).
10
-Mishima-lIshii (1984)
Present work
Kelessidis-Dukler (1989)
Das et al (1999b)
Julia et al (2009) (Exp)

S100 CS






10 C
10 10 10
jg [m/s]
Figure 3. Comparison of models with experimental data for
the CS to C transition.

Mishima and Ishii model (1984) does not provide accurate
results, showing that, in this flow regime transition, the flow
channel geometry plays a major role. Kelessidis and Dukler
(1989) and Das et al. (1999b) models provide good results for
jf >1.8 m/s. However they consider the transition between
dispersed-bubbly to chur flow regime and not between
cap-slug and chur flow regime as showed in the
experiments.

The model developed in this work presents the best prediction
accuracy for all the range of liquid velocities. In addition, it
is easy to be implemented in computational codes since it is
based on a critical void fraction value.

Churn to Annular Transition
In this flow regime transition the existing models provides
quite different predictions. The physical phenomena


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

involved in the flow regime transition criteria are different in
some of the models. Most of the models do not consider the
flow channel geometry.

In this work, a new transition criteria is proposed based on
the model of Hibiki and Mishima (2001) for rectangular flow
channels. Some geometrical modifications are needed in
order to consider the annulus geometry.

w=7t(R22-R12 )/( R2-R1)
4 I


Figure 4. Modification of the annulus to rectangular
geometry .

In the new model, w and s has been calculated in order to
keep the flow channel area in both geometries. The
criterion assumes two different mechanisms, (a) flow
reversal in the liquid film section along large bubbles; (b)
destruction on liquid slugs or large waves by entrainment or
deformation.

Flow reversal criterion can be derived from the pressure
drop for the liquid film and gas core in the flow channel.
Thus,


2w 2w
Pfg ws(1- T +) -(1 -
wsIl-a) wsIl-a 0C


dp 2w
--= pg+-z. (9)
dz wsa
where z, and zf are the interfacial shear stress and the wall
shear stress in the liquid film and are given by,


T fi V2
Zi Pg r


Twf =PfVf Vf
2.


where v, vf are the relative velocity between the phases and
the liquid velocity, respectively.

For the flow reversal condition jf=0. From equations (8 to
10) the following condition can be obtained for the flow
regime transition,


i Apg(a (1- (a))s
W r 9


where the Wallis equation for the interfacial friction factor,
f, is assumed





Paper No


f, =0.005[1+75(1-a)] (13)

The distribution parameter and drift velocity given in
equations (1) and (7), respectively, are used to obtain the
jf-jg flow map.


91 p f


The second criterion can be obtained from the onset of
droplet entrainment. The onset of entrainment criteria for
film flow can be developed from a force balance on the
liquid wave crest between the shearing force of the vapour
drag and the retaining force of the vapour tension [10].
Since this criterion may be determined by the local
condition of the liquid film, the channel geometry may not
affect the model significantly. The condition in given by
[10],

j gAp N -0.2 (15)

where


Np
[pa /(gAP]2


This criterion can be used for


2 N 2/(gAp),-0.4
3[(1-0.11Co)/Co]


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

Figure 5 shows the flow regime transition boundaries given
by the available models as well as the new model compared
with the experimental data of Julia et al. (2009).

The condition for using the drop entrainment criteria is
s<0.025 mm, so only the flow reversal condition will be used
in the figure.


Mishima-lshii (1984)
Hibiki-Mishima (2001)
- Kelessidis-Dukler (1989)
SPresent k
- Julia et al. (26t) (Exp.)


10
10






10
10-


jg [m/s]
Figure 5. Comparison of models with experimental data for
the C to A transition.

The best results are obtained by the Mishima-Ishii (1984)
criterion. However, the criterion proposed in this work also
provides accurate results.

Table 3 provides the flow regime transition criteria for the
model developed in the previous paragraphs.


Table 3. Flow regime transition criteria for the proposed model.


Transition Physical phenomena Criteria

U, = 0.2 for s < Db
Coalescence of small bubbles
Bubbly to modified in order to consider a,, -2-+ 0.15 for D, s < 3D,
cap-slug 20Db
cap-slug channel geometry
ma, =0.3 for s > 3Db

Cap-slug to Coalescence of cap bubbles () =0.44
chum

Flow reversal in the liquid film jApg(a)3 (1-(a))s (gAp 0.2
section along large bubbles Jg = ; j' g > N,0.- for
Chur to (modified for annular channel) P
annular Destruction of liquid slugs or 2 N/(gAp)NP 0.4
large waves by entrainment or DH > 0.11C NI = 1/
deformation 3 1-0.1 /)/ Lpc/(gAp)j






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


Comparison with Experimental Results


In the next section, the prediction accuracy of the developed
model will be checked against the flow regime maps
available in literature and summarized in Table 2.


101







I 100


jg [m/s]
a)


10 10 10
Jg [m/s]
b)


10 10 10
Jg [m/s]
c)


100


B CS A



10
10 10 10 10 10
Jg [m/s]
d)

101
Model
Hernandez et al (2010)




-t
100


B CS C




10-2 10 100 10
jg [m/s]
e)
Figure 6. Comparison of model with flow regime maps: a)
Julia et al. (2009), b) Kelessidis and Dukler (1989), Das et
al. (1999b), Caetano et al. (1992), Hernandez et al. (2010).

The model presents good prediction accuracy for the case of
bubbly to cap-slug flow regime transition. Only some
discrepancies can be found with the flow regime maps
measured by Kelessidis and Dukler (1989) and Das et al.
(1999b) for high liquid velocity values.

The prediction accuracy for the cap-slug to chum flow
regime transition of the model can be clearly improved if the
Kelessidis and Dukler (1989) and Das et al. (1999b) flow
regime maps are considered. However, these flow regime
maps do not show noticeable liquid phase velocity
dependence for this flow regime transition. If the model is
compared with the other three flow regime maps the
prediction accuracy is quite reasonable. It is remarkable the
good prediction results provided by the model for the case of
boiling flow regime map.

For the chum to annular flow regime transition the model
provides a good agreement with all the flow regime maps.

Conclusions

A new flow regime transition model for annular flow channel
geometry has been developed. The transition criteria is easy


Paper No






Paper No


to be implemented in numerical codes and provides good
prediction results even in boiling flow conditions.

In the bubbly to cap-slug flow regime transition the criterion
provided by Hibiki and Mishima (2001) for rectangular ducts
is used. This criteria s based on he classical maximum
package approach, but considering the coalescence in narrow
gaps.

A new transition criteria is proposed for the cap-slug to churn
flow regime transition based on the model of Schlegel et al.
(2009) for the cap-bubbly to chur flow regime transition in
large diameter pipes. This criteria is based on the coalescence
of both cap and small bubbles in the flow channel and it can
be applied since complete Taylor bubbles can not exist in the
annulus.

For the case of the chur to annular flow regime transition a
new transition criteria is proposed based on the model of
Hibiki and Mishima (2001) for rectangular flow channels.
Some geometrical modifications are needed in order to
consider the annulus geometry. Flow reversal in the liquid
film section along large bubbles or destruction on liquid slugs
or large waves by entrainment or deformation are considered
in the model depending on the channel gap size.

In all the cases, the distribution parameter given by Ozar et al.
(2008) for annulus and drift velocity given by Ishii (1977) are
used to obtain thejf-jg flow map.

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