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

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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).

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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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