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FLOW P TTERN TR NSITION FOR VERTIC L DOWNW RD

TWO PH SE FLOW

DVORA BARNEA*, OVADIA SHOHAM and YEHUDA TAITEL

School of Engineering Tel-Aviv

University Ramat-Aviv israel

Received 4 May 1981; occepled

10 August 1981)

Ahshwt-Experiments of flow paltern for vertical downward gas-liquid flow are reported. In addition theoretically

based transition criteria for the flow pattern are presented. The experimental results compare resonably well with

the theoretical model for the prediction of flow pattern in vertical downward flow.

In contrast to

the extensive research

in two phase flow of

horizontal and upward flows there are only few in-

vestigations of gas liquid mixtures in downward flow.

Golan and Stenning[l] considered downward flow in

an inverted U tube consisted of a vertical riser followed

by a vertical downcomer. In the downcomer they

identified the transition from slug and bubble flow to

annular flow. In between the two boundaries they found

an oscillatory regime which results probably because of

the U type configuration of the pipe. Martin[2] in-

vestigated the transition from bubble to slug flow in

downward flow of air water in a 14 cm dia. pipe. The data

was correlated on a map of Flowing volumetric con-

centration versus Froude number and on a map of gas

flux versus liquid flux. Martin[3] investigated experi-

mentally vertical downward slug flow of air-water mix-

tures in pipes and measured the terminal velocity of

descending, stationary and ascending bubbles in down-

ward flows. Kulov et al.[4] measured pressure drop, film

thickness and entrainment in downward two phase flow,

and proposed relationships for calculating the measured

parameters as a function of gas and liquid flow rates.

Recently Spedding and Nguyen [5] published flow regime

map for vertical downward flow which does not com-

pare well with our data probably owing to Speddiogs

different classification of the flow pattern.

The objective of this work is to provide a complete

flow pattern map for vertical downward flow as well as

to propose a physical mechanism for the transition

boundaries and to model these transitions.

EXPERIMENTALRESULTS

Experiments were conducted in

2.5

and 5.1

cm

dia.,

10 m long pipes using air-water. The flow pattern were

observed for a wide range of flow rates of water and air

at room temperature and 0.1 MPa (outlet pressure).

The results were plotted on flow pattern maps using

Ye* and I(~* (the superficial velocities) as coordinates

(see Figs. I and 2).

Only three flow regimes were observed: annular flow,

Author to whom correspondence should be addressed.

Fig. 1 Flow pattern map, vertical downward flow 2.5 cm pipe:--,

experiment;---, theory

Fig. 2. Flow pattern map, vertical downward flow. 5.1 cm pipe:

-,

experimental; --- theory.

slug flow and dispersed bubble flow. The most natural

regime in vertical downward flow is the annular flow

which takes the form of falling film at low gas rate and

typical annular flow for high gas flow rate.

At high liquid flow rates of about 0.6 m/set the tran-

sition annular to slug flow is observed. This transition

occurs at relatively constant liquid flow rate. At very

high gas flow rates the transition line to slug flow moves

slightly towards higher liquid flow rates.

At higher liquid flow rates the transition to dispersed

bubble is observed. For the 2.54 cm dia. pipe (Fig. l), this

transition is almost at the same position as in horizontal

and vertical upflow [6,7] while in the 5.1 cm dia. pipe the

transition to dispersed bubble occurs at relatively lower

liquid Bow rates and the slug flow regime shriiks

some-

what Fig. 2).

741

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D V O R ABARNEAel al.

TRANSITION MECHANISMS AND MODELLING

ated from

When liquid at low flow rate is introduced into a

vertical downward pipe, without gas, it moves as a

symmetrical falling film. When gas is introduced

cocurrently with the liquid, the gas flows along the pipe

core while the liquid along the tube periphery. Therefore

the process of analyzing transition between flow regimes

in downward flow starts from the condition of annular

flow. The approach is to determine the mechanism by

which a change from annular to slug flow is expected to

take place and then to determine the mechanism for the

slug-dispersed bubble transition. The fist step is the

development of the relationship between the film thick-

ness and the flow parameters.

where

D =4A,~4&-&~)

L s

I .

D r ;= + = ( I - -2 & D

( 8 )

Consider an equilibrium annular (or falling film) flow,

as shown in Fig. 3, a momentum balance on each phase

yields

In this work the following coefficients were used:

C, = CL = 0.046, n = m = 0.2 for the turbulent flow and

Co = CL = 16, n = m = 1.0 for laminar flow.

A solution of (3) yields the film thickness as a function

of the superficial liquid and gas velocities, the physical

properties of the fluids and the pipe diameter.

The criteria for transition between annular and slug

flow win be based on the same concept as in [6]. A stable

slug will be formed when the supply of liquid in the film

is large enough to provide the liquid needed to maintain

such a slug. When the liquid holdup in

the slug is twice

the liquid holdup in annular flow then transition to slug

flow occurs. It is visualized that such a slug is formed

when owing to the presence of waves an axial transfer of

fluid from the wave trough is transfered to the wave

crest. When enough liquid is present at the crest cross

section a blockage occurs which leads to transition to

slug flow.

- @) - r,S,+poA~g =0.

(2)

Equating pressure drop in the two phases yields:

Substituting

S,= n - D S , = a - ( D - 26)

, = ~ ( 0 8 - 6 )

(4)

Yields

where g= 8 /D .

The shear stresses are evaluated in the conventional

manner

r,++

7 _ fi PC&G - ur12

2

(6)

with the liquid and the interfacial friction factors evalu-

Fk. 3. Annular downward vertical tlow.

u r *

ur-=v)

U, =

4&.

l-46+4

(9)

Assuming the liquid holdup in slug is 0.7[7], the tran-

sition to slug flow will take place at

&=O.S or +=a.35

The transition line based on the above criteria is

plotted on Figs. 1 and 2 and show a good agreemen t

with

the experimental data for D = 2 .5 cm and somewhat

higher values but still acceptable for D = 5.1 cm.

The mechanism of transition from slug to dispersed

bubble flow is the same as for the case for upward

vertical flow[7]. This transition takes place when tur-

bulent forces overcome interfacial tension to disperse

the gas phase into small bubbles. Thus the result of [7] is

basically applicable

here

and may be

given by the tran-

sition line

Although eqn (11) agrees generally with our experi-

mental results, better accuracy could be achieved by

improving the aforementioned model to include the rela-

tive small effect of the gas holdup on the process of

coalescence

and breakup and on the resulting bubble

size.

Calderbank[8] investigated the interelation between

coalescence, breakup and bubble

size in a gas-liquid

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Flow pattern trilnsition

743

system and found that the critical bubble diameter in-

creases in proportion to the square root of the gas

holdup. Considering that at negligible gas holdup

Hinzes [9] correlation is valid and based on Calderbanks

measurements the following correlation evolves which

includes the effect of the void fraction on the bubble size

d

max

I 2

- 4 15 a* + 0.725

(al&) 5e- S - *

As before[7] the terms in (12) are calculated as follows

(13)

(14)

The turbulent breakup prevent agglomeration when the

bubble size is small enough to cause the bubble to remain

in a stable spherical shape. Deformed bubbles are also

those that will easily coalesce into large Taylor bubbles.

Brodkey[lO] used

[

0.40

I

112

d&l = (& - pG)g

(17)

as a criteria where bubbles that have smaller diameter

behave as solid spheres.

Equation (17) estimates the lower limit at which bub-

bles behave as rigid spheres but based on data [ll] they

do maintain their spherical shape up to about twice the

values given by (17). Thus we consider here that

whenever d (eqn 12) is lower than the aforementioned

values the flow will be coalescence resistant, namely

dispersed bubble flow. The transition line is thus given

by

2

C

pL,,,] eL) [a

CL ~)-pI3-v5

=0.725+4.15 h

)

0.5

(W

Equation (18) agrees somewhat better with experi-

mental results than (11) in particular it predicts well the

slight upward trend of the transition line for increasing

the gas flow rate (Fig. 1).

Calderbanks data were limited to void fraction below

o = 10% and the validity of (12) for high gas holdup is

open to question. Nevertheless for the purpose of this

work, this correlation will be used

up

to (I = 0.52171

where a maximum packing is reached.

For (I z 0.52 the transition to dispersed bubbles is

given by the line of constant a

u,.=u,,++(l-a)uo

(19)

where a = 0.52 and u0 is the rise velocity of the bubbles

relative to the liquid which is estimated by

Harmathy[lZ].

ug= 1.53

[

&?(PL PO)0 I14

Pr 2 3. (20)

Similar to the case of vertical upward flow the bubble

flow pattern can exist below the aforementioned tran-

sition line provided

(a) The pipe diameter is larger than

D > 4.36 [s]?

(21)

(b) The gas holdup is below a = 0.25

Conditions (a) and i ) represent the situation where

coalescence is negligible and bubbles keep their separate

identity even under relatively low liquid rate.

Condition (a) is associated with the difference between

the rise velocity of Taylor bubbles and small spherical

bubbles. A necessary condition for bubble flow to exist is

that whenever a random Taylor type aglomeration is

formed its upward velocity should exceed the bubbles

velocity. This condition is satisfied for pipe diameter

given by (21). In the case of smaller pipe diameter the

faster rising bubbles approach the back end of the Taylor

bubble coalescing with it and increasing its size. Under

these conditions bubbly flow cannot exist.

Condition (b) states that al low liquid rate and low

density of bubbles coalescence is not likely to occur

even at pipe diameter larger than given by (21). Thus for

large pipe size the value of IX= 0.25 was chosen [7] as the

transition line separating slug and bubble flow. This

transition line is given by (19)

for (Y= 0.25 and is shown

in Fig.

2.

Thus for pipe size of 5 cm the transition to dispersed

bubble is composed of 4 different sections dependin g on

the mechanism of transition. Proceeding from right to

left (see F ig. 2) the first section is the transition line of

a = 0.52 (19) below which bubbles cannot exist b ecause

of their high

density. The second section is the transition

iine caused by turbulent breakup (18). The third section is

the cx= 0.25

line for which, as discussed, bubble can exist

even at low turbulent conditions provided LI (0.25 and

coalescence is negligible. Finally the fourth section is the

extension of the transition to annular flow that for low gas

flow rate represent annular-dispersed bubble transition

while for higher gas flow rate it is the annular

slugtransition

line.

For

pipe diameter of 2.54 the transition to dispersed

bubble is shown in Fig. 1 to consist of only 2 sections.

The ~1 = 0.52 (19) line and the condition given by (18). As

mentioned for small diameter pipe bubbles cannot exist

at liquid flow rate below transition (18).

As seen

in Figs. 1 and 2 also the experimental results

show considerable dierent trend of tbe transition to

dispersed bubble for 2.54 and 5.1 cm pipes which follow

reasonably well the trend predicted by the theory.

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744

Dvoa~ BARNEAef ul.

SUMMARY AND ON LUSlONS

For vertical downward Row three flow patterns are

observed: annular flow, slug flow and dispersed bubble

flow.

Models for predicting the flow boundaries are presen-

ted.

The transition boundary between annular and slug flow

is obtained whenever the calculated liquid holdup in

downward annular flow is twice the slug hold up.

The

boundary

between slug and dispersed bubble

flows is predicted using an improved version of Taitel ef

al. [7] Hinze

breakup theory

C

d

f

Et

n

P

s

u

x

NOT TlON

flow cross sectional area

constant in the friction factor correlation

pipe diameter

bubble diameter

friction factor

acceleration of gravity

exponent, eqn (7)

exponent, eqn (7)

pressure

perimeter over which the stress acts

velocity in the x direction

coordinate in the downstream direction

G r e e k s ym b o l s

a void fraction

6 liquid film thickness

E energy input per unit mass and time

IJ kinematic viscosity

p density

LT

surface tension

+

shear stress

Subscri~ls a n d s u p e r s c r i p l s

crit

diameter at which bubble behaves as

rigid

sphere

G gas

i liquid gas interface

L liquid

s superficial for one phase flow alone in the pipe

- dimensionless variable

0 free rise

I

REXEREN ES

[II Golan L. P. and Stenning A. H., Proc. Insr. Me c h . E n g r s

196s70 184 108.

[21 Martin C. S., Transition from bubbly to slug flow of a

vertically downward air-water pollution. A SM E S ym -

p o s i um , p . 49 . Atlanta, 2622 June 1973.

t31 Martin C. S., I. F I u i d s Eng ng 1976 98 715 .

[41 Kulov N. N., Maksimov V. V. Maljusov V. A. and

Zhavorovkov N. M. Chem. Engng J. 1979 18.

I51 Spedding, P. L. and Van Thahn Nguyen, Chem.

E n g n g S c i .

1980 35 779.

R Taitel Y. and Dukler A. E., A.I.Ch.E.3. 1976 22 47.

I71

Taitel Y., Barnea

D. and Dukler A. E., A .1 .Ch .E . J . 1980 26

345.

IS ]

Caldcrbank P. H., I-rant. Inst. Chem.

E n g r s

1958 36 443.

[91 Hinze J. O., A .1C h .E~ 1955 1289 .

I101 Brodkey R. S., The Phenomena of F l u i d M o t i o n . Addison

Wesley, Reading, Mass. 1967.

[llJ Migagi O., Phil. &fug. 1925 SO 112.

[12J Harmathy, T. Z., A .Z .Ch .EJ . I 0 6 281.