flow pattern transition for vertical two phase flow
TRANSCRIPT
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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).
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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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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.