Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 12.3.2 - Measurement of Droplet Quality of Carryover from Free Surface using Throttling Calorimeter
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 Material Information
Title: 12.3.2 - Measurement of Droplet Quality of Carryover from Free Surface using Throttling Calorimeter Experimental Methods for Multiphase Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Tamai, H.
Nagayoshi, T.
Katono, K.
Ito, T.
Takase, K.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: throttling calorimeter
droplet quality
carryover
free surface flow
 Notes
Abstract: Some advanced small/medium size BWRs intend to utilize natural-circulation cooling systems and the Free Surface Separation (FSS) concept because they are more economical. The development of a predictive model for the droplets entrained with the steam (carryover) from the free surface is indispensable in the design of BWRs. Dominant factors in the carryover have therefore been investigated in our series of studies. In this paper, the droplet quality was measured with a throttling calorimeter that could measure the droplet quality based on the isenthalpic process between wet and superheated steam through the throttle. The measurements were carried out under the conditions of a pressure of 1.5-2.5 MPa and a steam volumetric flux of 0.39-1.94 m/s. The temperature of the superheated steam after passing through the throttle was confirmed to be strongly related to the quality of the wet steam. A modified model based on the measurements proved to be capable of predicting the droplet quality within the range of the database. Evaluating the droplet quality under BWR conditions validated the feasibility of the design of the natural-circulation type BWR that utilizes the FSS concept.
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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Volume ID: VID00304
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: 1232-Tamai-ICMF2010.pdf

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


Measurement of Droplet Quality of Carryover from Free Surface
using Throttling Calorimeter


H. Tamai*, T. Nagayoshi**, K. Katono**, T. Ito*** and K. Takase*


Nuclear Science and Engineering Directorate, Japan Atomic Energy Agency, Ibaraki, 319-1195, Japan
** Energy and Environmental Systems Laboratory, Hitachi, Ltd., Ibaraki, 319-1221, Japan
*** Nuclear Design Department, Hitachi-GE Nuclear Energy, Ltd., Ibaraki, 317-0073, Japan
tmiwli hideiistd1C. i ( iCi ,-'o ip

Keywords: throttling calorimeter, droplet quality, carryover, free surface


Abstract

Some advanced small/medium size BWRs intend to utilize natural-circulation cooling systems and the Free Surface Separation
(FSS) concept because they are more economical. The development of a predictive model for the droplets entrained with the
steam (carryover) from the free surface is indispensable in the design of BWRs. Dominant factors in the carryover have
therefore been investigated in our series of studies. In this paper, the droplet quality was measured with a throttling calorimeter
that could measure the droplet quality based on the isenthalpic process between wet and superheated steam through the throttle.
The measurements were carried out under the conditions of a pressure of 1.5-2.5 MPa and a steam volumetric flux of
0.39-1.94 m/s. The temperature of the superheated steam after passing through the throttle was confirmed to be strongly
related to the quality of the wet steam. A modified model based on the measurements proved to be capable of predicting the
droplet quality within the range of the database. Evaluating the droplet quality under BWR conditions validated the feasibility
of the design of the natural-circulation type BWR that utilizes the FSS concept.


Introduction

The Innovative Water Reactor for Flexible Fuel Cycle
(FLWR) (Uchikawa 2007) and some other advanced
small/medium size BWRs are intending to adopt
natural-circulation cooling systems for economic and safety
reasons. In addition, the Free Surface Separation (FSS)
concept is also considered in taking advantage of its low
flow velocity design. In the upper plenum of the BWRs
utilizing the FSS concept, large droplets entrained with
steam (carryover) from free surface are gradually separated
from the steam and fall down due to gravitational force, so
that no steam separators are required. Since devices in the
upper plenum can be thus simplified, the costs of
construction and maintenance are reduced.
Several natural-circulation type BWRs utilizing the FSS
concept; namely the EBWR (Petrick 1963), JPDR (Uga
1967), and Dodewaard (Wouters 1992), were designed, and
the characteristics of the carryover were investigated. In the
EBWR, the quality of carryover was derived by a heat
balance technique, and dependence of the carryover on
reactor power and water column level was investigated. The
JPDR tests showed the relationship between exit steam
quality measured by a calibrated flowmeter and reactor
power. In the Dodewaard, carryover after leaving a steam
dryer was derived from Na concentration, and the water
level where the sharp transition from small to large
carryover took place was plotted against reactor power.
These full-scale tests in the natural-circulation type BWRs
have provided valuable information. However, since the
characteristics of carryover are correlated with macro
parameters such as reactor power and water level, the


applicability of their carryover data may be limited to the
individual BWR system.
Kataoka and Ishii (1983, 1984) developed a physical model
of carryover after considering the dominant factors such as
droplet size distribution, initial velocity of entrained
droplets, droplet motion and void fraction under free surface.
They showed that the carryover phenomenon depends on
gas velocity, height above free surface, vessel diameter and
fluid properties, and the comparison of their carryover
model with experimental data from previous small-scale
tests (Garner 1954, Sterman 1958) resulted in a good
agreement over a wide range of conditions. However,
experimental verification of droplet motion, void fraction
under free surface and dependence on vessel diameter under
high velocity conditions was unfortunately limited due to
the lack of experimental data, and it is important subject to
be resolved.
We planned to carry out a steam-water test for the purpose
of expanding the database on the carryover and
investigating the dominant factors involved in carryover
shown in Figure 1. The most important and terminal factor
for the design of BWRs utilizing the FSS concept is the
carryover rate, which correlates with gas velocity, height
above free surface, vessel diameter and fluid properties.
However, the carryover rate strongly depends on the droplet
motion such as falling of large droplets due to gravitational
force and deposition into a wall. The droplets are generated
from free surface in fluctuations that are caused by the
two-phase flow under the free surface. The purpose of our
series of studies is therefore to investigate the three
dominant factors outlined in Fig. 1 through small-scale tests
under high pressure and high velocity conditions.









Measurement parameters and measurement techniques for
each of the dominant factors are summarized in Table 1.
Droplet diameter and droplet velocity are measured with a
direct-imaging technique in order to obtain the droplet
motion. Measurements of a cross-sectional distribution of
void fraction using a wire-mesh sensor (Richter 2002) are
carried out in order to investigate the two-phase flow under
free surface. This paper describes how the quality of the
droplets was measured with a throttling calorimeter
(Yoshihara 1956) and the measurements then used in
evaluating the carryover under BWR conditions.
Some researchers have already measured droplet quality of
carryover from the free surface in steam-water tests using
several measurement techniques. Sterman (1958) measured
the droplet quality using the salt content in the droplet flow.
Garner et al. (1954) determined the droplet quality both
from the size distribution of the droplets viewed through a
microscope and from the concentration of salt in the
condensed steam. Wilson et al. (1965) measured the droplet
quality of carryover through steam sampling nozzles with a
superheating calorimeter. The main test parameters used in
those studies are summarized in Table 2. In this study a
throttling calorimeter (Yoshihara 1956) was utilized in order


Dryer
Dominant factor

Free 1 of carryover
surface *
A .- Carryover rate

Droplet motion

Two-phase flow


Natural-circulation type BWR
Figure 1: Dominant factor of carryover


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

to measure the carryover rate over a high droplet quality
range and under high velocity conditions.

Nomenclature

DH Vessel diameter (m)
Efg carryover rate (-)
g gravitational acceleration (ms 2)
h height above free surface (m)
i enthalpy (kJkg 1)
iios heat loss due to heat dissipation (kJkg 1)
j volumetric flux (ms-1)
N,, gas viscosity number
P pressure (Pa)
T temperature (K)
x quality (-)
Greek letters
Ap density difference (= pd G)
p density (kgm 3)
cy surface tension (Nm'1)
gL viscosity (Pas)
Subsripts
d droplet phase
G gas phase
1 state before throttle
2 state after throttle

Experimental Method

Figure 2 provides a schematic of the test section and
throttling calorimeter. The working fluid was purified water
that had been deionized and degassed. Steam was produced
in a steam generator and eventually flowed into stagnant
water at the bottom of the test section. Droplets entrained
with the steam from the free surface were passed through an
isokinetic sampling tube into the throttling calorimeter. The
axial differential pressures were measured with pressure
gauges in order to evaluate the level of the free surface. The


Table 1 Measurement parameters and measurement techniques for each of dominant factors


Dominant factor Measurement parameter Measurement technique
Carryover rate Droplet quality Throttling calorimeter
Droplet motion Droplet diameter and droplet velocity Direct-imaging
Two-phase flow Cross-sectional distribution of void fraction Wire-mesh sensor


Table 2 Comparison of test conditions between this study and previous studies


Vessel diameter, Pressure, Steam volumetric Height above free
Reference
DH (I) P (MPa) flux, jG (m/s) surface, h (m)
This study 0.12 1.5, 2.0, 2.5 0.39 1.94 0 1.5
Sterman (1958) 0.24 1.72 18.7 0.01 1.3 0.5-0.9
Garner et al. (1954) 0.30 0.1 0.3 -1.3 0.5 1.0
Wilson et al. (1965) 0.457 6.9, 8.3 0.4 0.9 0.61








inner diameter and height of the test section were 0.12 m
and 7.5 m, respectively. The exit pressure of the test section
was maintained with a pressurizer to be within an error of +
0.3%. The error in the steam flow rate was within + 1.8%,
which was evaluated using a heat balance technique.


Droplet flow


Droplet

Throttling
calorimeter


Superheated steam
(P2,T2)
Wet steam
(P ,T,,x)


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

steam volumetric flux jG and the height above the free
surface h were controlled to be the specified conditions. The
range of test condition parameters used in this study is
shown in Table 1 and compared with that used in the
previous studies (Sterman 1958, Garner 1954, Wilson 1965).
The test conditions used in this study ranged within higher
steam volumetric flux conditions when compared with the
previous studies. Here, h was evaluated using the axial
distribution of the void fractions, which were estimated by
differential pressures assuming a frictional pressure loss was
negligible. The typical distribution of the void fractions is
shown in Figure 3. The void fraction in a two-phase flow
under free surface is a constant value (= 0.55) whereas the
void fraction in a mist flow over free surface is equivalent to
one. The void fraction in the region with the free surface
fluctuation ranges from the constant value to one. Thus, the
level of the free surface was defined as the center in the
region with the fluctuation. The range of the free surface
fluctuation is plotted against the steam volumetric flux in
Figure 4. The range increases when the steam volumetric
flux is smaller than 1.5 m/s, whereas the range is constant or
decreases when the flux is larger than 1.5 m/s. The transient
point corresponds to the void fraction of 0.7 where
transition of the flow pattern might occur.


+0.12 Steam

Unit: m Stagnant water

Figure 2: Schematic of a test section and a throttling
calorimeter

Throttling calorimeter

The throttling calorimeter consisted of a throttle and an
expansion chamber, as revealed in Figure 2. When wet
steam flowed through the throttle and was depressurized, it
changed into superheated steam through the isenthalpic
process. The enthalpy ii of the wet steam before the throttle
was equivalent to the enthalpy i2 of the superheated steam
after the throttle, with the isenthalpic process being provided
by


i (Pi, T, Tx)= i2 (P2,T2 )


The droplet quality of the wet steam could then
consequently be estimated using measurements of P2 and T2
of the superheated steam. Yoshihara and Onishi (1956)
investigated the characteristics of the throttling calorimeter,
thus obtaining the effects of the throttle diameter and
expansion chamber size. They also pointed out that the
measurement error strongly depended on heat dissipation
from the throttling calorimeter. Equation (1) was modified
to be


il(Pl,Ti,x)=i2 (P2,T2) +i1,-


i&o, was provided by the results of preliminary experiments
with the steam single-phase flow (x = 1) under each of the
test conditions.

Test Conditions

The quality of the droplets was measured after pressure P,


7

E
06
o
4-



a>


I I I
P= 2.0 MPa
JG = 0.74 m/s

-S


*
- *


B I I I I 1
4 0.6 0.8 1 1.2
Void fraction evaluated
by differential pressure, a [-]
Figure 3: Axial distribution of void fractions

1

|o 0.8 /-

S/ 0.6- /

t 0.4 -
a, [ Pressure
S0.2- 1.5 MPa
Sc --W-2.0 MPa
rr -v- 2.5 MPa
0 0.5 1 1.5
Steam volumetric flux, jG [m/s]
Figure 4: Range of free surface fluctuation






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


Results and Discussion


Figure 5 provides a typical measurement of the time
variations of T2 and h. The height above the free surface h
fluctuates within the period of about 20 seconds that
depends on the fluctuation of the two-phase flow under the
free surface. The fluctuation in h varies the quality of the
wet steam that passes through the isokinetic sampling tube,
thus causing the fluctuation in temperature T2 of the
superheated steam after passing through the throttle. The
period of the fluctuation with T2 is also about 20 seconds.
This result indicates the strong relationship that exists
between the quality of the wet steam and T2. Similar results
were observed under all the test conditions.


Sx

Co
a) 0


--.C
..

0 -
0 >


P1 = 2.0 MPa, P2 = 0.12 MPa, h = 1.7 m/s


Time, t [s]
Figure 5: Time variations of T2 and h


-E

CD






0
n
CU
5.Q

(-

T_


Kataoka and Ishii (1983, 1984) developed a physical
carryover model that depended on the gas velocity, the
height above the free surface, vessel diameter and fluid
properties, using mainly the Sterman's data (1958). A
comparison of the calculations by the Kataoka model and
the measurements in this study and previous studies
(Sterman 1958, Wilson 1965) under a high droplet quality
condition is shown in Figure 6(a). The model tends to
underestimate our test section data with a vessel diameter of
0.12 m, whereas the model tends to overestimate Wilson's
data (1965) with a vessel diameter of 0.457 m. The model is
thus sensitive to the effect of the vessel diameter on
carryover under the high droplet quality conditions. The
Kataoka model was therefore modified to exclude the term
of the vessel diameter under high droplet quality conditions.
Details of the modified model are provided in the Appendix.
A comparison of the calculations by the modified model and
the measurements is shown in Figure 6(b). The modified
model proved to be capable of predicting the effect of the
vessel diameter within the range of the database.


ZCx
3 _
0 )
-C~U

yE
-o-


OE
a),
70-
1w
cO -C
"i
1 1


3-3 10- 10
Measured droplet quality, 1-x [-]
(a) Original model


10-3 10-2


Measured droplet quality, 1-x [-]
(b) Modified model
Figure 6: Comparison between measured and calculated
droplet quality

Figure 7 shows a comparison of measured droplet quality,
which was defined to be the average for 100 seconds under
each of the conditions, and the calculations made using the
modified model. The error bar in the figure corresponds to
the standard deviation of the average. The measured droplet
quality decreased with increasing height above the free
surface and decreasing steam volumetric flux, This trend is
similar to that in the previous study (Sterman 1958, Wilson
1965). The calculations agreed well with the measurements
under all the conditions. This therefore confirmed the
modified model to be capable of predicting the dependence
of the droplet quality on the steam volumetric flux, the
height above the free surface and the pressure.


















J [m/s]
1.94
1.30
0.65
1 1.5 2


Height above free surface, h [m]
(a) P = 1.5 MPa


--",. P = 2.0 MPa
S\ .\ .





Cal. Exp. j3 [m/s]---
--- V 1.70
-- 1.46
-- A 0.98
-- 0.49
, , I , , I , , I , ,


0.5 1 1.5
Height above free surface, h [m]
(b) P = 2.0 MPa


0.5 1 1.5 2
Height above free surface, h [m]
(c) P = 2.5 MPa


Figure 7: Comparison between measured and calculated
droplet quality

The droplet quality under BWR conditions was then
evaluated using the modified model. Figure 8 shows a
schematic of a natural-circulation type BWR with the FSS
concept used in the reactor design. Steam above the free
surface was separated from a large portion of the droplets
through use of the FSS concept, and then passed through a
dryer into the turbine. The droplet quality at the bottom of
the dryer needed to be less than 10% in achieving
acceptable droplet quality at the turbine. The major
dimensions of the BWR design are given in Table 3. The
range of the steam volumetric flux was 0.5-1.0 m/s, and the
distance between the free surface and the bottom of the
dryer 2.5 m. A droplet quality map evaluated usnig the
modified model under the BWR condition is provided in


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

Figure 9. The droplet quality over the range of the BWR
design was much less than 10%, which is what is needed at
the bottom of the dryer. This result revealed the feasibility
of the design of the natural-circulation type BWR utilizing
the FSS concept.


surface


Figure 8: Schematic of the natural-circulation type BWR
adopting the FSS concept

Table 3 Major dimensions of the BWR design

Pressure 7.2 MPa
Steam volumetric flux 0.5 1.0 m/s
Vessel diameter 5 m
Distance between free surface
2.5 m
and the bottom of the dryer


E.7


c 5
6t
5

"4
04
a 3

4--
a)
>2


a z
I
Z 0
-1-


0.1% Drc



Re(
at b


P=7.2MPa

plet quality


1uest
ottom of dryer


Range of
design 109%


0.5 1 1.5
Steam volumetric flux, jG [m/s]


Figure 9: Droplet quality map under the BWR condition

Conclusions

The droplet quality of the carryover from the free surface
was measured with a throttling calorimeter that could
measure the droplet quality based on the isenthalpic process


P = 1.5 MPa


Cal. Exp.
- A
--- *


100

10-1
X 10-2

10-3

Co
0- 10-4

- 10


10-7
0


100

10-1

10-2

10-3

10-4
10-5

10-6

10-7
0


--,". P = 2.5 MPa

_o\%
I\ .
- V -


Cal. Exp. jG [m/s] .......
1.37
1.18
A 0.78
-- 0.39


i\. r


-


-









between the wet and superheated steam through the throttle.
The measurements were carried out under the conditions of
a pressure of 1.5-2.5 MPa and a volumetric flux of
0.39-1.94 m/s. The temperature of the superheated steam
after passing through the throttle was confirmed to be
strongly related to the quality of the wet steam with droplets.
Droplet quality data was measurable under the high steam
volumetric flux conditions. The modified carryover model
proved to be capable of predicting the dependence of the
droplet quality on the steam volumetric flux, the height
above the free surface, the pressure and the vessel diameter
within the range of the database. Evaluating the droplet
quality under BWR conditions based on the present and
previous experimental studies revealed the feasibility of the
design of the natural-circulation type BWR that utilized the
FSS concept.

References

Gamer F.H., Ellis S.R.M. and Lacey J.A., The Size
Distribution and Entrainment of Droplets, Trans. Instn
Chem. Engrs, Vol. 32, 222-235 (1954).

Kataoka I. and Ishii M., Mechanistic Modeling and
Correlations for Pool-Entrainment Phenomenon,
NUREG/CR-3304 (1983).

Kataoka I. and Ishii M., Mechanistic Modeling of Pool
Entrainment Phenomenon, Int. J. Heat Mass Transfer, Vol.
27, 1999-2014 (1984).

Petrick M. and Spleha E. A., Thermal Hydraulic
Performance Characteristics of EBWR (0 to 100 Mwt),
ANL-6693 (1963).

Richter S., Aritomi M., Prasser H.-M. and Hampel R.,
Approach towards Spatial Phase Reconstruction in Transient
Bubbly Flow using a Wire-Mesh Sensor, Int. J. Heat Mass
Transfer, 45, 1063-1075 (2002).

Sterman L. S., On the Theory of Steam Separation, J. of
Tech. Physics, 28(7), 1562-1573 (1958).

Uchikawa S., Okubo T., Kugo T, et al., Conceptual Design
of Innovative Water Reactor for Flexible Fuel Cycle
(FLWR) and its Recycle Characteristics, Journal of Nuclear
Science and Technology, Vol. 44, No. 3, 277-284 (2007).

Uga T, JPDR Thermal and Hydraulic Characteristics
Measured by an Instrumented Fuel Assembly (IFA) and
their Analysis by a Computer Code "JP-Hydro", JAERI
1136 (1967).

Wilson J. F., Littleton W. E., Yant H. W. and Mayer W. C.,
Primary Separation of Steam from Water by Natural
Separation, ACNP-65002 (1965).

Wouters J. A. A., Oppentocht P, F. J. van der Kaa and
Nissen W. H. M., The Effect of Water Level on the Behavior
of the Dodewaard Natural-Circulation BWR, International
Conference on Design and Safety of Advanced Nuclear
Power Plants, Tokyo, Japan, Oct. 25-29, Vol. 3, 25.1-8
(1992).


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


Yoshihara H. and Onisi F., On the Study of Measurement of
Steam Wetness (1) Basic Investigation on Throttling
Calorimeter, Reports of the Himeji Kogyo Daigaku, No.6,
41-47 (1956), [in Japanese].

Appendix

The modified model was developed by removing the term
of the vessel diameter under the high droplet quality
conditions of the Kataoka model (1983, 1984). The model
consists of three regions that depend on the height above the
free surface. For each of the regions, the correlation of the
carryover rate Ef, is provided in terms of the dimensionless
gas volumetric flux jG*, dimensionless height above the free
surface h* and gas viscosity number N~G, and can be
defined by


S PdJd Xd
PGjG 1-Xd

( 1/4
o gAp
jG* = G 2
PG )


h* = h/
gAp


NV G
DGG = /gAp2


(A-1)



(A-2)



(A-3)



(A-4)


(1) Near surface region
In this region the carryover consists of all the droplets
entrained from the free surface. The range and the carryover
rate are provided by the following respective equations:


0/ 0.23
0 h* < 8.907 x 103 jG iGO5 PG
Ap)


Efg =4.84 x 10-3 rPG
SAp


(A-5)



(A-6)


(2) Momentum controlled region
In this region the carryover consists of both droplets that
attain the height due to their initial momentum and droplets
whose terminal velocity is less than the gas velocity. This
range is given by

/ 5 0.23 / 0 0.23
8.907 x O3JG *G N .5G
(A-7)

This region is subdivided into three regimes that depend on
the gas volumetric flux.
(2-1) For the low gas flux regime limited to


JG /h* <6.39 x 10-4


(A-8)





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


the carryover rate is given by:


/ >-0.31
Eg 1.328x103NG1.5 PG (G*/h*). (A-9)
Ap

(2-2) For the intermediate gas flux regime limited to

/ ,0.10
6.39x10-4
(A-10)


the carryover rate is given by:


/ --0.31
E = 3.25x 109 1.5 G -G */ h *)3. (A-11)
2Ap5


(2-3) For the high gas flux regime limited to


G */h* > 6.64 x 10-5 N


the carryover rate is given by:


Ef (jG h*) .


0 .10
0.5 PG (A-12)
l )Ap '


(A-13)


(3) Deposition controlled region
In this region the carryover consists of droplets whose
terminal velocity is less than the gas velocity. The range and
carryover rate are provided by the following respective
equations:


S 0.23
h* > 1.69x 104N 0.33 G P
Ap


Efg=7.13x10 4jG*3NG PG exp(-0.205(h/DH
forAp< 1.8
for h < 1.8 m


( >1.0
Efg =7.13x10- 4jG*3NG0.5( PG exp(-0.205(15-ha
for> 1.8m
forh> 1.8 m


(A-14)



ha/ D))
(A-15)


/DH))

(A-16)


Here, ha is the height between the momentum controlled
region and the deposition controlled region, which is
provided by Equation (A-14).




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