7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Prediction of Polydisperse Steam Bubble Condensation in SubCooled Water using the
Inhomogeneous MUSIG Model
C. Lifante*, T. Frank*, A.D. BurnsA*, D. Lucast and E. Kreppert
SANSYS Germany GmbH, Staudenfeldweg 12, Otterfing, D83624, Germany
School of Process Material and Environmental Engineering, CFD Centre, University of Leeds, LS2 9JT, UK
t Institute of Safety Research, Forschungszentrum DresdenRossendorf, POB 510 119, Dresden, D01314, Germany
Email: Conxita.Lifante@iansvs.com
Keywords: CFD, water/steam flow, MUSIG, polydisperse flow, phase change
Abstract
The aim of this paper is to present the validation of a new methodology implemented in ANSYS CFX (ANSYS,
2009), that extends the standard capabilities of the inhomogeneous MUltipleSIze Group model (MUSIG) by additionally
accounting for bubble size changes due to heat and mass transfer. Bubble condensation plays an important role in
subcooled boiling or steam injection into pools among many other applications of interest in the Nuclear Reactor Safety
(NRS) area and other engineering areas. Since the mass transfer rate between phases is proportional to the interfacial area
density, a polydisperse modelling approach considering different bubble sizes is of main importance, because an accurate
prediction of the bubble diameter distribution is required.
The standard MUSIG approach is an inhomogeneous one with respect to bubble velocities, which combines the size
classes into different socalled velocity groups to precisely capture the different behaviour of the bubbles depending on their
size. In the framework of collaboration between ANSYS and the Forschungszentrum DresdenRossendorf (FZD) an
extension of the MUSIG model was developed, which allows to take into account the effect of mass transfer due to
evaporation and condensation on the bubble size distribution changes in addition to breakup and coalescence effects.
After the successful verification of the model, the next step was the validation of the new developed model against
experimental data. For this purpose an experiment was chosen, which was investigated in detail at the TOPFLOW test facility
at FZD. It consists of a steam bubble condensation case at 2MPa pressure in 3.9K subcooled water at a large diameter
(DN200) vertical pipe. Subcooled water flows into the 195.3 mm wide and 8 m height pipe, were steam is injected at z=0.0
m and is recondensing. The experimental results are published in (Lucas, et al., 2007). Using a wiremesh sensor technique
the main characteristics of the twophase flow were measured, i.e. radial steam volume fraction distribution and bubble
diameter distribution at different heights and crosssections.
ANSYS CFX 12.0 was used for the numerical prediction. A 60 degrees pipe sector was modelled in order to save
computational time, discretized into a mesh containing about 260.000 elements refined towards the pipe wall and towards the
location of the steam injection nozzles. Interfacial forces due to drag, lift, turbulent dispersion and wall lubrication force were
considered. The numerical results were compared to the experimental data. The agreement is highly satisfactory, proving the
capability of the new MUSIG model extension to accurately predict such complex twophase flow.
Introduction
Computational Fluid Dynamics (CFD) simulations are
increasingly used for analyses of potential accident
scenarios in Nuclear Reactor Safety (NRS) analysis.
Typical examples for the relevance of bubble condensation
in NRS are subcooled boiling in core cooling channels or
emergency cooling systems, steam injection into pools or
steam bubble entrainment into subcooled liquids by
impinging jets, e.g. in case of Emergency Core Cooling
Injection (ECC) into a partially uncovered cold leg (Lucas
et al., 2009). All these cases are connected with
pronounced 3dimensional flow characteristics, thus
adequate simulations require the application of CFD codes.
Many activities were conducted in the last years to
improve the modelling of adiabatic bubbly flows in the
frame of CFD. In this case models for momentum transfer
between the phases are most important. Usually they are
expressed as bubble forces for interphase momentum
transfer. Experimental investigations as well as Direct
Numerical Simulations (DNS) showed that these bubble
forces strongly depend on the bubble size. In addition to
the well known drag force, also virtual mass, lift, turbulent
dispersion and wall forces have to be considered (Lucas, et
al., 2007). The lift force even changes its sign in
dependence of the bubble size (Tomiyama, 1998) and
E6tvos number. In consequence large bubbles are pushed
to the opposite direction than small bubbles if a gradient of
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
the liquid velocity perpendicular to the relative bubble
velocity exists (Lucas, et al., 2001) (Prasser, et al., 2007).
To simulate the separation of small and large bubbles,
more than one momentum equation is required (Krepper, et
al., 2005) For this reason the socalled Inhomogeneous
MUSIG (MUlti SIze Group) model was implemented into
the ANSYS CFX code (Frank, et al., 2006) (Krepper, et al.,
2005). It allows to consider a number of bubble sizes
independently for the mass and momentum balance, also
called bubble classes. For a proper modelling of bubble
coalescence and breakup, a large numberof bubble classes
(e.g. 1525) is required. Different independent groups of
bubble classes can be considered for the momentum
balance as well. They are called velocity groups. Fewer
number of velocity groups (e.g. 23) are usually considered
due to the high computational effort in solving individual
sets of momentum transport equations. A common criterion
for the classification can be derived from the dependency
of the bubble forces on the bubble size, e.g. the change of
the sign of the lift force. In the conventional version of the
Inhomogeneous MUSIG model, only mass transfer
between the bubble classes due to bubble coalescence and
breakup can be modelled. In case of flows with phase
change, additional transfers between the single classes and
the liquid, and transfers between bubble classes caused by
growth or shrinking of bubbles due to evaporation and
condensation processes have to be considered. The
additional terms for the extension of the MUSIG model are
described later in the paper, and were implemented into a
customized solver based on ANSYS CFX 12.
These extensions of the Inhomogeneous MUSIG model
permit the simulation of flows with phase change. For a
simulation based on physics, proper closure models for
evaporation and condensation rates are further required.
Usually these phase transfer rates are assumed to be
proportional to the interfacial area density and the
overheating or subcooling. For this reason detailed
information on the evolution of local bubbles size
distributions and local temperature profiles is needed. In
the past, wiremesh sensors were successfully used to
measure local bubble size distributions in airwater (Lucas,
et al., 2008) and adiabatic steamwater (Prasser, et al.,
2007) flows in a vertical pipe. These data were used to
validate models for bubble forces and to extent also models
for bubble coalescence and breakup. Experiments using the
wiremesh sensor technology were done to investigate
bubble condensation in an upwards directed vertical pipe.
They clearly showed the effect of interfacial area density
by comparison of experimental results for which only the
initial bubble size distribution was modified by using
different orifice sizes for bubble injection, but keeping the
gas and liquid flow rates constant (Prasser, et al., 2007).
The goal of this paper is to validate the extension of the
Inhomogeneous MUSIG model against one of these
condensation test case configurations.
Nomenclature
ri
t
r,
U
SM
Ms,
Al
Spatial position (m)
Time (s)
Phase volume fraction ()
Velocity (ms1)
Pressure (Nm 2)
Specified mass sources (N)
Gravitational acceleration (ms2)
Momentum sources (N)
Interfacial forces (N)
FD Drag force (N)
FL Lift force (N)
FwL Wall lubrication force (N)
FVM Virtual mass force (N)
n Bubble number density (kg m 3)
m Mass (kg)
BB Bubble birth rate due to break up (kg m 3s 1)
DB Bubble death rate due to break up (kg m 3s1)
Be Bubble birth rate due to coalescence (kg m 3s1)
Dc Bubble death rate due to coalescence
(kg m3s1)
N, iclass bubble number density (m3)
f, iclass size fraction ()
B,, Discrete iclass bubble birth rate due to break
up (kg'm 3s)
Dgi Discrete iclass bubble death rate due to break
up (kg'm 3s)
Bc. Discrete iclass bubble birth rate due to
coalescence (kg'm 3s )
Dc, Discrete iclass bubble death rate due to
coalescence (kg'm 3s1)
Sfci Discrete mass transfer rate to class i due to
phase change (kg'm 3s )
g Specific break up rate (kg 's1)
Q Specific coalescence rate (kg's1)
X11k Fraction of mass due to coalescence ()
m, iclass bubble mass (kg)
J Superficial velocity (ms1)
T Temperature (K)
AT Sub cooling temperature (K)
D, iclass bubble diameter (Nm2)
a Interfacial area density
A,B....,R Measurement elevations
Greek letters
F Mass transfer rate (kgm 3s1)
uL Viscosity (Pas)
p Density (kgm 3)
Subscripts
S Steam
W Water
G Gas
L Liquid
S Saturation
B Break up
C Coalescence
i Bubble class
j Velocity group
a,13 Phase name
Injection
Reference
Governing equations
The inhomogeneous MUltiple SIze Group model (MUSIG)
is based on the Eulerian multiphase flow modeling
approach (ANSYS, 2009)(Frank, et al., 2006). It is based
on ensemble mass and momentum transport equations for
all phases. Therefore, the continuity equations read as
(p )+V.(rp~~ f)
at
P=1
s Y a
where r. is the phase volume fraction, pa the phase density,
Np the number of phases, Ul the phase velocity, Ss
specified mass sources and F p is the mass flow rate per
unit volume from phase 3 to phase a.
The phase momentum equations read as:
Va (r ) + V (rpUf+ U )=
V* ( (VuJ + (vU )) rVp + rjpg + (2)
Np1
P[1
FUa) + SM + Ma,
where ~, represents the phase viscosity, p the pressure, g
the gravitational acceleration, FT+ fp Ifa a describes
the momentum transfer induced by mass transfer and SM
refers to momentum sources due to external body forces
and user defined momentum sources. M0 describes the
interfacial forces acting on phase a due to the presence of
other phases (drag, lift, wall lubrication, turbulent
dispersion and virtual mass force):
M = a,D + fa,L fa,1WL faTD faVM (3)
Since the sum of all phases must occupy the whole domain
volume, the following constraint must be satisfied
Np
a= 1
C=l
Extension of the Inhomogeneous MUSIG model
The inhomogeneous MUltiple SIze Group model (MUSIG)
assumes that the disperse phase is polydisperse, i.e. it is
composed of different size particles (classes). This
methodology can be applied both to bubbles and to
droplets, although the work here presented is focused on
bubbly flows. The user selects a set of initial bubble
diameters (dl) and defines a reference density (Pref), and
the corresponding masses of the bubble classes are then
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
computed In =p.fd This is the value which is
6
going to characterize the class and remain constant during
the simulation.
The different kinds of bubbles are then split into the
socalled velocity groups, and all bubble classes in the
same velocity group share the velocity field and other main
variables. As mentioned, it is wellknown that small and
large bubbles behave in a significant different manner.
Small bubbles flow with the fluid phase, large bubbles are
more influenced by buoyancy. On the other hand side the
lift coefficient changes its sign at a critical bubble diameter,
which depends on the E6tvos number and hence on
pressure and temperature. These are just some examples of
the differences in the movement of bubbles of different
size. In order to get an accurate prediction of the flow
pattern, all these particularities must be solved. Defining
different velocity groups for differently behaving groups of
bubble size classes, these bubbble size effects can be taken
into account. Nevertheless, the standard formulation of the
inhomogeneous MUSIG model allows only mass transfer
between velocity groups due to break up and coalescence
of bubbles. The extension of the method presented here
considers mass transfer due to condensation or evaporation
as well, i.e. the growth and shrink of the bubbles or even
the appearance/disappearance of bubbles due to phase
change are also considered. For this purpose the
formulation of the MUSIG model has been modified, and
one more term which accounts for the mass transfer due to
phase change has been included.
The MUSIG model is a population balance approach, i.e.
an equation for the bubble number density can be written.
In its standard form the MUSIG model reads:
a a
Sn(m, r, t) + (U(m, r, t)n(m, t)) +
at Or (5)
=B D +B DC
where n is the number of bubbles of mass m per cubic
meter at position r and time t. The four terms on the RHS
of Eq. (5) correspond to the birth and death of bubbles due
break up and coalescence, and can be written as:
BB = g(s; m)n(s, t)d (6)
DB =n(m, t)J g(s; m)ds (7)
Bc =JI Q(m s;s)n(m s,t)n(m,t)ds (8)
Dc= n(m, t)J Q(m; s)n(s, t)dt, (9)
being g(m;e) the specific breakup rate (the rate at which
particles of mass m break into particles of mass e and me)
and Q(m;e) the specific coalescence rate (the rate at which
particles of mass m coalesce with particles of mass e to
form particles of mass m+e).
In order to extend the capabilities of the model in order to
consider phase change effects, the following term was
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
included into the LHS of Eq. (5):
an(m, r, t) am(r, t)
am Bt
The bubble number density equation (Eq. (5) + Eq. (10))
can now be discretized into size classes by integrating it
between the limits of each bubble class. A bubble number
density for each bubble class can then be defined as
follows:
m,+1/2
N,(t) Jf n(m,t)dm (11)
m, 1/2
Since mN, = pdrd, being Pd the density of the disperse
phase, rd the volume fraction of the disperse phase, and fl
the size fraction of iclass bubbles, the extended equation
can be rewritten in terms of a size fraction equation as
(p)rd a (PrdUf,) = BB,
at Sxf
+ Sf,
DB, + Bc, Dc,
(12)
being B,,, DBi, Bc,,, Dc the result of the mathematical
manipulation of the corresponding break up and
coalescence terms (BB, DB, Bc and Dc), and Sf1c the
transformation of the term in Eq. (10). The first four are:
BB, =Pdrd (mi;m ,)f (13)
lm +m
DB Pdrd 2 E g(mi; m mi) (14)
Bc =(Pdrd)2 11ZZ Q(mj;ml)Xjklfjfkmj + mk
2j ki i nmmk k
(15)
DC, =(Pard)2 ZQ(ml;m)ffl (16)
where
(mi + mk) m,
X1m(i 1 + < m + mk < m1
ml m 1
ml (m + mk)
X jk = m < m + mk < m,
ml+l m
0 otherwise
(17)
is the fraction of mass due to coalescence between class j
and k at time t which goes into class i. Finally the last term
reads as:
m F
S 11
m m
F,
Sm. r
m i i
in,m
(evaporation)
(condensation)
(18)
where m, is the mass of bubbles in class i, and F, the direct
mass transfer per unit volume and time between the
continuous liquid phase and the bubble size class i. These
source terms reflect the effect of mass transfer between
liquid and bubble size class i, as well as the transfer
between MUSIG groups due to bubble growth or shrinking.
This can be checked by considering the net transfer at the
group boundary. In case of condensation, bubble sizes
shrink, i.e. bubbles are shifted to smaller mass classes.
Considering the net transfer at the lower boundary of
bubble size group i there is a sink in bubble size group i
according to the Eq. (18) equal to mi F,1. On the
m,1 m
other hand the related source in bubble size group i1 is
m
equal to ' F, Summation of gain and loss
n,mlI
m, m,
results in m m F1 = 1.
m, ml
Assuming spherical bubbles, the Sauter mean diameter for
the velocity group j is obtained according to:
r
d 
d,
The sum runs over all MUSIG classes i which belong to
the velocity group j. The mass transfer for the MUSIG
groups i is evaluated based on the Sauter mean diameter,
the interfacial area density, and the mass transfer per unit
volume and time for velocity group j (F,):
Sa
FI
6r / Fjr d
/ds,j
where a represents the interfacial area density.
The mass transfer per unit volume and time for velocity
group j (Fj) can be computed from the volume related heat
flux to the interface and heat of evaporation
F= (hG,(TG T)hL,(TL Ts) (21)
H LG
Herein TG, TL and Ts are the gas, liquid and saturation
temperatures, HLG the heat of evaporation, and hG,j and hL,
the heat transfer coefficients from gas and liquid side to the
interface.
Validation case description
After the derivation of the model, and its implementation
in a customized solver based on ANSYS CFX 12, a
verification process was carried out. A collection of
simplified test cases with given condensation or
evaporation rates were analyzed and compared to their
analytical solution. Several configurations regarding
boundary conditions, bubble class and velocity group
definitions were investigated, providing in all cases the
same result as the analytical solution. Details of the
verification are not included here and can be obtained from
(Lifante, et al., 2009a) and (Lifante, et al., 2009b)
Once the new implementation was completed, a complex
validation case was chosen to test the adequateness of the
model for applications where break up, coalescence and
phase change take place simultaneously.
The present work was performed in collaboration with the
Forschungszentrum DresdenRossendorf,and a condensa
tion case experimentally investigated at the TOPFLOW
test facility was selected for the model validation.
2 wiremesh diametral line of 16 TC
sensors p> P
sensors N L L/D level
72 x0 0 37 0,2 @
72x0.1 221 1,1 A
32x0 4 E 278 1,4 B
72x01 E 335 1,7 C
72 x 1 494 2,5 D
32x04 551 2,8 E
72x I 1 1 608 3,1 F
72x01 1438 7,4 G
32x04 1495 7,7 H
72x01 A 1552 7,9 I
72x0 1 2481 12,7 J
32x04 2538 13,0 K
72x0 A1 1 2595 13,3 L
72xe1 4417 22,6 M
32x04 4474 22,9 N
72x0o I1 4531 23,2 0
T mix.
72x01 7688 39,4 P
32x04 7745 39,7 Q
72x0 1 1 7802 39,91 R
TCmix
Jcold water
Jstflm Jsat. water
Figure 1: Geometry details of the TOPFLOW test facility
at FZD (DN200 vertical pipe)
The TOPFLOW facility (see Figure 1) consists of a large
vertical DN200 pipe (8 m height, 195mm pipe diameter).
By means of injection chambers like the one in Figure 2
(left) ,gas can be injected into the fluid flowing through the
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
pipe at different height of the test section. In the
investigated case sub cooled water was flowing upwards
and steam was injected through 72 small injection nozzles
of 1 mm diameter. Using a wire mesh sensor technique
(Figure 2, right) (Prasser, et al., 2007) and placing it at a
constant position at the end of the test section in varying
distance to the used injection chamber, the
experimentalists at FZD measured radial steam volume
fraction distributions and radial bubble size distributions
for different length of flow development in the pipe. These
values were determined for the different elevations of the
steam injection named with letters, being A the injection
level closest to the sensors (22cm above it), and R the
furthest (7.8 m below the wiremesh sensors).
Figure 2: Left: Injection chamber at the TOPFLOW
facility. Right: Wire mesh device.
Experimental results of the chosen configuration, in
addition to many others, are compiled in (Prasser, et al.,
2007). From the different arrangements investigated in that
paper, the socalled run #3 is the one which is investigated
in this paper by means of CFD simulation. The main
physical properties defining this case are summarized in
Table 1:
Table 1: Main physical characteristics of the selected
validation test case from TOPFLOW measurements.
Figure 3 shows the experimental results regarding the
radial steam volume fraction distributions at the mentioned
distances between steam injection and measurement
crosssection. For level A a local maximum of about 30%
can be observed, as expected from the ratio between the
water and the steam superficial velocities in this particular
test case. This large value evidences the complexity of the
application. It can be noticed that substantial steam
condensation is taking place along the pipe, and the larger
is the injectionmeasurement distance, the lower amount of
steam is present in the pipe.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Radial Gas Distribution
0 20 40 60 80 100
Radial Position Imm]
LeelA Level C Level D Le LvelF vel G L Level I Le L Level O Level R
Figure 3: Experimental radial steam volume fraction distribution at different elevations (levels A to R)
Bubble Size Distribution
0 10 20 30 40 50 60 70 80
Bubble Size Imm]
LevelA Level C Level D Level F Level G Lee v I el L Level O Level R
Figure 4: Radial bubble size distribution (dr /dDB ) at different elevations of steam injection (levels A to R)
In addition, Figure 4 shows the radial bubble size
(diameter) distribution at the same elevations, represented
by the quantity dr /dDB In this manner the crosssectional
average of the steam volume fraction can be computed by
evaluating the integral area under each profile. The
condensation effect is visible here as well since the
enclosed area under the curves decreases along the pipe.
Being this a condensation case, one would expect that the
maximum of the mentioned curves (representing the most
common bubble class at each elevation) is shifted towards
smaller bubble diameters along the pipe. However, except
for the upmost elevations, this value remains almost
constant close to 9 mm. This indicates that not only
condensation is playing a role in the application but
coalescence as well. This was a further reason for choosing
this case for the validation of the extension of the MUSIG
model.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
The turbulence of the continuous phase was modelled by
the SST turbulence model (Menter, 1994). As in all
multiphase applications, the consideration of the interfacial
momentum, heat and mass transfer is crucial for the
accuracy of the numerical results. In the present case Grace
drag, Tomiyama lift and FAD turbulent dispersion force
were considered, as well as the Tomiyama wall lubrication
force (ANSYS, 2009).
Break up and coalescence were modelled following the
standard approach in ANSYS CFX using the Luo &
Svendensen and Prince & Blanch models respectively
(Luo, et al., 1996) (Prince, et al., 1990). The corresponding
break up factor (0.025) and coalescence factor (0.05) were
chosen from previous investigations (Krepper, 2008).
The gaseous phase was assumed to be at saturation
temperature and to be composed of 25 different bubble
classes, distributed into three velocity groups, whose limits
were
* First group [0 mm, 3 mm]
* Second group [3 mm, 6 mm]
* Third group [6 mm, 30 mm]
CFD Model validation CFD Setup definition
A threedimensional model containing one sixth of the
geometry was considered for the numerical simulations. In
this way the threedimensional effects due to the steam
injection through discrete nozzles can be reproduced, and
computational time can be saved in comparison with the
simulation of the whole domain. Symmetry boundary
conditions were applied to the two side planes of the
symmetry sector An inlet boundary condition based on
the water superficial velocity, outlet boundary condition
based on averaged static pressure and adiabatic pipe wall
were considered for the simulation. Since no experimental
information about water velocity distribution or turbulence
quantities at the pipe inlet was available, the computational
domain was enlarged by two meters in front of the steam
injection in order to ensure that the flow is completely
developed when it reaches the steam injection locations.
A numerical grid containing 260.442 elements was
employed. It was refined towards the wall and near the
injection locations. No gridindependency analysis was
performed becauseprevious numerical studies for adiabatic
air/water flow through the TOPFLOW test facility (Frank,
2006) carried out for several different superficial velocity
ratios had proven the adequateness of this grid resolution.
The injection nozzles were modelled by means of source
points located close to the wall. The original nozzle
diameter in the experiments was 1 mm. Due to the large
steam superficial velocity, this leads to an extreme large
steam injection velocity
1 JsRTOPFLOW 1 (0.195/2)2
=0.54 = 285 m/s
nm 72 R2 72 (0.001/2)2
In initial investigations this had strongly deteriorated the
convergence of the numerical simulations. Therefore, for
part of the computations, a larger nozzle diameter was
considered (4 mm), keeping the steam mass flow rate
constant, but providing a lower injection velocity.
The selection of the velocity group boundaries was chosen
depending on the E6tvos number, which allows to predict
the critical diameter at which the sign of the lift coefficient
in the lift force formulation of Tomiyama changes. Using
this value the different bubble classes were arranged into
velocity groups where the coefficient is clearly positive,
transitional or close to zero, or clearly negative.
Results and discussion
Figure 5 shows the radial steam volume fraction at level C
(33 cm above the steam injection) for the different
simulations conducted and the corresponding experimental
values (crosses). Results corresponding to the first
simulation (green dashed profile) show an over prediction
of the local maximum amount of steam (55% against 30%),
and additionally its location is shifted towards the wall in
comparison with the experiments. This simulation allowed
us to get detailed knowledge and to optimize the numerical
parameters to reach convergence (like the necessary
integration time step among others). However, results were
still far from the experiments. Therefore some
changes/improvements in the setup were carried out. The
first modification consisted of displacing the position of
the source points (SP) from the wall to 75 mm away from
the centre of the pipe. This was the location where the
experimentalists at FZD observed the maximum
concentration of steam at steam injection to measurement
distance of level A. By applying this change, a reduction of
the local maximum of steam and a displacement of it
towards the centre of the pipe could be observed (brown
dashed profile). Next step was the consideration of the wall
lubrication force, which was not taken into account in the
previous two simulations.
Iso onfig
Is
Config 3i
10 nfig 2
0
0 20 40 o0 80 100
Rdial Position lirm]
Extend. MUsi
S Extend. MUsIOe S71 mm
 Extend. MUSIO SP7 m WLF
Extend. MUSIO SP7 n WLF + CTBM1.S
 Extmd. MUSIO SPi 71 + nWLF + CTD1. N (Tnmlyam)
Extend. MUsHO SPIE7 Im + WLF 4 CTUO1.5 Nu (TimlyaIm) 4 D1 mm
X Exprlmd.. Lvl C
Figure 5: Radial steam volume fraction distribution at
level C (33 cm above the injection level) for different setup
configurations.
As expected the steam was thereby further kept away from
the wall and for the steam volume fraction directly at the
wall a more physical behavior could be observed. Further,
the influence of the turbulent dispersion force was
increased by enlarging the turbulent dispersion coefficient
from 1.0 to 1.5 (dash dotted light green), which
corresponds to the level of uncertainty regarding this
model parameter in accordance to the model derivation by
different authors in literature. A slight improvement could
be observed. The parameter which had the largest influence
in the numerical results was the correlation used for the
heat transfer. First results were obtained using the
RanzMarshall correlation. It was proven in this
application, as well as in the literature, that this correlation
under predicts the heat transfer and therefore the
condensation rate in applications with large amount of
steam and with bubble diamters larger than lmm. Instead,
a new correlation suggested by Prof. Tomiyama
(Tomiyama, 2009) was implemented (blue profile),
providing a satisfactory agreement with the experimental
results regarding both the value of the local amount of
steam volume fraction and the radial position of its
maximum value. Only at the centre of the pipe the steam
volume fraction is still under predicted. The last test of this
first investigation consisted of using the improved setup
(shift of source points location, consideration of the wall
lubrication force, increase of the turbulent dispersion
coefficient and use of the Tomiyama heat transfer
correlation) and the original injection nozzle diameter in
order to evaluate the importance of the radial momentum
of steam injection, which was not considered when a larger
nozzle diameter was applied in the CFD simulations. The
computational time required due to the larger injection
velocity was significantly increased. The effect of this
modification can be observed in Figure 5 (red solid profile)
since the predicted steam volume fraction maximum is
thereby moved towards the centre of the pipe.
Detailed results for three of the presented simulations will
be shown next. They will be named Configuration 1 (basic
setup results green curve), Configuration 2 (improved
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
setup blue curve) and Configuration 3 (improved setup
and original nozzle diameter red curve). Main
characteristics in setup of these simulations are
summarized in Table 2.
Config. 1 Config. 2 Config. 3
SP 97[mm] 97[mm] 75[mm]
 / /
CTD 1.0 1.5 1.5
0.5 0.3 0.8 0.5 0.8 0.5
Nu 2+0.6Rep Pr 2+0.15Rep Pr 2+0.15Rep Pr
Dinj l[mm] l[mm] 4[mm]
Table 2: Main CFD setup differences between selected
configurations: Location of the source points; consideration
of the wall lubrication force; turbulent dispersion
coefficient; heat transfer correlation for Nusselt number;
injection nozzle diameter.
The crosssectional averaged steam volume fraction at
different steam injection elevations and for the three
selected CFD setup configurations are plotted in Figure 6.
The horizontal axis corresponds to the distance between
steam injection and the measurement plane, being zero at
the injection location, and 8m for the largest distance in the
TOPFLOW experiment. The results corresponding to the
first configuration are able to reproduce the accumulation
of steam right after the injection and the trends of the
experimental results. However, after L>0.5m the steam
volume fraction is strongly over predicted. The second and
third configuration behave in a similar way during the first
two meters of the pipe after the steam injection. Finally,
the prediction using the third CFD configuration shows a
good quantitative agreement to the experimental values as
well.
Nh
~4h~
o0 1 2 3 4 5 6 7 8
z [m]
Config  Config 2 Config 3 X Experiment
Figure 6: Crosssectional averaged steam volume fraction
at different elevations with respect to the injection level
and compared for the three selected CFD configurations.
Figure 7 shows the total steam volume fraction at steady
state at a vertical plane between two adjacent injection
nozzles for the three different CFD configurations. As
already observed in Figure 5 for level C, it can be seen that
for the first configuration the steam remains all along the
pipe near to the wall. This is in contradiction with what
was observed during the experiments, where the steam was
forming a kind of ring shaped pattern in the measurements.
This radial steam distribution is however present at the
pictures corresponding to the second and third
configuration. Both results are qualitatively analogous.
Nevertheless the influence of the nozzle diameter is
evident from this comparison, since the steam is slightly
shifted towards the centre of the pipe in the third case and
a higher amount of steam volume fraction (less
recondensation) is predicted along the pipe as well.
Detailed results corresponding to the three selected
configurations are presented in Figure 8 and Figure 9.
Figure 8 shows the radial steam volume fraction
distribution at the elevations A, C, F, I, L and O (i.e.
measurement at 22, 33, 60, 155, 259 and 451cm above the
steam injection location). At elevations A, C and F it can
be seen that the first configuration is predicting the steam
to remain close to the wall while the distribution of the
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
steam for the second and third configuration approaches
reasonably the experimental results. The larger radial
momentum of steam injection in the third CFD
configuration causes the steam to move in the direction of
the centre of the pipe in comparison with the second
configuration. For the upper elevations (L, L and 0) less
steam is predicted. The second and third configuration
results show significant better agreement to the
experiments in comparison with the first simulation, and as
already observed in Figure 6 the third configuration
predicts slightly more steam as the second one.
For the same distances between steam injection and
measurement cross section the radial bubble size
distributions can be analyzed. For all elevations the first
configuration is only able to reproduce the location of the
maximum of the dr /dDB profile, but due to the strong
over prediction of the steam volume fraction in the domain
this profile is strongly over predicted as well. The second
and third configuration are in much better concordance
with the experiments and are able to reproduce reasonably
good the experimental values for all investigated steam
injection elevations.
A~!SIfS
(iSS
Total Gas Volume Fraction
Plane 1
0.19
Total Gas Volume
Plane 1
Fraction
Total Gas Volume Fraction
Plane 1
S0.25
I J
Figure 7: Steady state steam volume fraction at a vertical plane between two adjacent injection nozzles. L
1; Middle: Configuration 2; Right: Configuration 3.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
o10
Jh
0 20 40 60 80 100
Radial Position [mm]
Config 1 Config 2 Config 3 X Experiment Level I
0 20 40 60 80 100 0 20 40 60 80 100
Radial Position [mm] Radial Position [mm]
Config 1 Config 2 Config 3 X Experiment Level C Config 1 Config 2 Config 3 X Experiment Level L
60 60
50 F F F 50
40 4 8 0400
o            o
I .
a
10 1 .. 20
0 20 40 60 80 100 0 20 40 60 80 100
Radial Position [mm] Radial Position [mm]
Config 1 Config 2 Config 3 X Experiment Level F Config 1 Config 2 Config 3 X Experiment Level 0
Figure 8: Predicted and experimental radial steam volume fraction distributions at elevations A, C, F, I, L and 0 (22 cm, 33
cm, 60 cm, 155, 259 and 451 cm respectively above the injection level).
i.................  ................    
   ........... ....... .....................
_. . . ... . .
                  .. . . . . .. . . . . . ^
       ^  ^         ^ ^         
   
 
             
   
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
0 5 10 15 20 25 30 35 40
Bubble Diameter [mm]
Config 1 Cofig 2 ConfiCog 3 X Experiment Level A
0 5 10 15 20 25 30 35 40
Bubble Diameter [mm]
Config 1 Config 2 Config 3 X Experiment Level C
Config 1 Config 2 Config 3 X Experiment Level I
2
1.5
1
0.5
0 5 10 15 20 25 30 35 40
Bubble Diameter [mm]
Config 1 Config 2 Config 3 X Experiment Level L
2 2
1.5 1.5
E E
EI
0.5 0.65
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40
Bubble Diameter [mm] Bubble Diameter [mm]
Config 1 Co Conig2 Config 3 X Experiment Level F Config 1 Config 2 Config 3 X Experiment Level O
Figure 9: Predicted and experimental radial bubble size distributions (dr /dDB ) at elevations A, C, F, I, L and O (22 cm,
33 cm, 60 cm, 155, 259 and 451 cm respectively above the injection level)..
Conclusions
A new methodology to extend the capabilities of the
Multiplesize group model (MUSIG) has been presented in
this paper. The implemented MUSIG model extension
allows simulating twophase flow applications where not
only coalescence and break up of bubbles take place, but
where bubble size distribution changes under the influence
of mass transfer due to phase change. The new model is
able to predict the shrink or growth of bubbles when
evaporation or condensation takes place.
The new extended inhomogeneous MUSIG model was
developed in collaboration of ANSYS with FZD and has
been implemented into a customized solver based on
ANSYS CFX 12. In order to validate the extended
population balance model for polydisperse bubbly flows a
complex water/steam experiment has been chosen. It
consists of sub cooled water flowing upwards through the
DN200 vertical pipe of TOPFLOW (FZD), into which
large amount of steam has been injected. The validation
case shows locally values up to 30% of steam volume
fraction, where condensation and steam bubble
coalescence are the main phenomena taking place. Thanks
to the detailed measurements performed at FZD the
evolution of the flow along the whole pipe is known, and
corresponding measurement data have been used to carry
out an extensive analysis of the numerical results obtained
by applying the proposed new MUSIG model formulation.
Several configurations of the numerical setup have been
investigated.. For three of them a detailed comparison
against experimental data has been presented. First
obtained CFD results (configuration 1) have been
improved by modifying some of the numerical parameters
and physical submodels. For the socalled configurations 2
and 3, a satisfactory agreement to the experimental data
has been obtained. Both simulations are able to reasonably
predict the radial steam volume fraction at all elevations
along the pipe. The bubble size distribution at the same
positions, in terms of the variable dr,/dDB has been
also investigated, being likewise satisfactorily estimated in
the numerical simulations. Results corresponding to the
third configuration approach slightly more accurately the
experimental investigations than the second one. However,
it is also more computational time demanding due to the
high steam injection velocityies..
Acknowledgements
This research has been supported by the German Ministry
of Economy (BMWi) under the contract number 150 1328
in the framework of the German CFD Network on Nuclear
Reactor Safety Research and Alliance for Competence in
Nuclear Technology, Germany.
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