Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 11.6.2 - Cavity Formation in Particles Obtained from a High Temperature Oxidic Melt Jet Disintegration in Water
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Permanent Link: http://ufdc.ufl.edu/UF00102023/00292
 Material Information
Title: 11.6.2 - Cavity Formation in Particles Obtained from a High Temperature Oxidic Melt Jet Disintegration in Water Multiphase Flows with Heat and Mass Transfer
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Kudinov, P.
Kudinova, V.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: oxidic melt
debris quenching
formation of cavities
debris formation
 Notes
Abstract: Present work is motivated by numerous observations of cavities which regularly appear inside debris particles formed as a result of quenching of high temperature molten oxidic jet in a water pool (Kudinov et al. 2010). The cavity is open with a small hole in the particle surface. The cavities and the holes are observed inside particles with diameters down to few hundreds of microns. In the paper we explore physical mechanisms which could be responsible for the formation of the cavities and the holes and propose an explanation for why the cavities and the holes appear so regularly in wide ranges of particle sizes. We demonstrate that one of the key phenomena for the hole formation is non-uniformity of the film boiling heat flux over the surface of the particle falling in a water pool. To verify our hypotheses we perform simulations of transient process of molten droplet solidification taking into account of changes in densities of liquid and solid phase of melt material. Sensitivity study shows conditions at which non-uniformity of the heat flux distribution has significant effect on the morphology of the cavity.
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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Bibliographic ID: UF00102023
Volume ID: VID00292
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: 1162-Kudinov-ICMF2010.pdf

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


Cavity Formation in Particles
Obtained from a High Temperature Oxidic Melt Jet Disintegration in Water


Pavel Kudinov*, Valentina Kudinova*

Royal Institute of Technology (KTH), Division of Nuclear Power Safety,
AlbaNova University Center, 10691, Stockholm, Sweden
E-mail: pavel@safety.sci.kth.se


Keywords: Oxidic melt, debris quenching, formation of cavities, debris formation



Abstract

Present work is motivated by numerous observations of cavities which regularly appear inside debris particles formed as a
result of quenching of high temperature molten oxidic jet in a water pool (Kudinov et al. 2010). The cavity is open with a
small hole in the particle surface. The cavities and the holes are observed inside particles with diameters down to few
hundreds of microns. In the paper we explore physical mechanisms which could be responsible for the formation of the
cavities and the holes and propose an explanation for why the cavities and the holes appear so regularly in wide ranges of
particle sizes. We demonstrate that one of the key phenomena for the hole formation is non-uniformity of the film boiling
heat flux over the surface of the particle falling in a water pool. To verify our hypotheses we perform simulations of transient
process of molten droplet solidification taking into account of changes in densities of liquid and solid phase of melt material.
Sensitivity study shows conditions at which non-uniformity of the heat flux distribution has significant effect on the
morphology of the cavity.


Introduction

This paper is concerned with the mechanisms responsible
for morphology of the particle obtained in the process of
high temperature melt pouring and quenching in a water
pool. The work pertains to the DEFOR (Debris Bed
Formation) research program (Kudinov et al. 2010)
motivated by quantification of ex-vessel debris coolability
in Swedish type Boling Water Reactor (BWR) plants. In
case of severe core meltdown accident molten core
materials coriumm) will be ejected from the vessel into a
deep water pool. It is expected that melt will fragment,
solidify, quench, settle and form a coolable debris bed.
Decay heat generated by core debris has to be removed by
natural circulation. Non-coolable debris bed can re-melt
itself and attack containment base-mat threatening the
plant's containment integrity. Coolability of the debris bed
is contingent, among other factors, on the properties of the
bed as a porous media. Particle morphology is an
important microscopic factor which affects macroscopic
porosity, permeability and total volume of the debris bed.
Present work is motivated by the DEFOR-S (Snapshot)
experimental findings (Kudinov et al. 2010) about the
morphology of debris obtained in the process of high
temperature melt jet pouring into a water pool. Heavy
binary oxidic mixtures were used as corium simulant
materials (Kudinov et al. 2010). Observation of
round-shape morphology of the particles (Fig. 1 Fig. 4)
suggests that at low subcooling of water particle
morphology is largely affected by (i) hydrodynamic
breakup, and (ii) solidification of the melt (Kudinov et al.
2010). Intriguing finding was regular formation of


encapsulated cavities open with a small hole on the particle
surface (Fig. 1 Fig. 4). The cavities and the holes are
observed in particles with sizes down to few hundreds of
microns (Fig. 1 Fig. 3). Big particles with sizes more
than 10 mm also contain open cavities (Fig. 4) although
particle shape significantly deviates from spherical.
In the paper we explore hypotheses about what physical
mechanisms can be responsible for such regular formation
of the hole and the cavity in such chaotic process as
disintegration of high temperature melt jet in a water pool.
Formation of a cavity inside a solidifying melt is a well
known and undesired phenomenon in the metal casting
technology. When molten metal enters a mould it starts to
solidify from the mould wall proceeding inwards. As solid
has normally higher density than liquid, contraction of the
solidified material volume leads to formation of a void
called shrinkage cavity.
Previous experimental studies of prototypic corium melt
mixtures interaction with water (e.g. Huhtiniemi &
Magallon 2001) and sodium (e.g. Schins et al. 1984;
Schins & Gunnerson 1986) were mostly concerned with
phenomenon of steam explosion. Morphology of the debris
was not systematically studied. Nevertheless there are
some scarce indications that shrinkage cavity formation
can be expected in case of molten corium-coolant
interaction.
Experimental and analytical studies on solidification of
liquid droplets and formation of the shrinkage cavities
have been performed in the past for various technical and
scientific applications (e.g. Forgac & Angus 1981, Pravdic
& Gani 1996, Klima & Kotalik 1997, Kotalik & Valenik
2001, Kiroly & Szdpvolgyi 2003, Chan & Tan 2006,





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


Kumar & Selvarajan 2007, Grugel & Brush 2007).


i7
a
d ^^--


figure 1: ueons ootamea as a result or molten Dinary
oxidic mixture pouring into a water pool at 250C
subcooling (DEFOR-S8, Kudinov et al. 2010).


Figure 2:
al. 2010).


Figure 3: Encapsulated cavity inside a broken particle
(DEFOR-S8, Kudinov et al. 2010).


Figure 4: Large particles obtained in water at 470C
subcooling (DEFOR-S11, Kudinov et al. 2010).

In the present work we distinguish three characteristic
geometrical configurations (morphologies) of the
shrinkage cavity:
I. Completely encapsulated cavity. Diameter of the
cavity is smaller or equal to the depth of the
cavity 2 < H/Ra,, (Fig. 5).
II. Open cavity with a small hole on the particle
surface. Diameter of the cavity is bigger than
the depth of the cavity, but depth is bigger than
the radius 1 < H/R < 2 (Fig. 1 Fig. 4,
Fig. 6).
III. "Doughnut-shaped" particles. Open shrinkage
cavity in the form of a large but shallow dimple
located on the particle surface. Radius of the
cavity is bigger than the depth of the cavity
H/Rc, <1 (Fig. 7).
Completely encapsulated cavity has been observed
experimentally or considered analytically in most of the
previous works (e.g. Forgac & Angus 1981, Pravdic &
Gani 1996, Klima & Kotalik 1997, Kotalik & Valenik
2001, Kiroly & Szdpvdlgyi 2003, Chan & Tan 2006,
Kumar & Selvarajan 2007, Grugel & Brush 2007). Regular
formation of open cavities reported in Kudinov et al.
(2010). "Doughnut-shaped" particles were observed by
Kumar & Selvarajan (2007).
The goal of the present work is to explore what physical
mechanisms and conditions of melt-water interaction are
responsible for the morphology of the cavity.
Our hypothesis is that key factors in the formation of the
different particle-cavity configurations are: (i) melt
material properties (melting temperature, thermal
conductivity, etc.), (ii) particle size, and (iii)
non-uniformity of the film boiling heat transfer over the
surface of the particle falling in a water pool.
If heat transfer is uniformly distributed over the droplet
surface then solidification front propagates inwards also
uniformly and resulting cavity is spherically symmetrical
(Chan & Tan 2006). Non-uniform distribution of the heat
flux may result in asymmetry of the solidification front.
For example Grugel & Brush (2007) found considerable
discrepancy between predicted and observed shell
thickness in case of solidification of silver droplets falling
in a gaseous atmosphere. Observed thickness was found









approximately twice of that calculated. Two possible
explanations for the departure were proposed: (i) deviation
of liquid drop from spherical shape, and (ii) deviation of
the local Nusselt number around the drop from uniformity,
which can provide non-spherically symmetric
solidification and asymmetric position of the remaining
liquid core (Grugel & Brush 2007). It worth mentioning
that observed by Grugel & Brush (2007) cavities were
completely encapsulated.

/*=0


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

Heat transfer on the surface of a hot melt droplet falling in
a water pool is determined by combination of radiation and
convective heat fluxes. Radiation heat flux is pretty
uniform as it depends mostly on the local surface
temperature of the molten droplet. If particle surface
temperature is high enough and radiation heat transfer is
dominant then cavity is expected to be encapsulated and
close to spherical symmetrical.
It is well known that film boiling heat flux on the surface
of moving spherical particle is non-uniform (e.g. Hsiao et
al. 1975, Dhir & Purohit 1978). There is a number of
models for prediction of the film boiling heat transfer on a
spherical particle (e.g. Hsiao et al. 1975, Dhir & Purohit
1978, Kolev 1995), yet there are considerable uncertainties
in the influence of water subcooling, particle size, velocity,
material and roughness of the particle surface (Dhir &
Purohit 1978, Shoji et al. 1990, Ohtake & Koizumi 2004,
Freud et al. 2009, Kenning 2004). Variation of the average
heat transfer coefficient for a hot sphere moving in
subcooled water was reported in the ranges from 0.2 to 1.1
kW m2 K (Dhir & Purohit 1978). Local thickness of the
vapor film, which determines local heat transfer, can vary
by few orders of magnitude between the bottom and the
top of the sphere e.g. Fig. 8 Kenning (" 114).


Figure 5: Encapsulated cavity.


Figure 6: Open cavity.


Figure 7: "Doughnut-shaped" particle.


a) b) c)
Figure 8: Film boiling on 20 mm sphere moving in water
(Kenning 2004): a) sphere at 5130C, water at 800C,
velocity 1.4 m/s; b) sphere at 4550C, water at 900C,
velocity 0.9 m/s; c) sphere at 5130C, water at 1000C,
velocity 0.9 m/s.

Nomenclature

c heat capacity (J kg' K-')
H depth of the cavity (m)
h convective heat transfer coefficient (W m-2 K-')
k thermal conductivity (W K- m'1)
L latent heat of fusion (kJ kg-')
R outer radius of the droplet (m)
r radial coordinate (m)
T temperature (K)
t time (s)

Greek letters
1p radial position of the crust leading edge (radian)
8 thickness of the crust at the particle bottom (m)
C Emissivity
S fraction of liquid melt
VP angle (radian)









p density (kg m 3)


Subsripts
cav cavity
fb film boiling
in inner
liq liquidus
m melt
max maximum
min minimum
s surface
sol solid
w water
* critical configuration
non-dimensional value


Approach

In the present work we develop a simplified model for
prediction of the cavity morphology. Application of higher
fidelity models which could resolve in direct simulation
3D dynamics of droplet solidification is not feasible at this
stage taking into account number of uncertain parameters
and thus number of cases which have to be simulated for
sensitivity analysis.
Let's consider spherical molten droplet at initial
temperature T,,, which is higher than liquidus temperature
of the melt T7q, instantaneously immersed into a water
pool at temperature T,. The droplet is falling downwards
thus film boiling heat flux reaches its maximum hmx at
the bottom of the sphere and decreases to its minimum
hn at the top. Under such non-uniform cooling the
molten droplet will solidify starting from the bottom
(Fig. 8). Solid crust thickness at the bottom of the droplet
we define as 8 (Fig. 8). Position of the leading edge of
the crust (point where liquid fraction is less than unity) we
will denote by angle / (Fig. 8).


- - - -
~---N




I? R


K ---1


Figure 8: Solidification of the spherical droplet.

Volume of the particle shrinks due to the difference
between densities of solid p,,, and liquid plhq melt
material. We assume that solidified crust doesn't deform,
and thus a shrinkage cavity is expected to form.
Morphology of the shrinkage cavity is a matter of
competition between (i) rate of volume shrinkage due to


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

crust thickening in radial direction ( (t)), and (ii) speed of
the crust growth in the azimuthal direction ( p(t)).
Configuration of the solidifying droplet when liquid
surface becomes flat (Fig. 9) we call "critical"
configuration. We denote azimuthal position of the crust
and its thickness in the critical configuration as /* and
6* respectively. Angle /* is an important parameter
which defines the size of the opening for the shrinkage
cavity. Once the critical configuration with f* > 0 has
been reached, further progress of solidification will make
liquid free surface concave and eventually will lead to
formation of the open cavity such as in Fig. 6 (type II) or
Fig. 7 (type III). Non-zero critical angle (/p* > 0) can be
achieved if crust of considerable thickness is formed at the
bottom prior to the time moment when f becomes 0
(Fig. 9). If crust is growing in azimuthal direction much
faster than in the radial one, then /* -> 0 and completely
enclosed cavity (type I, Fig. 5) is formed.






-R


f --1--1--1--1-M- -- -- --
-- ---- --- -- -

-. ---- - - - -
--: -:-: --:-:-:---- R -





Figure 9: Critical state of the solidifying droplet.

In order to relate p* to the morphology of the cavity and
to non-uniformity of the heat flux we make a number of
simplifications in the further analysis. First, we assume
that inner surface of the crust has spherical shape (Fig. 8).
Second, we neglected by gradual changes in the curvature
of the liquid free surface, assuming that the radius of the
curvature is constant and equal to R until the critical
state of the droplet is achieved (Fig. 9). We assume further
that the shape of the cavity after complete solidification of
the droplet is also spherical. With the listed above
assumptions we can define the thickness of the crust at the
bottom of the droplet at the critical state 8* as a function
of f*
S= l+cosf*-y, (1)
where 8* = S*/R and y is solution of the following
equation


yv + 3 sin2 /y 2 4 cos/ (2+cos/*)
1 Phq
Pso;


0 (2)








Ratio of the cavity depth to cavity radius H/Rav, after
complete solidification of the droplet defines different
types of the particle morphology (I, II, or III, see
introduction). The ratio also can be expressed as a function
of critical angle /*
H I\ 2H (3)
Rcav H + sin2 '
where H is solution of the following equation

H3+6Hsin2/ +2(1 -cosp )2(2+cos*p)= 8 1 2Ph (4)
I Psol)
If non-dimensional crust thickness 8 is known at certain
moment of time t, then correspondent / *( (t at the
critical state can be calculated as a solution of the
transcendental equation (1), (2). Then the ratio of the
cavity depth to its radius can be considered as a function of
non-dimensional crust thickness in the critical state
H/Rcv = f (f (*t*))) and can obtained as a solution of
equations (3), (4).
To calculate the thickness of the crust at the bottom of the
particle as a function of time we neglect by
multidimensional effects and solve one-dimensional
problem of heat transfer and solidification in the radial
direction:
pFc, +L 9 ST(r,t) 18 r2k9ST(rt) (5)
S 9STJ at r2 9r r )
T(r,o)= T, (6)


k T(r,t)
Sr r=R


h(T Tj)+e(T4 T4) (7a)


c9T
T = 0 (7b)
Sr r=0
Equation (5) with initial condition (6) and boundary
conditions (7a), (7b) is solved numerically by finite
volume numerical method proposed by Swaminathan &
Voller (1997). Time derivative is approximated by second
order Crank-Nicholson scheme. One dimensional mesh
with 300 nodes along the radial direction is used in all
calculations.
Taking into account that significant uncertainties exist in
film boiling heat transfer we use a simplified approach to
modeling of the dynamics of solidified droplet in order to
perform numerous simulations necessary for sensitivity
study. We assume that boiling heat flux is non-uniformly
distributed over the particle surface. For the sake of
simplicity we assume in further analysis that heat flux
reaches its maximum hmax at the bottom of the sphere
and decrease to its minimum hmin at the top as a linear
function of the azimuthal angle (calculated from bottom to
top)
h(p)= hmax hmax -h min (8)
7-
Then the surface averaged coefficient of the film boiling
heat transfer on a sphere can be calculated as follows
hB = 0.5. h(9p)sin qpdp = 0.5. (hmax + hm ) (9)

The h, is reported to be order of 1 kW m2 K1 (Dhir &


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

Purohit 1978) for a spherical particle moving at 0.45 m/s in
a water pool at 500C subcooling. Then hmax can be
estimated as -2 kW m2 K- if hmn is considerably
smaller than hma In the present work we use for
sensitivity analysis hmn =100 200 W m2 K-.
It is important to note that not every / ( )) calculated
according to (1), (2) has a physical meaning. The reason is
that, at given assumptions, the crust thickening in the
radial direction 6(t) doesn't depend on hmin while
speed of the crust growth in the azimuthal direction p(t)
depends on h(p,hmn,hmax) according to formula (8).
Thus S(t) and p(t) are independent to a certain degree
in the present model. The critical state f*( (t*)) is
physically meaningful if azimuthal coordinate of the crust
leading edge p(t) (Fig. 8) at the time t* is equal to the
critical angle (Fig. 9) at the same moment of time, i.e.
/t*, hmn, hm)= 8 *, hmax)) (10)
To calculate the azimuthal position of the leading edge of
the crust as a function of time f(t, hmin hma) we solve
problem (5)-(7) for a set of given heat transfer coefficients
h(pj) (8), where pj E [0, T]. For each solution obtained
at given h(pj) we record time t, at which liquid
fraction on the surface becomes less than unity 0 < 1.0.
Then position of the leading edge of the crust is tabulated
as a function of time tj
j(tj,hmin, hmax)= / p(t) (11)
Then, according to formulas (1)-(4), (8)-(10), the particle
morphology can be calculated as function of
non-uniformity of the heat flux distribution
H/R as. = f/( ...... h.... ) (12)
The algorithm for implementation of (12) can is illustrated
in Fig. 10. First of all, in each series of calculations we fix
hmin and keep it constant. Then for a fixed diameter of the
particle the following procedure is executed:
1) For each value of hmax, e [hin, hmaxo] the
thickness of the crust (equations (5)-(7)) and
correspondent critical angle (1), (2) are calculated
as a function of time: = P* (t,hmax)) (blue
curves in Fig. 10).
2) Position of the leading edge of the crust is
calculated as a function of time (11) for each
given hmax, : f(tj,hmin,hma,) (red curves in
Fig. 10).
3) For each combination of hmin,hmax, we find
time t,* = t (hmin, hmaxi) at which condition (10)
is satisfied (black dots which denote intersections
of red and blue curves in Fig. 10).
4) Resultant dependency H/R,, = f(hmin hmax)
can be calculated then according to (3), (4) as
follows: (H/R ), =j(P ( (hmin hmax).
Discussion of particle morphology sensitivity analysis is
presented in the next section.










1- Beta(hmax=2000)
S2- Beta(hmax=1000)
--- 3- Beta(hmax=600)
4- Beta(hmax=400)
S5- Beta(hmax=250)
S6- Beta*(hmax=2000)
S 7- Beta*(hmax=lO00).
8- Beta*(hmax=600)
S9- Beta*(hmax=400)
--10- Beta*(hmax=250)
-0-Beta


0.0 1.0 2.0 3.0
Figure 10: Melt simulant.
melt superheat 200 K,
hml =100 W m2 K-.


4.0 5.0
Melting
droplet


6.0 7.0 8.0 t s
temperature 1200 K,
diameter d=4 mm,


Results and Discussion

Formation of the shrinkage cavity inside high temperature
melt droplet quenched in a water pool is contingent upon a
number of uncertain parameters. In the present work we
address the question about sensitivity of resultant particle
morphology to: (i) melting temperature, (ii) initial melt
superheat, (iii) non-uniformity of film boiling heat flux
distribution over the particle surface, and (iv) size of the
droplet.
Results of two series of calculations are presented in the
paper. One series is performed for the UO2 melt. Its
properties are relatively well known (e.g. SCDAP 1993).
The U02 has very high melting temperature which hinders
formation of the open cavities as it will be shown later.
Second series of calculations is performed for a "virtual"
simulant material which has melting temperature 1200 K.
This melting temperature is close to that of the BizO3-W03
melt used in the DEFOR-S experiments (Kudinov et al.
2010). Unfortunately not all necessary thermo- mechanical
properties of the BizO3-WO3 mixture are known. Therefore
we use virtual simulant material with UO2 temperature
dependent properties calculated at the rescaled temperature
3120
T* = (T 273) + 273, (13)
1200
where T actual local temperature inside the particle;
T* rescaled temperature used only for calculation of
material properties; 3120 K is melting temperature of UO2;
1200 K is assumed virtual simulant melting temperature. In
such a way we obtain a "simulant" which has all
characteristic properties of UO2 but in the different
diapason of temperatures. Both U02 and BizO3-WO3 are
heavy ceramic type materials.
In the Fig. 11 Fig. 14 the cavity morphology maps
(H/R.0. = f(hminh max)) are presented for the simulant
material. The following summarizes observations from the
sensitivity study:
1) Non-uniformity of the heat flux is necessary for
the formation of the open cavity. Reduction of the


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

ratio hmin/hmax which characterizes
non-uniformity of film boiling flux distribution
around the particle surface, generally gives
smaller ratio of the cavity height to radius
H/R , or in other words bigger hole on the
particle surface.
2) On the other hand, if heat flux distribution is
extremely non-uniform ( hmin/hax <0.05 )
adverse tendency is observed. It worth
mentioning that such high non-uniformity of the
heat flux may not be physically reasonable.
3) Open cavity can be readily formed inside a large
particle at relatively uniform heat flux distribution
(bigger ratio of hmin/hmax ). On the other hand,
smaller ratio of H/Rc,, (morphology closer to a
doughnut-shaped particle) can be achieved with
smaller particles if sufficiently non-uniform of the
heat flux is provided.
4) Strongly non-uniform heat flux distribution
( hmin /hmax < 0.2) is required for the formation of
the open cavity in the droplets with sizes smaller
than 0.5 mm. It is interesting to note that
minimum size of particles with open holes
observed in the DEFOR-S experiment is about
0.4 mm.
5) Increased to 200 K initial melt superheat
facilitates formation of the open cavities at more
uniformly distributed heat flux (hmin/hmax 0.5).
6) Higher values of the minimum heat flux (see
results for hmin =200 W m2 K-1) at the top of the
droplet also assists to formation of the open
cavities.
In general, predicted behavior of the simulant material
with melting temperature 1200 K agrees well with
experimental observations about morphology of the debris
obtained in the DEFOR-S tests (Kudinov et al. 2010). Such
qualitative and sometimes quantitative agreements are
encouraging as indirect confirmation that assumptions and
simplifications employed in modeling still allow us to
capture some of the key physical mechanisms responsible
for the cavity formation.
Comparison of the maps obtained for the simulant (Fig. 11
- Fig. 14) and for the UO2 melt (Fig. 15 Fig. 18)
confirms our hypothesis that formation of the particle with
open cavity is mostly contingent upon the non-uniform
distribution of the heat flux over the particle surface. In
case of the U02 droplet radiation heat flux is dominant at
the initial stage of the particle cooling and solidification
because of the high melting temperature (3120 K). As an
outcome of the radiation dominated cooling of the U02
particles in most cases they have encapsulated cavities
(H/Ra, = 2, Fig. 15 Fig. 18). Influence of hmin is less
important than the influence of the melt superheat in case
of UO2. However we can mention some tendencies similar
to that observed with the simulant melt. Namely open
cavities can be readily formed in big (8-16 mm) particles.
Formation of the open cavity in a small U02 droplet
requires extremely non-uniform distribution of convective
heat flux. However (as in the simulant case) smaller ratio
of H/Ra, can be achieved in the small particles.






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


/Rcav
2, 0-------


H/Rcav
2.0

1.8 ------

1.6 -- ---- ------ --- ----------
1.4 -----





00 -m 1 -mm -
Smm
0.8 --------- ------ c 1~~; ~. MM ------

0.6 J- ---------------------- 4 mm
0.4 -----------.---------. ------. 8m m.. ......... ....
16 mm
0.2 -

OxQ -;----------\.----------. --------;----------- I-- ------- -

0.0 0.1 0.2 0.3 0.4 0.5 hmm
max
Figure 11: Cavity morphology map. Melt simulant,
melting temperature 1200 K, melt superheat 100 K,
hmin =100 W m-2 K.


H/R,
2 n Li


1.8







O o -;---------.-- ------- ----- --- - ------- ----- ----;
1 18 :----------- ---v --- --m -- --- ---



1.4 -l -------- -- --- .- -

1.2 --------- --- -- ----------- ----- --
10x ----- -- -- -------- 0.5mm ---------*-

0.8 -- --- m-------- mm .....-.... .
24 mm
0.6 --------- --- ------- mm-: -
0.4 - -_- __--___-;-- _mm- .--------'-. _
1 16 mm
0.2 .............. ............ ...................








hmnx =100 W m2 K.


H/R,


0.8
0.6 '


1.4 ,-
1.2 ------ ----- -
0.0 -:----------------------------.5mm----------*-












0 .8 -". .-.. . . . . . .. . . .




0 .2 - - - - - - -

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 hmm
hmax

Figure 13: Cavity morphology map. Melt simulant,
melting temperature 1200 K, melt superheat 100 K,
hmin =200 W m-2 K-1.
2.0 -- -

1.8- - - - - -

1 6 - -- - - - - - -

1 .4 - - - -I- - - -






0 48 --- -8 - -- - --- -

0.2 ------------------ ; ------

0.0 -:------ ------------------------ -8mm----------


-0.25 mm
-- 0.5 mm --- -
..- -..... .-- --- 1 mm .... -.....-
4d2 mm
84 mm
-: - - ---6- mm - -
-16 mm
- - -- - ---- -- - - - - - - - - . .


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 hmm
hmax
Figure 14: Cavity morphology map. Melt simulant,
melting temperature 1200 K, melt superheat 200 K,
hmin =200 Wm-2 K1.


H/R,
2.0

1.8

1.6

1.4
1.2

1.0
0.8

0.6

0.4

0.2
0.0


av


S--0.25 mm
----- 0.5 mm
.. ....... ....[... .. ..-.. 1m rm ......
-+2 mm
--------- L------- ; mm
4 mm
---------- --------- -------- 8 .mm ---------
-16 mm
" ---", ------. --. . .------ - --- -- ___ ------------ ---

I_ -- - - - --__ _ L _ _ _ _ _-11- - - - -_I1_ _ _ _ _1 _


0.0 0.1 0.2 0.3 0.4 0.5 hmm
hmax
Figure 15: Cavity morphology map. U02, melting
temperature 3120 K, melt superheat 100 K,

hmin =100 W m2 K1.


HIRcav
2.0

1.8 -

1.6 -- ......-------- --------- --------. ----------
1.4 -
1.2 -




1.2. .;- --------------- --------- -------- 1--;------- T -
1.0 --- -0.5 -- ---------
0.8 ..... ... .. ......-- 1 m m ......
-.2 mm'

0.2 ------ j---------- ------- -- m-1 m ----------

0.0 .


0.0 0.1 0.2 0.3 0.4 0.5 hmlm
h
hmax
Figure 16: Cavity morphology map. U02, melting
temperature 3120 K, melt superheat 200 K,
hmin =100 W m-2 K.


."


----


-------- ---









H/Rcav
2.0
1.8
-.-,--- -------
1.6
1.4 ---------- --- ----
1.2.25 mm
0.5 mm
0. --- .- --------- -- ----- 1 mm. ..... .
os------------:-------:--------------
0.0.. ------------ ----------------- -- mm-----------


S 0.1 0.2 0.3 0.4 0.5 0.6 0.7
16 mm
0 .2 -- ------- ------- ------- ------- ------- ------.......
o x .0 ----- ------.. .. ------------ ------ -- -- ------... .. .. .

0.0 0.1 0.2 0.3 0.4 05 0.6 0.7

Figure 17: Cavity morphology map. UO2,
temperature 3120 K, melt superheat
hm =200 W m-2 K1.


H/R,
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0


hmin
hmax
melting
100 K,


----- ------------ ------ --- mm -- -----
-- -------:----:- ---- -----------

-4 mm
-- ------ ------ ----- 8 mm.
-s
-I-- ---- ------ ---- = -- ---
,/16 mm
._..____________.. ---- ------ ------ ....... ___" ______ ..


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7


hmm
hmax
max


Figure 18: Cavity morphology map. UO2, melting
temperature 3120 K, melt superheat 200 K,
hmin =200Wm2 K-'.

Conclusions

The work is motivated by observations of regular cavities
encapsulated inside the debris formed in the process of
quenching of high temperature molten oxidic jet in a water
pool (Kudinov et al. 2009). In order to explain such regular
behavior the hypothesis is proposed that non-uniformity of
the boiling heat flux is a pre-requisite and one of the
governing factors for the morphology of the cavity.
In order to validate the hypothesis we propose
classification of different morphologies of the cavities and
develop simplified computationally efficient model
capable of quantification of the cavity morphology.
Results of simulations confirms that one of the key
phenomena for the formation of the open cavities is
non-uniformity of the film boiling heat flux over the
surface of the particle falling in a water pool.
Study of the cavity morphology sensitivity to different
parameters of the melt droplet-coolant interaction has been
performed. The influences of (i) melting temperature of the


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

melt, (ii) initial melt superheat, (iii) non-uniformity of film
boiling heat flux distribution over the particle surface, and
(iv) size of the droplet are addressed for high (3120 K)
melting temperature UO2 melt and for virtual simulant
material with lower (1200 K) melting temperature. The
results of the sensitivity study suggest that formation of the
open cavities in the U02 melt is hindered by radiation heat
transfer which makes distribution of the total heat flux
over the particle surface more uniform. On the other hand
formation of the open and even doughnut-shaped particles
in case of lower melting temperature simulant material is
very likely, which is confirmed by experimental
observations in the DEFOR-S tests (Kudinov et al. 2009).
Further investigation with multidimensional simulation
methods is necessary in order to validate the assumptions
and simplifications in the proposed approach. Nevertheless
it is very likely that higher fidelity methods will be too
computationally expensive for parametric sensitivity
studies such as presented in the paper and which are
necessary for addressing the intrinsic phenomenological
uncertainties in the melt-coolant interaction processes.

Acknowledgements

The authors are grateful to Professor Truc-Nam Dinh from
Idaho National Laboratory for discussions and valuable
comments.
The work was performed within the MSWI project, funded
by the APRI group (Swedish Nuclear Radiation Safety
Authority (SSM) and power companies); the Swiss Federal
Nuclear Safety Inspectorate ENSI, the EU SARNET
Project and the Nordic Nuclear Safety Research Program
(NKS).


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