Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 8.6.1 - Experimental study of heat transfer between droplets and wall in Leidenfrost regime
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 Material Information
Title: 8.6.1 - Experimental study of heat transfer between droplets and wall in Leidenfrost regime Multiphase Flows with Heat and Mass Transfer
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Lelong, F.
Gradeck, M.
Maillet, D.
Seiler, N.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: droplet impact
Leidenfrost regime
LOCA
 Notes
Abstract: This study focuses on the cooling capacity of a damaged PWR reactor core (Pressure Water Reactor) during a Loss Of Coolant Accident (LOCA). During the reflooding phase of such accident, core cooling is first provided by a vapor flow carrying water droplets, which may impact the fuel cladding. As the temperature of the fuel assemblies is widely above the Leidenfrost temperature, the droplet impact regime is the bouncing regime: locally and beneath the droplet, a thin layer of steam is instantaneously generated when the droplet impacts the hot clad. This vapour layer partly insulates the wall and enables the droplet rebound. A wall cooling flux is also generated during the drop-wall interaction. In this general background, the aim of the present study is to accurately estimate heat transfer between one droplet and a hot wall. In this purpose, an experimental device has been designed in accordance with droplets and wall features (droplet velocity and diameter, wall temperature) representative of LOCA conditions.
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: VID00209
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Resource Identifier: 861-Lelong-ICMF2010.pdf

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Paper No 7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Experimental study of heat transfer between droplets and wall in Leidenfrost regime.


F.Lelong1 2, M. Gradeck2, D. Maillet2 and N.Seiler1


1 IRSN, DPAM/SEMCA, BP 3, 13115 Saint Paul lez Durance, France
2 LEMTA, Av. de la foret de haye, 54500 Vandoeuvre les Nancy, France

franck.lelong@irsn.fr


Keywords: Droplet impact, Leidenfrost regime, LOCA.


Abstract

This study focuses on the cooling capacity of a damaged PWR reactor core (Pressure Water Reactor) during a Loss Of Coolant
Accident (LOCA). During the reflooding phase of such accident, core cooling is first provided by a vapor flow carrying water
droplets, which may impact the fuel cladding. As the temperature of the fuel assemblies is widely above the Leidenfrost
temperature, the droplet impact regime is the bouncing regime: locally and beneath the droplet, a thin layer of steam is
instantaneously generated when the droplet impacts the hot clad. This vapour layer partly insulates the wall and enables the
droplet rebound. A wall cooling flux is also generated during the drop-wall interaction. In this general background, the aim of the
present study is to accurately estimate heat transfer between one droplet and a hot wall. In this purpose, an experimental device
has been designed in accordance with droplets and wall features (droplet velocity and diameter, wall temperature) representative
of LOCA conditions.


Introduction

Liquid cooling is unavoidable in applications where the
required power dissipation is very large. Possible liquid
cooling technologies include single-phase boiling,
immersion flow boiling, jet impingement cooling, spray
cooling. This topic is crucial for the safety of a nuclear PWR
(Pressured Water Reactor) reactor and as such it is studied
by the "Institut de Radioprotection et de Sfirete Nucleaire"
(IRSN) in the frame of its research program in nuclear fuel
safety. Indeed, during a LOCA (Loss of Coolant Accident, a
designed basis accident for a PWR reactor), a pipe rupture
in the primary circuit could lead to an important rise of the
fuel rod temperature owing to water vaporisation in the core.
This may induce a thermo mechanical swelling of the clad
and lead consequently to the rupture of this ballooned fuel
clad (Fig. 1).


Figure 1: View of a real ballooned zone from the
experiment PHEBUS LOCA.

During such an accident, the reflooding phase is initiated by


water injection after activation of the security systems.
During this phase, liquid water is injected into the reactor
core in order to cool down the fuel rods, heated by the
nuclear residual power. This water, rising along the rods, is
instantaneously vaporized by contact with the wall at very
high temperature. The important amount of vaporized water
yields a high vapour flow rate, which pulls up and drags
some water droplets above the moving liquid surface also
called the quench front.

Nomenclature


Droplet (m)
Thickness (m)
Energy (J)
Kinetic Energy (J)
Frequency (Hz)
Specific latent heat (J.kg-1)
Mass (kg)
Heat flux (W)
Radius (m)
Surface (m2)
Resident time (s)
Temperature (C)
Droplet velocity (m.s-1)
Weber number (-)


Greek letters
94 Vapour layer thickness (m)
e Effectiveness (-)
A Thermal conductivity (W.m .K-')
0 Angle ()
p Density (kg.m-3)
a Surface tension (N.m-1)





Paper No


Subscripts
Cony Convective
d Droplet
DC Direct contact (between vapour cushion and wall)
FF Front face
inc Incident
inj Injection
k Harmonic of order k
L Liquid
Leid Leidenfrost
n normal
Ni Nickel
Rad Radiative
RF Rear face
SAT Saturation
W Wall

Superscripts
est Estimated
exp Experimental


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

small part of the droplet evaporates, and that the heat
removed from the wall because of the droplet bounce could
be characterized by a heat exchange effectiveness, noted E.
This quantity is the ratio of the exchanged energy during the
bounce (EDc) and the energy required to completely
evaporate this droplet (md L,):

S=- D (1)
mdLV
Kendall found that this effectiveness lies between 0. 001 and
0.003. Ueda (1979) found higher values for lower slab
temperature with an effectiveness belonging to
[0.005-0.007] interval, under a broad range of conditions.

Guo ('" '12 assumes that the heat removed by a single
droplet impinging the wall is an integral, over the droplet
resident time on the wall, of the conductive heat flux
between the droplet base (assumed at T=TsAr) and the wall
(at T=T,), through the vapour layer (6,):

tR Sd( (
EDC A dt (2)
o v


Sd being the droplet base surface.


LOCA conditions and heat transfer by the droplet
impact

Depending on their velocity and mass, the droplets may
impact the hot clad. Since the fuel clad temperature is well
above Leidenfrost temperature (Leidenfrost (1966)), each
droplet is unable to wet the wall surface. A thin vapour layer
actually appears between droplet and clad. For a low Weber
number (We = PLDdV ), droplets rebound on this vapour

cushion.


Figure 2: 300 um droplet stream impinging onto the slab
(T, 6000C)

Wachters (1966) studied the impact of water droplets
impinging on a horizontal surface heated at 4000C. The
outcomes of the impact were classified into three general
categories depending on the droplet Weber number. For We
< 30, the droplet perfectly rebounds. For intermediate
Weber numbers (30 < We < 80), the droplet undergoes a
similar behaviour except that the droplet splits into a large
droplet and small satellite droplet. Finally for We > 80, the
droplet breaks into several small droplets. In LOCA
conditions, the encountered low Weber number testifies that
the observed impact regime is the perfect bouncing one.
Even if many experimental studies concerning the dynamics
of droplets impacting a heated surface have been
extensively reported in the literature (e.g. Karl (2 '''1.)), very
few focus on heat exchange between droplet and wall in the
bouncing regime. Kendall (1978) however derived a
corresponding heat transfer model. He assumed that only a


The vapour layer thickness (68) is controlled by vapour
production on the face of droplet facing the wall. & is
derived through solution of the Navier-Stokes equations in
the vapour layer. It appears that this parameter is governed
by the droplet spreading process during impact.

According to our knowledge, no experimental data are
currently available to validate this transfer model and to
study the droplets/wall heat exchange in bouncing regime.
Nevertheless, these previous studies underline the main
parameters governing the droplets/wall heat exchange:

The spread diameter D,,
The resident time tR.

In this general context, an experimental setup has been
carefully designed. The aim of this paper is to present
experimental results of both dynamical and thermal aspect
of drops impact on a very hot surface. The importance of
parameters such as spread diameter and resident time are
experimentally emphasized.

Experimental Facility

A scheme of the experimental set-up is shown in figure 3. A
piezoelectric injector (1) can generate a monodisperse
droplets stream (2), with droplets diameter lying in the
[50-400 Fm] range. The stream of monodisperse water
droplets impacts a disk-shape Nickel sample (radius RN, =
12.5 mm, thickness eN, = 500 gm) (3) that has been
previously heated above Leidenfrost temperature by an
induction device (4), located below the insulating support
(7). Droplet velocity, in the [5-20 m.s-1] interval, is
controlled by the injector vibration frequency (f,) and by
the pressure in the water tank (5). These vibrations, that
break the water jet into a droplet stream, are induced by a
piezoceramic powered by a high frequency voltage device





Paper No


(6). The injector direction can be selected thanks to rotation
plates that enable to investigate some different incident
angles. Experiments with incident angles, in the range
[10-90], can be carried out. Impingement of the droplets
stream occurs on the top face (named front face) of the
sample. Their movement is recorded by a fast frame camera
(8) while the temperature field of the other face of the
sample (named rear face) is observed by a focal plane array
infrared camera (9) through a mirror (10). An example of
the infrared picture recorded by the IR camera is shown in
figure 4. Thanks to this experimental set-up, measurement
of both droplets/wall heat exchange and spread diameter can
be achieved.





5, 0

. q 4
,_ ^^ Ii ^









Figure 3: Schematic view of the experimental set-up


.............. Nickel sam ple
border


...........Impact zone






Figure 4: Infrared image (black=cold, white=hot):
Dd=250 pm, ,,nc=15 V=15 m.sl, f, 9800 Hz.

The infrared camera (Cedip JADE III) is build
around a focal plane array of photonic detectors working in
the [3-5 Fm] spectral interval. The IR camera is equipped
with a narrow [3.97-4.01pm] filter. It allows the
measurement of up 320*240 pixels/frame at sampling
frequencies of the order of 60 Hz. The extracted heat flux is
estimated through inversion of the rear face measured
temperature field using a pertinent Inverse Heat Conduction
(IHC) technique, see Lelong (2010): solving an IHC
problem consists in using discrete temperature
measurements inside a solid or at one of its external
boundary, as well as a given corresponding heat transfer
model, in order to recover time and/or space boundary
conditions (e.g. the distribution of the cooling heat flux).


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

The model used here is the analytical solution of a 2D
axisymmetric transient heat equation in a cylindrical
reference frame. The use of a spatial integral transformation,
see Maillet ( 1 11), namely a Hankel transform (noted
here), leads to a linear relationship (in Hankel space)
between the kh harmonic of the rear face temperature

(T,RF ) and the kt harmonic of the heat flux lost by the
front face (qkF ), a component of which corresponds to
the heat flux towards the vapour cushion created by the
droplet bounce, qDc convective and radiative losses being
its complementary components. We consider now on
column-vector (bold characters) of the same quantities, each
component being a value of the harmonics at a given time t,.
The model can be written, for zero initial temperature, as:


tkRF = Xkk,FF (3)
where Xk, a lower triangular (Toplitz) matrix stands for
the sensitivity matrix linking temperature responses (in a
time step At) to droplet/wall heat flux input (in Hankel
domain). Once T,RF has been estimated through
experimental measurements (e.g. from infrared camera
pictures), qk,FF can be calculated thanks to an inversion of
equation (3). Because of the standard noise deviation of the
experimental rear face temperature profile TRF an
ordinary least square operator is used to obtain the best
estimation of the droplet/wall heat flux in Hankel domain:


,exp )(j \ f-1 exp
kFF = (XXk) Xk k,RF


Hankel inversion leads to the heat flux lost on the front face
in real space-time domain.
Sk opt r \
qexp ) 2 Jot (k (,) (5)
R2 0J 2(akR)

The heat flux removed by droplet impacts can be then
corrected thanks to the knowledge of radiative and
convective losses having been already estimated during a
run without droplets stream (e.g. a calibration which must
be made previously).
2 R
QFF (t) = qFF(r,t)rdr (6)
0


QDC QFF QRad -Com


Finally, the energy removed by a single droplet can be
expressed as:
SQDC
EDC f (8)


Impact images on the front face are recorded by
a fast-frame rate camera (Photrom Ultima APX-RS); An
example of recorded pictures is displayed in figure 2, in






Paper No


the case of 300 Fm droplets impinging the disk. The
camera is equipped with a 10 bits CMOS sensor that can
provide up to 3000 frames per second (fps) at full
resolution (1024*1024 pixels) and 250000 fps at a reduced
(minimum) resolution (128*56 pixels). The droplets are
illuminated from behind using a white light source which
enables to get very sharply contrasted images of the droplet
contour by shadow imaging and a macro-lens is used to
well observe the droplet deformation. The magnification
factor is determined prior to measurement by imaging a
reference target whose size is accurately known. Numerical
processing of the resulting images allows measurement of
kinetic parameters of the incoming droplets (diameter,
velocity, impact angle). Aside from the kinetic parameters
of the incoming droplets, the measurement of the
deformation of droplet diameter during the impact (or
resident) time is also achieved. Figure 5 shows an example
of results obtained on this bench.
500 so


0 50 100 150 200 250 300
t(rps)
Figure 5: droplet diameter evolution during the resident
time Dd= 210 pm, Vn= 2 m.s-,, fn 10 kHz, T,=5000C.


Impact regime observation:

Figure 6 shows the evolution of the rear face temperature
field during the impact of a water droplet stream with the
following parameters: Dd=165 pm and V,= 7 m.s-'. At initial
time, heating is shut down and the droplets stream is
generated. At that time, the temperature of the Nickel disk is
almost uniform above 6000C that is above Leidenfrost
temperature. Then, a black spot (cold temperature) appears
at the centre, where the droplet stream impinges. It is
worthwhile to mention that all the droplets of the stream
reach the surface at the same location. This black spot
remains thus axisymmetric while the droplets bounce on the
surface. When the wall temperature becomes lower than the
Leidenfrost (t >19s), a liquid film appears at the centre: it
wets the surface and leads thus to an increase of the
removed heat flux. In figure 6, it can be noticed that the
black spot is not symmetrical any more because the liquid
film grows towards flows on the sample, in the same
direction as the impinging droplet stream.
From these 2D temperature fields T (x, y, t), the temperature
profile T (n t) necessary for the flux estimation, see previous
section, is calculated. This transient radial temperature field
is the input of our inverse problem. Figure 7 displays an
example of the temperature evolution (rear face) at the
droplets impingement location (r = 0). Figure 8 presents the
energy lost by the front face of the wall and caused by the


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

impact of the droplet stream in the same impact
configuration as Fig.6. As already mentioned, when the slab
temperature is over Leidenfrost temperature (T, > 350 C
for t < 19s in Fig.7), a thin vapour layer exists beneath the
droplets. This vapour layer insulates the droplets and limits
considerably the heat exchanged between the droplets and
the slab (EDc = 0.4 mJ, for wall temperatures larger than
4600C). A decrease (about 0.2 mJ) of the removed energy is
observed later on till the wall temperature reaches 3500C
(for wall temperatures Tw= 550 to 3411:C). Our present
opinion is that this phenomenon is linked to the increase of
the convective component of the wall heat flux created by
the vapour flow generated by vaporization of the droplet at
the level of the vapour "cushion": when a droplet impinges
on the hot slab, the heat removed from the hot wall could be
divided into two components: the heat enabling vaporization
of a part of the droplet (considered by Kendall (1978) and
Guo (' "2)) and the heat removed by convection in the
generated vapour flow. This second part, increases together
with the wall temperature decrease, in its cooling process.

In the remaining part of this process, the slab is cooled
below Leidenfrost temperature (T, < 3500C for t > 19s) and
the droplets, entering in contact with the slab, might be
completely vaporized. Nevertheless, this complete
vaporisation is only achieved if the droplets injection
frequency is relatively low, i.e. if the time between two
successive droplets is larger than the evaporation time. In
our experimental measurements for wall temperature below
Leidenfrost temperature, the high injection frequency leads
to an accumulation of droplets onto the slab creating a liquid
film. This boiling liquid film increases heat transfer (Ec =
1.6 mJ). These interpretations are consistent with the
observations of the infrared frames for the same impact
(Fig.6).

Furthermore, the Leidenfrost threshold as well as the
Leidenfrost temperature is clearly observed in such a test
(see Fig.7). This temperature is defined as the minimum
wall temperature for which a vapour cushion exists beneath
the droplet. From our results, Leidenfrost temperature seems
to depend on dynamic characteristics of the incident droplet.
Figure 9 shows the influence of both the normal velocity
and the droplet diameter on this temperature. The increase
of the diameter or of the normal velocity leads to a rise of
the needed temperature for observing the Leidenfrost
phenomenon. This experimental finding could be explained
by the increase of the normal kinetic energy of the incident
droplet with its diameter or with its normal velocity. This
increase could be responsible for a collapse of the vapour
cushion created beneath the drop regarding a certain wall
temperature.
The insulation of the droplet is thus lower and the droplets
succeed to reach the plate for a higher wall temperature than
if it would have for a smaller diameter or a lower normal
velocity.

Within the present framework of evaluation of the cooling
capacity of a damaged PWR, we are more especially
interested in the heat removal in the Leidenfrost regime. We
will now focus on the right hand side part of the heat
quantity plotted in figure 8 delivering data in our domain of
interest.


t;+ + +-H-B


+*
-HH+


,I +






Paper No


t = Os









t= 18s


t= lOs









t= 19s


t = 15s









t = 20s


Figure 6: Infrared image (black=cold, white=hot),
Dd=165 pm, ,nc=30 , V=14 m.s, f, = 10000 Hz


650

600 ........ ....

550


a ,


350.................







Figure 7: Evolution of the rear face temperature of droplet
in time during the resident time at the droplets impingement
point.
Dd= 165 um, 8,nc=30, V=14 m.s', f, = 10 kHz.


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

380,


U L W 11 r


300

280

260

240


4
Normal velocity (m.s')


Figure 9: Effect of the droplet normal velocity on the
Leidenfrost temperature.



Droplet dynamic parameter effects on the energy
exchange in Leidenfrost regime



Figure 10 displays the effect of the droplet diameter on the
quantity of heat exchanged for a droplet stream (normal
velocity before impact V, 2.5 m.s ) impacting a Nickel
slab whose temperature beforehand heated at a level Tw =
550 oC. Moreover, figure 11 shows an example of the
influence of the normal velocity on this exchanged heat. It is
clear that the increase of the droplet dynamic parameters
(velocity and diameter) leads to a rise in the heat exchange.


* V = 2.5 m.s
0 v~ =r~sm.s"1


Tieid


300 350 400 450
Temperature ("C)


ol
140


160 180 200 220
Diameter (I m)


240 260


Figure 10: Effect of droplet diameter on the droplet/wall
exchange for T, = 550 oC.


S0.5

0.45-


0.35-

500 550 600 0.3-
1U


Figure 8: Energy exchanged by a single droplet with the
Nickel slab
Dd= 165 pm, 8,n=300, V=14 m.s', f, = 10 kHz.


3 4
Droplet normal velocity (m.s')


Figure 11: Effect of the droplet velocity on the droplet/wall
exchange: (Dd= 165 pm and Tw = 550 oC).


1.8
1.6
1.4
1.2-


W 0.8
0.6-
0a-
01-
I


280 300






Paper No


As mentioned in the introduction, the droplet spread
diameter and the resident time are the main parameters that
seem to be positively correlated with the level of heat
transferred between droplet and slab. They depend on the
experimental conditions in a way we will present next.

The droplet spread diameter:

The rise of the spread diameter is correlated with the
increase of the exchange interface between liquid and
vapour over the slab and with the decrease of the vapour
layer thickness and therefore with the heat exchange
increase.
During the droplet deformation, part of kinetic energy is
converted into potential energy. The deformation induces an
internal flow in the droplet which dissipates energy by
viscous shear. Because of the existence of a surface tension,
the droplet recovers its spherical shape if the viscous
dissipation is not too high. The Weber number allows an
appraisal of the outcome of the competition between droplet
inertia and surface tension. The inverse spread factor,
defined as the ratio between the initial droplet diameter and
the maximum spread diameter, is directly governed by this
competition and consequently by the Weber number.

The inverse spread factor is plotted versus the Weber
number in figure 12 for several liquids (Water, Isopropyl,
Ethanol, Decane). As displayed, the increase of the Weber
number (resulting from a high incident kinetic energy or of a
low surface tension) induces the rise of the maximum spread
diameter.

Biance (2006) established an experimental correlation to
evaluate the maximum spread diameter:


Dd =We-O 25
D
171X


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


The resident time:

The increase of the resident time and of the level of the
heat quantity exchanged between wall and droplets are
linked. Indeed the higher resident time, the longer droplet
exchanges with the wall.
Most of researches predict that the resident time of a drop
on a hot surface and the first order vibration period of a
freely oscillating droplet are of the same order of
magnitude. As derived by Rayleigh (1897), this period, and
consequently the resident time, is expressed as:


PLD 8


C=


Equation (10) shows that the resident time increase rapidly
with the drop radius whereas it seems to stay quite
independent to normal velocity. These observations are
experimentally confirmed by Biance (2006). However,
they experimentally found a value of about 2.65 for C in
case of water droplets impact.
Figure 13 displays the experimental resident time of a
water droplet versus the droplet diameter for several
incident velocities. This figure shows a good agreement
between the experimental results and Biance's correlation
(equation (10) with the value of 2.65 for C).


(9) {411


This correlation is also compared with our experimental
data in figure 12. We notice quite a good agreement between
Biance's correlation and the experimental data and this,
whatever the fluid.

1.2-
I Blance (2006)
+ Expermental


- + i
:+ ++ + i i i i


0 10 20 30 40 50
Weber


70 80 90


Figure 12: Inverse spread factor versus the Weber number
for several liquids.


Diameter (pm)


Figure 13: Resident time versus water droplet diameter
for different incident droplet velocity.


Effectiveness of the droplets/wall exchange

The experimental effectiveness, calculated from equation
(1), is plotted in figure 13 versus the slab temperature, for
several normal velocities lying in the [5-7 m.s-'] range and
for a droplet diameter equal to 160pm. For instance, the
experimental effectiveness reaches 0.03 for T, 490 C and
Vn 5 m.s-'. The effectiveness is thus an order of magnitude
higher than the values reported for in the literature (between
0.001 and 0.007, see Kendal (1978) and Ueda (1979)). In
fact, our experimental effectiveness of the exchange during
the droplet impact, as defined by Kendall (1978), is a
decade higher than the values given by these authors. Indeed,
their effectiveness is not evaluated from the total energy






Paper No


transmitted from the wall through the droplet impact but it
takes only into account of heat flux directly transmitted to
the droplet for vaporization. We could assume, as Guo
(2' '12), that this part of the heat is transferred by conduction
through the vapour cushion located between the droplet and
the hot wall in the Leidenfrost regime. The remaining part
of the transferred heat is evacuated by convection in the
vapour cushion where an internal flow develops. Indeed, the
vapour generated at the liquid/vapour interface is
accelerated and heated in the cushion inducing this flow.


0.07 -

0.06


V =6.7 m.s'
V=6 m.s-1
V,=5m.s-1


0.04k


0.02-


380 400 420 440 460 480
Temperature (C)


500 520 540


Figure 13: effectiveness plotted versus slab temperature for
several normal velocities (Dd- 165 pm and Tw = 550 C):
equation 1.

Conclusion

This study is carried out in the framework of the evaluation
of the coolability of a damaged PWR reactor core during a
Loss Of Coolant Accident. In the reflooding phase of such
an accident, core cooling is first provided by a vapour flow
carrying water droplets which impact the fuel cladding. The
slab temperature is widely above the Leidenfrost
temperature. So, the observed impact regime is the perfect
boucing one. Although many experimental studies of the
dynamics of droplets impacting onto a heated surface exist,
very few studies focus on the heat exchange between the
droplet and the wall in this bouncing regime. That is why, a
new experimental set-up, designed to accurately measure
the cooling flux, was performed.

The initial results highlight the effect of the main kinetic
parameters which are the droplet normal velocity and
droplet diameter. The increase of these parameters induces a
rise of the droplet/wall heat exchange and, consequently, to
the rise of the spread diameter and of the resident time. The
existing correlation of Biance (2006) for the maximum
spread diameter and of Rayleigh (1897) and Biance (2006)
for the resident time have been compared to our
experimental data. The agreements are good whatever the
fluid is.

This paper shows that a non negligible amount of heat is
transported by the internal flow in the vapour cushion, the
ratio of the heat convected to the heat conducted being of


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

about 10.

Numerous experimental runs are currently performed in
order to create an important data base on Nickel and
Zircaloy slabs. The study of the effects of the slab properties,
and of gravity, is underway. This data base will enable to
validate the model of heat exchange between droplet and
hot wall in bouncing regime which is currently under
development.

References

Biance A. L., Chevy F., Clanet C., Lagudeau G., Quere
D., On the elasticity of an inertial liquid shock, J. Fluid.
Mech., 552, 47-66 (2006).

Harvie D.J.E., Fletcher D.F, A hydrodynamic and
thermodynamic simulation of droplet impacts on hot
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