1-s2.0-s0306454913004052-main

7/30/2019 1-s2.0-S0306454913004052-main

1/11

Evaluation of debris bed self-leveling behavior: A simple empirical

approach and its validations

Songbai Cheng a,, Hirotaka Tagami a, Hidemasa Yamano a, Tohru Suzuki a, Yoshiharu Tobita a, Bin Zhang b,Tatsuya Matsumoto b, Koji Morita b

aAdvanced Nuclear System R&D Directorate, Japan Atomic Energy Agency (JAEA), 4002 Narita, O-arai, Ibaraki 311-1393, Japanb Department of Applied Quantum Physics and Nuclear Engineering, Kyushu University, 744 Moto-oka, Nishi-ku, Fukuoka 819-0395, Japan

a r t i c l e i n f o

Article history:

Received 12 February 2013

Received in revised form 15 May 2013

Accepted 28 July 2013

Keywords:

Sodium-cooled fast reactor

Core disruptive accident

Self-leveling

Debris bed

Empirical approach

Model validation

a b s t r a c t

During a hypothetical core-disruptive accident (CDA) in a sodium-cooled fast reactor (SFR), degraded core

materials can form roughly conically-shaped debris beds over the core-support structure and/or in the

lower inlet plenum of the reactor vessel from rapid quenching and fragmentation of core material pool.

However, coolant boiling may lead ultimately to leveling of the debris bed that is crucial to the relocation

of molten core and heat-removal capability of debris bed. To clarify the mechanisms underlying this self-

leveling behavior, several series of experiments were elaborately designed and conducted in recent years

under the collaboration between Japan Atomic Energy Agency (JAEA) and Kyushu University (Japan).

Based on the experimental observations and quantitative data obtained (mainly the time variation of

bed inclination angle), a simple empirical approach to predict the self-leveling development depending

on particlesize, particle density andgas velocity was proposed. To confirm the rationality andwide appli-

cability of this approach, over the past few years extensive efforts have been made by performing mod-

eling investigations against a large number of experimental data covering various conditions, including

difference in bubbling mode, bed geometry and range of experimental parameters. The present contribu-

tion synthesizes these efforts and gives detailed comparative analyses of the performed validations, thus,

providing some insight for a better understanding of CDAs and improved verifications of computer mod-els developed in advanced fast reactor safety analysis codes.

2013 Elsevier Ltd. All rights reserved.

1. Introduction

The disaster in March 2011 at the Fukushima Dai-Ichi nuclear

power plant in Japan makes more and more people to realize that

severe accidents might occur, even if their probability is extremely

low. During a postulated core disruptive accident (CDA) in a so-

dium-cooled fast reactor (SFR), possibly as a consequence of rapid

quenching and fragmentation of core materials, a multiphase flow

system can form that could be composed of a mixture of liquid so-

dium, molten fuel, molten structure, refrozen fuel, solid fuel pel-lets, fission gas, fuel vapor, and other materials (Tentner et al.,

2010). Deposition of this system will lead to the formation of deb-

ris beds over the core-support structure and/or in the lower inlet

plenum of the reactor vessel (as depicted in Fig. 1) (Zhang et al.,

2011). Typically, the debris bed, with particle size widely distrib-

uted (possibly up to a scale of millimeters) (Magallon et al.,

1992), will form roughly conically-shaped mounds. However, cool-

ant boiling caused by decay heat, might lead ultimately to leveling

of the debris bed (Zhang et al., 2008, 2009). This mechanism, as

illustrated in Fig. 2, defines the term debris-bed self-leveling.

To prevent the penetration of the reactor vessel by molten fuel

and distribute molten fuel or core debris formed in a CDA into non-

critical configurations, in-vessel retention devices are used in some

SFR designs (Waltar and Reynolds, 1981). Multi-layer debris tray

installed in the bottom region of the vessel is one of such devices

(Nakai et al., 2009, 2010). During a hypothetical CDA, discharged

molten fuel after being quenched and fragmented into fuel debris

in the lower plenum region, is expected to accumulate on the dif-ferent layers of the debris tray (Nakai et al., 2009, 2010). To stably

remove the decay heat generated from debris bed on the tray, the

size, retention capability, and allocation of the tray should be care-

fully designed. Self-leveling is an important inducing factor to trig-

ger molten fuel to transfer among the trays. Thus, the study on this

behavior is of essential importance to the design of the tray. In

addition, self-leveling behavior will greatly affect the heat removal

capability of debris beds (Zhang et al., 2010, 2011).

Unfortunately, over the past decades, although some informa-

tion on debris bed hydrodynamics andheat transfer has been avail-

able (Cheng et al., 2010a), very little work related to self-leveling

has been performed. Most of these studies generally assume that

0306-4549/$ - see front matter 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.anucene.2013.07.050

Corresponding author. Tel.: +81 29 267 4141; fax: +81 29 266 2317.

E-mail address: [email protected] (S. Cheng).

Annals of Nuclear Energy 63 (2014) 188198

Contents lists available at ScienceDirect

Annals of Nuclear Energy

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a n u c e n e
http://dx.doi.org/10.1016/j.anucene.2013.07.050mailto:[email protected]://dx.doi.org/10.1016/j.anucene.2013.07.050http://www.sciencedirect.com/science/journal/03064549http://www.elsevier.com/locate/anucenehttp://www.elsevier.com/locate/anucenehttp://www.sciencedirect.com/science/journal/03064549http://dx.doi.org/10.1016/j.anucene.2013.07.050mailto:[email protected]://dx.doi.org/10.1016/j.anucene.2013.07.050http://crossmark.dyndns.org/dialog/?doi=10.1016/j.anucene.2013.07.050&domain=pdf

7/30/2019 1-s2.0-S0306454913004052-main

2/11

the upper surface of the debris bed is level. Noting the importance

of self-leveling in the heat removal capability, Hesson et al. (1971)

and Gabor (1974) began some pioneering experimental studies onthis subject. In separate experiments, they validated the existence

of self-leveling behavior respectively by introducing a bubbling air-

flow through a particle bed and by volume-heating of a particle

bed composed of UO2-salt water. Following these studies, using

copperwater beds Alvarez and Amblard (1982) further concluded

that boiling even with small power promoted the leveling.

To clarify the mechanisms underlying this behavior, in recent

years several series of experiments were elaborately designed

and conducted under the collaboration between Japan Atomic Energy

Agency (JAEA) and Kyushu University (Japan) (Cheng et al., 2013a;

Cheng et al., 2013b). In those experiments, to simulate the coolant

boiling during CDAs, various bubbling methods including the

depressurization boiling, bottom-heated boiling (Zhang et al.,

2008, 2009, 2010, 2011) as well as gas-injection (Cheng et al.,2010a,b, 2011a,b, 2012a,b, 2013a,b,c), were employed. Furthermore,

based on the experimental data and evidence observed, modeling

studies and numerical simulations have been launched (Cheng

et al., 2011b). For instance, SIMMER-III, an advanced fast reactor

safety analysis code (Tobita et al., 2006), is currently being devel-oped by incorporating several computer models treating the parti-

cleparticle and particle-bubble interactions (Guo et al., 2012a,b;

Zhang et al., 2012). However, due to the extremely complex and

uncertain nature of the three-phase flow involved in the leveling

phenomenon (Cheng et al., 2011b; Zhang et al., 2010), empirical

approach is still regarded as an attractive and indispensable option

at present stage because of its distinct advantage in calculation

efficiency. On one hand, with an effective empirical model, exper-

imental database can be expanded (interpolated or extrapolated)

with much lower cost. On the other hand, the derivation and anal-

yses of empirical approach do provide useful knowledge for com-

puter model improvement and verifications. In our previous

publications (Cheng et al., 2010b, 2011b), by performing regression

analysis, a set of empirical correlations was successfully advancedto estimate the transient variation in the bed inclination angle for a

preliminary quasi-2D test using gas-injection. Those correlations

yielded good statistical performance over the validity range, which

to some extent demonstrated the possibility of empirical predic-

tors to the self-leveling behavior. Motivated by the potential of

extending this approach to actual reactor accident conditions, re-

cently several validation projects have been initiated under the

lead of JAEA with an aim to validate its wide applicability (Cheng

et al., 2012a, 2013a,c). The validations involve a great amount of

experimental data from various conditions, including difference

in bubbling mode, bed geometry and range of experimental param-

eters. The current paper is dedicated to the synthesis and compar-

ative analyses of these efforts. The performed leveling-related

experiments, which support empirical approach development,are outlined in Section 2, while the details of developed empirical

model as well as its validations are described and discussed respec-

tively in Sections 3 and 4.

Nomenclature

A cross-section area (mm2)Cp specific heat capacity of the vapor (J/kg K)dp particle diameter (mm)H bed height (mm)h1g vaporization heat of the coolant (J/kg)

Qg gas flow rate (L/min)q power density of debris bed (W/cm3)R(t) ratio of inclination angle at time t to the initial angle

(0 s) ()t time (s)t0 a specific time (s)DTsub sub-cooled degree (K)Ug gas velocity based on cross-section of particle bed (cm/

s)

Ugc critical gas velocity (m/s)Vpb volume of particle bed (mm

3)VT terminal velocity of a single particle in stagnant liquid

(cm/s)

Greek letterses solid holdup (%)qp particle density (kg/m

3)qg vapor density (kg/m

3)q1 liquid density (kg/m

3)l liquid viscosity (Pa s)r liquid surface tension (N/m)

Fig. 2. Self-leveling behavior.

Fig. 1. Debris bed profile.

S. Cheng et al. / Annals of Nuclear Energy 63 (2014) 188198 189
http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-

7/30/2019 1-s2.0-S0306454913004052-main

3/11

2. Experimentation

Fig. 3 depicts the constitution of the performed leveling-related

experiments. Overall, it seems that those experiments can be gen-

erally divided into two categories, namely the microscopic flow re-

gime investigations and macroscopic leveling experiments. Due to

the nontransparency of particle beds, the macroscopic leveling

experiments are mainly conducted with the aimto clarify the over-all leveling characteristics. On the other hand, to obtain convincible

visual evidence (esp. bubbleparticle interaction) supporting the

overall understandings, the microscopic flow regime investigations

are specifically performed to ascertain the flow characteristics

within particle beds.

The flow regime investigations consist of several series of

well-organized tests performed at various bubbling conditions. To

facilitate the qualitative identification as well as acquirement of

quantitative data (e.g.characteristic bubbling frequency and bubble

size), the investigations were primarily conducted by injectinga sin-

gle train of nitrogen bubbles through a narrower two-dimensional

(2D) rectangular viewing tank (200 mm 10mm 300 mm)

(Cheng et al., 2010a, 2011a), though the obtained findings were

quantitatively verified as well at normal three dimensional (3D)

system and more generalbubbling conditions (suchas multi-bubble

injection and bottom-heated boiling) (Cheng et al., 2013b). The

schematic view of the 2D setup using the single-bubble injection

is shown in Fig. 4(a), while its 3D counterpart can be visualized by

substituting the apparatus in the dashed box with the apparatus

shown in Fig. 4(b). Evidently, the major difference between the 2D

and 3D systems is that to reduce the wall effect for the 3D system

a comparatively larger cylindrical container (60 mm diameter and

500 mmheight)was employed. In addition, to avoidthe convex dis-

tortions caused by the cylinder, a transparent rectangular container

was installed outside the cylinder and filled with the same liquid as

that inside the cylindrical vessel.

As for the macroscopic leveling series, although in real reactor

situations, coolant is heated to boiling point by the decay heat of

fuel debris (thereby initializing self-leveling of the debris bed),

the depressurization instead of conventional boiling methods

was initially employed to simulate an axially increasing void distri-

bution in the particle bed (Zhang et al., 2011). On the other hand, to

provide more convincing argument validating the use of depres-

surization method, a detailed series of conventional bottom-heated

scenarios was also conducted. The bottom-heated boiling was cho-

sen among the various conventional methods after comprehensive

comparison in cost, level of difficulty, and reliability of experimen-

tal results (Zhang et al., 2011).

Fig. 3. Constitution of the performed leveling-related experiments.

Nitrogen

Cylinder

N2

GasExhaust

Valve 3

Valve 2

PressureTransducer

Flow meter 1

Valve 1

F

Liquid Collector

VideoMonitor

Video

Camera

High-speed

Camera

Bubble

Viewing Tank

Water Level

Back- Lighting

Two Dimensional

Particle Bed

Viewing Tank

Rectangular Container

Bubble

Water Level

Three Dimensional

Particle Bed

To Valve 1

To Flow meter 1

(a) 2D setup (b) 3D setup

Fig. 4. Schematic view of setup for single-bubble injection flow regime experiments.

190 S. Cheng et al./ Annals of Nuclear Energy 63 (2014) 188198

7/30/2019 1-s2.0-S0306454913004052-main

4/11

The experimental setup used in the depressurization method is

shown schematically in Fig. 5(a). The particle bed is contained in adouble-walled glass cylindrical tank (on the left side, 605 mm in

height and 300 mm in diameter) with a vacuum gap to minimize

radial heat losses (a connecting vacuumpump maintains a vacuumat all times). An inverted funnel, with its apex connected to a 200 L

VaccumPump

T.C.

T.C.

Steam Flow

VaccumPump

Vacuum Vessel

(Volume:200L)

(a) Depressurization boiling method

(b) Detailed configuration of bottom heater (bottom-heated method)

Fig. 5. Schematic diagram of setup for leveling experiments using boiling method.

NitrogenCylinder

N2

Gas

Exhaust

Valve 1

Valve 2

Pressure

Transducer

Valve 4

Valve 9

Valve 10

Valve 11

Valve 8

Valve 5

Valve 6Valve 7

Valve 12

Valve 3

F

F

Flow meter 1

Flow meter 2

Rear Light

Viewing tank

Debris bed

Airstone

Gas flow rate

measurement system

Liquid Collector

Rear Light

Video Camera

Fig. 6. Schematic diagram of the quasi-2D system for leveling experiments using gas-injection.

http://-/?-http://-/?-

7/30/2019 1-s2.0-S0306454913004052-main

5/11

vacuum vessel via a piping tube, covers the upper portion of the

water tank. Before starting an experiment, a vacuum pump evacu-

ates the vessel. Most components used in the bottom-heated

method are the same as those in a depressurization setup, aside

from the bottom portion of the test tank, in which a heater is

equipped (as illustrated in Fig. 5(b)). This heater is actually a thin

hot plate sandwiched between an alumina cylinder and a stainless

steel cylinder.

Compared to boiling methods, a gas phase can be adjusted and

controlled more easily using the gas-injection method. Therefore,

extensive experimental runs become more viable completion

which supports empirical model development and future code ver-

ifications. For this reason, two series of leveling experiments,

namely the quasi-2D small-scale one and a large-scale one, wereperformed. Fig. 6 depicts the schematic setup of the quasi-2D sys-

tem. With effective dimensions of 500 mm height, 250 mm width

and 55 mmgap thickness, a rectangular viewing tank made of glass

was utilized to permit visual observation and video-recording.

Over the bottom of the viewing tank, an air-stone (30 mm in diam-

eter, 223 mm in height) served as gas distributor ensuring a rela-

tively uniform percolation of nitrogen gas. It is worth pointing

out that the quasi-2D experiment plays a bridging role for all the

experiments listed in Fig. 3 (Cheng et al., 2013b).

To reduce the wall effect as well as achieve experimentation at

much larger range of gas velocities needed for the extrapolations of

experimental findings, the large-scale experiments were specifi-

cally performed (shown in Fig. 7). Similar to the above quasi-2D

leveling system, to ensure a comparatively uniform percolation

of nitrogen gas, over the bottom of the viewing tank porous media

(Sumitomo Electric make) were employed. It is validated that with

this system, equipped with five nitrogen gas vessels, a driving flowrate up to 10,000 L/min (equivalent to boiling intensities of several

tens of W/cm3) is theoretically feasible by regulating the gas deliv-

ery pressure (Cheng et al., 2012b).

Fig. 7. Schematic view of the large-scale setup for leveling experiments using gas-injection.

Table 1

Conditions of experiments.

Experiment Self-leveling Flow regime

Boiling Gas injection Single-bubble injection Multi-bubble

injection

Bottom-heated

boilingDepressurization Bottom-

heated

Quasi-2D Large-scale 2D 3D

Viewing tank Shape Cylinder Rectangle Cylinder Rectangle Cylinder Rectangle Rectangle

Dimension

(mm)

/300 605 250 55 500 /310 1000 200 10 300 /60 500 250 25 504 300 25 504

Par ticle material Alumina, zirconia,

stainless steel, lead

Glass, alumina,

zirconia

Alumina,

zirconia,

stainless steel

Glass, acrylic,

alumina,

zirconia

Glass Glass

Particle size

(mm)

0.56.0 2.06.0 2.06.0 0.46.0 0.46.0 0.46.0

Particle shape Spherical, non-

spherical

Spherical Spherical Spherical Spherical Spherical

Water depth

(mm)

250, 400 400 180 250 400 400

Boiling intensity

(W/cm3)

$0.43 Nab

Gas flow rate

(L/min)

$8.0 $300.0 1.7a, 2.7a 1.0, 4.0 $0.43

Bed height (mm) 100160 180 90 30200 250 200

Initial inclination

angle (Degree)

1525 1827 1720 0 0 0

a

mL/min.b Not available.


7/30/2019 1-s2.0-S0306454913004052-main

6/11

To obtain the general characteristics of leveling behavior, vari-

ous experimental parameters were used. Table 1 summarizes the

specific conditions of each experiment.

3. Development of empirical approach

As stated above, the spatial configuration of debris beds is a crit-

ical parameter for its coolability, e.g. tall mound shape debris bedishardly coolable. To quantitatively describe the leveling, inclination

angle of bed mounds was measured. Clearly, as depicted in Fig. 8,

the tangent of the inclination angle equals the ratio of the maxi-

mum height of the apex to the radius of the viewing tank. Thus,

the inclination angle defines the overall average shape of the par-

ticle bed rather than its local periphery shape. To evaluate the tran-

sient behavior associated with the leveling, we further introduce

R(t):

Rt Inclination angle at time t

Initial inclination angle 0s1

In the self-leveling experiments, we observed that the particles at

the surface of the debris bed are pushed up by the flow inside the

bed (caused by boiling or gas-percolation) and detach from the deb-ris bed to cascade down the slope to rest at the base of the particle-

bed mound. Cascading is influenced by convective flows in the

water pool. Fig. 9 schematically shows this movement which under-

pins particle bed leveling. Although in the past, numerous experi-

mental and model-based studies have been conducted in an

attempt to clarify the fluidization behavior in multi-phase systems,

their findings might not be directly applicable as for the self-level-

ing phenomenon the particle bed is far from fluidized.

However, we notice that when a particle is in a force balance

state (gravity force, drag force and buoyancy force), particles in

the medium have reached terminal velocity. Though self-leveling

behavior is quite different from the force balance state, the termi-

nal velocity of the particle or its transformative form might be

effective in characterizing the leveling (Zhang et al., 2011; Cheng

et al., 2011b). This thought is confirmable by several prior studies

regarding the analysis of packed bed movement. For instance,

Koide et al. (1983, 1984) and Abraham et al. (1992) experimentally

studied the critical gas velocity (Ugc) required for the suspension of

solid particles (or particle aggregates) in three-phase columns. In

their studies, column dimensions and shape, sparger design and

properties of the liquid and solid particles were observed to have

a strong influence on Ugc. Using the transformative form of particle

terminal velocity, they successfully proposed some rational empir-

ical correlations to estimate Ugc. Since there are obvious similari-

ties between those investigations and the self-leveling behavior

Fig. 8. Diagram of measured inclination angle.

Fig. 9. Schematic view of self-leveling mechanism.

(a) quasi-2D gas-injection

(b) Large-scale gas-injection

(c) Depressurization boiling

Fig. 10. Parity plot comparing predicted R(t)with experimental data.

http://-/?-http://-/?-http://-/?-http://-/?-http://-/?-

7/30/2019 1-s2.0-S0306454913004052-main

7/11

currently studied, in an analogous manner, for a specific time t0 we

assume that the following dimensionless form may be advanced

(Cheng et al., 2011b, 2013c)

Rt0 fUgVT

;

lVTr

;

qp qlql

2

Eq. (2) can be rewritten in functional form as

Rt0 K1UgVT

A1 lVTr

A2 qp qlql

A33

or in logarithmic form

log10Rt0 log10K1 A1log10UgVT

A2log10

lVTr

A3log10qp qlql

4

where K1, A1,A2 and A3 are empirical constants.

To predict the transient behavior, characteristics of the time

variation of inclination angle was analyzed (Cheng et al., 2011b,

2013c). It is noticeable that R(t)should be a decreasing function

with the following boundary conditions:

at t 0; Rt 1 5

at t t0; Rt Rt0 6

as predicted by Eq. (3)

Also, according to the definition, its domain should be

For any t RtP 0 7

To satisfy Eqs. (5)(7), the following dependency is assumed

after extensive testing and error analyses (Cheng et al., 2011b,

2013c)

1 Rt

1 Rt0

t

t0

n

8

(a) Quasi-2D gas-injection (Glass) (b) Large-scale gas-injection (Alumina)

(c) Depressurization boiling (Alumina)

Fig. 11. Effect of particle size on R(t).


7/30/2019 1-s2.0-S0306454913004052-main

8/11

where n is a characteristic exponent defined to express the average

leveling rate. Overall, the faster the leveling process is, the smaller

the n value is. Therefore, n should be able to be determined using

a similar relation of Eq. (4) (Cheng et al., 2011b, 2013c):

log10n log10K2 B1log10UgVT

B2log10

lVTr

B3log10q

p

ql

ql

9

4. Validations and discussion

Based on the experimental parameters and measured inclina-

tion angles from different experiments, the dimensionless terms

in Eqs. (4) and (9) (log 10R(t0),log 10n, log10UgVt

, log10

lVTr

and

log10qpq1q1

) are calculated. Further, by performing liner regression

analysis, constants Ki(i = 12), Aj(j = 1to3) and Bk(k = 13) could be

evaluated. Then, by combining Eqs. 4, 8, and 9, R(t) becomes calcu-

lable. Figs. 10(a)(c) depict the detailed comparison between

experimental and predicted values of R(t) for different experimen-

tal systems, respectively. The reason why the modeling results of

the bottom-heated leveling experiments are not included is be-

cause from previous analyses it has been confirmed that the self-

leveling behavior under the two boiling modes (depressurization

and bottom-heated) proceeds in almost the same way, though

some microscopic differences do exist (Zhang et al., 2011). The cal-

culation for the depressurization boiling setup becomes achievable

due to an effective gas velocity (Ug) defined based on energy con-

servation (Zhang et al., 2010; Cheng et al., 2011b):

Ug Vpbesq

ACpDTsubqg qghlg

Hesq

CpDTsubqg qghlg10

Overall, it seems that although uncertainties may be present in

the proposed equations, current empirical approach describes rel-

atively well all the experimental runs, regardless of bubbling

method (boiling or gas-injection), bed geometry and dimension

(quasi-2D rectangle or large-scale cylinder) and range of experi-

mental parameters.

To provide more confidence of our modeling, influence of exper-

imental parameters was examined. Fig. 11 illustrates the transient

variation of particle bed with particle size for several typical runs.

It is evident that whatever the experimental condition is, a slower

(a) Quasi-2D gas-injection (dp= 2mm) (b) Large-scale gas-injection (dp=6mm)

(c) Depressurization boiling (dp=2mm)

Fig. 12. Effect of particle density on R(t).

http://-/?-http://-/?-http://-/?-http://-/?-

7/30/2019 1-s2.0-S0306454913004052-main

9/11

decrease in R(t) can be observed as particle diameter increases.

This is because with the increase in particle size particles tend to

be more difficult to be moved by the gas flow inside the bed, as ob-

served in the flow regime investigations (Cheng et al., 2011a,

2013b). This influence can be well represented by the empirical ap-

proach, thereby demonstrating to some degree its ability in pre-

dicting self-leveling behavior.

The effect of particle density on the transient variation of parti-

cle bed is shown in Fig. 12. As particle density increases, self-level-

ing seems to proceed much slower for both experimental and

model predicted data, regardless of experimental condition. In

the studies of flow regimes, we also concluded that with particle

density increasing, particle becomes heavier, making it more diffi-

cult tobe pushedup bythe flow insidethe bed (Cheng et al., 2011a,

2013b). Again, the good agreement between the experimental and

model predicted data on the influence of particle density provides

confirmation of our empirical approach.

The effect of bubbling rate on the transient variation of particle

bed is illustrated in Fig. 13. Overall, higher gas flow rate or boiling

intensity seems to facilitate the leveling and result in faster de-

crease in R(t). This might be explained by the facts that as already

observed in the flow regime studies (Cheng et al., 2011a, 2013b),

bubbling rate does have influence on the regime transition, i.e. as

bubbling rate increases, a greater impetus for lifting solid particles

is attainable, thereby leading to the transition of bubbling behav-

iors. The inverse relation between the change in R(t) and bubbling

rate can be clearly observed in Fig. 13 for both experimental and

predicted data that substantiates the proposed approach.

To further clarify the mechanisms underlying the self-leveling

behavior, comparative analyses were made between different

experimental systems using the experimental data and

corresponding estimations calculated by the developed empirical

equations. Fig. 14 shows the comparisons of several typical cases

(a) Quasi-2D gas-injection (Glass, dp= 6mm) (b) Large-scale gas-injection (Alumina, dp= 4mm)

(c) Depressurization boiling (Alumina, dp=1mm)

Fig. 13. Effect of bubbling rate on R(t).


7/30/2019 1-s2.0-S0306454913004052-main

10/11

under the quasi-2D and large-scale gas-injection conditions. Over-

all, it seems that the larger the column dimension is, the faster the

self-leveling proceeds. This might be due to the fact that walls

(esp. front-rear walls) in the narrower quasi-2D tank to some extent

plays a restricting role to particle bed movement, while within the

large-scale system this effect is expectable to be much diminished.

Fig. 15 demonstrates the comparisons of several representative

runs under the depressurization boiling and large-scale gas-injec-

tion conditions. It seems that although the difference in depressur-

ization and bottom-heated boiling has no notable influence on the

leveling behavior (Zhang et al., 2011), an evident difference for the

leveling progression is observable between the boiling and gas-

injection conditions. This should be primarily due to the difference

in boiling or gas-percolation patterns encountered in the two

systems. Present comparison suggests that coolant vapor conden-

sation in the bed and the subcooled pool would significantly

change the characteristics of self-leveling dynamics.

Finally, we should notice that the values of constants shown in

Figs. 10(a)(c) are quite different. Aside from experimental differ-

ences encountered in these systems (such as bubbling method

(boiling or gas-percolation), and column dimensions and shape),

another reason we believe might be due to the different choice

of t0. Theoretically speaking, Eq. (4) would be valid for any time

period (Cheng et al., 2011b), however, the arbitrary choice of t0would lead to variations in constant values and possibly impair

the fitting accuracy. In addition, we need to also stress that as

aforementioned, apart from empirical model development, owing

to the experimental knowledge obtained from the flow regime

investigations that the various bubbling behaviors, dominated by

the different interaction mechanisms between solid particles and

bubbles, are common characteristics over a wide range of condi-

tions (regardless of bubbling method) (Cheng et al., 2011a,

2013b), currently several mechanism models treating the parti-

cleparticle and particle-bubble interactions (e.g. the discrete ele-

ment method) are being developed and incorporating into

SIMMER-III, an advanced fast reactor safety analysis code (Guo

et al., 2012a,b; Zhang et al., 2012). Therefore, this work, although

not covering the entire range of physical properties of fuel debris

and coolant, expands the existing experimental database and pro-

vides important insight for the verifications of improved SIMMER

code. Also, motivated by the prior requirement of a reliable data-

base for verifying the above-mentioned particle-based computer

models, though in actual reactor accident conditions debris bed

might be formed with various inclination angles, presently we

have not taken the initial bed angle as experimental parameters

(as shown in Table 1). We believe all these aspects might be solved

by the well-verified SIMMER code in the near future.

5. Concluding remarks

Debris bed self-leveling behavior is crucial in the heat removal

capability for fast reactors during CDAs. To further clarify the

mechanism of this phenomenon, based on experimental observa-

tions and a large database obtained for different particle sizes, par-

ticle densities and gas velocities from various conditions, with the

help of dimensional analysis technique, an empirical approach was

successfully proposed to evaluate the transient change of inclina-

tion angle during the leveling process. The proposed approach

can estimate the values of R(t)with respectable accuracy over a

wide range of conditions (including difference in bubbling mode,

bed geometry and range of experimental parameters). The fol-

lowed analysis of the influence of particle size, particle density

and bubbling rate further guarantees its rationality, which to some

extent demonstrates the wide applicability of this approach.

Fig. 14. Comparison between quasi-2D and large-scale leveling experiments using

gas-injection (dp = 2 mm).

Fig. 15. Comparison between depressurization boiling and large-scale gas-injection experiments (Alumina).

http://-/?-http://-/?-

7/30/2019 1-s2.0-S0306454913004052-main

11/11

Furthermore, using experimental data as well as corresponding

estimations by proposed empirical approach, comparative analyses

between different experimental systems are achieved, as a result

making the influence of wall effect and bubbling method on the

self-leveling recognized. However, to benefit future utilization of

the proposed approach on actual reactor conditions, further studies

are inevitably necessary, especially those elucidating the effects of

other parameters (e.g. particle shape) on the self-leveling behavior.

In addition, the characteristics of debris mound packed with multi-

sized particles are also of great importance to be investigated.

Acknowledgements

This work was supported by several annual joint research pro-

jects between Japan Atomic Energy Agency (JAEA) and Kyushu Uni-

versity. The experiments involved were mainly performed using

the facilities in Kyushu University.

References

Abraham, M., Khare, A.S., Sawant, S.B., Joshi, J.B., 1992. Critical gas velocity for

suspension of solid particles in three-phase bubble columns. Ind. Eng. Chem.Res. 31 (4), 11361147.

Alvarez, D., Amblard, M., 1982. Fuel Leveling. In: Proc. 5th Information Exchange

Mtg. on Post-Accident Debris Cooling, Karlsruhe, Germany, July 2830, 1982.

Cheng, S., Hirahara, D., Tanaka, Y., Gondai, Y., Matsumoto, T., Morita, K., Fukuda, K.,

Yamano, H., Suzuki, T., Tobita, Y., 2010a. Experimental study of bubble behavior

in a two-dimensional particle bed with high solid holdup. In: Proc. of 18th

International Conference on Nuclear Engineering (ICONE-18), Xian, China, May

1721, 2010.

Cheng, S., Tanaka, Y., Gondai, Y., Kai, T., Zhang, B., Matsumoto, T., Morita, K., Fukuda,

K., Yamano, H., Suzuki, T., Tobita, Y., 2010b. Experimental investigation on self-

leveling behavior in debris bed. In: Proc. of 7th Korea-Japan Symposium on

Nuclear Thermal Hydraulics and Safety (NTHAS7), Chuncheon, Korea,

November 1417, 2010.

Cheng, S., Hirahara, D., Tanaka, Y., Gondai, Y., Zhang, B., Matsumoto, T., Morita, K.,

Fukuda, K., Yamano, H., Suzuki, T., Tobita, Y., 2011a. Experimental investigation

of bubbling in particle beds with high solid holdup. Exp. Therm.Fluid Sci. 35 (2),

405415.

Cheng, S., Tanaka, Y., Gondai, Y., Kai, T., Zhang, B., Matsumoto, T., Morita, K., Fukuda,

K., Yamano, H., Suzuki, T., Tobita, Y., 2011b. Experimental studies and empiricalmodels for the transient self-leveling behavior in debris bed. J. Nucl. Sci.

Technol. 48 (10), 13271336.

Cheng, S., Kai, T., Gondai, Y., Nakamura, Y., Fuke, F., Zhang, B., Matsumoto, T., Morita,

K., Yamano, H., Tagami, H., Suzuki, T., Tobita, Y., 2012a. A simpleapproachto the

prediction of transient self-leveling behavior of debris bed. In: Proc. of 4th

International Symposium on Heat Transfer and Energy Conservation,

Guangzhou, China, January 69, 2012.

Cheng, S., Yamano, H., Suzuki, T., Tobita, Y., Gondai, Y., Nakamura, Y., Zhang, B.,

Matsumoto, T., Morita, K., 2012b. An experimental study on self-leveling

behavior of debris beds with comparatively higher gasvelocities. In: Proc. of 8th

Japan-Korea Symposium on Nuclear Thermal Hydraulics and Safety(NTHAS8),

Beppu, Japan, December 912, 2012.

Cheng, S., Yamano, H., Suzuki, T., Tobita, Y., Nakamura, Y., Taketa, S., Nishi, S., Zhang,

B., Matsumoto, T., Morita, K., 2013a. Recent knowledge from an experimental

investigation on self-leveling behavior of debris bed. In: Proc. of 21st

International Conference on Nuclear Engineering (ICONE-21), Chengdu, China,

July 29 August 2, 2013 (In press).

Cheng, S., Yamano, H., Suzuki, T., Tobita, Y., Nakamura, Y., Zhang, B., Matsumoto, T.,

Morita, K., 2013b. Characteristics of self-leveling behavior of debris beds in a

series of experiments. Nucl. Eng. Technol., .

Cheng, S., Yamano, H., Suzuki, T., Tobita, Y., Nakamura, Y., Zhang, B., Matsumoto, T.,

Morita, K., 2013c. Empirical correlations for predicting the self-leveling

behavior of debris bed. Nucl. Sci. Tech. 24 (1), 110.

Gabor, J.D., 1974. Simulation Experiments for Internal Heat Generation, Reactor

Development Program Progress Report ANL-RDP-32, Argonne National

Laboratory, Argonne, USA.

Guo, L., Morita, K.,Tobita, Y., 2012a. Numericalsimulation of three-phase flows with

rich solid particles by coupling multi-fluid model with discrete element model.

In: Proc. of 20th International Conference on Nuclear Engineering collocatedwith ASME 2012 Power Conference (ICONE20-POWER2012), Anaheim,

California, USA, July 30 Aug. 3, 2012.

Guo, L., Morita, K., Tobita, Y., 2012b. Numerical simulation of bubbling fluidized

beds by coupling multi-fluid model with discrete element method. In: Proc. of

8th Japan-Korea Symposium on Nuclear Thermal Hydraulics and Safety

(NTHAS8), Beppu, Japan, December 912, 2012.

Hesson, J.C., Sevy, R.H., Marciniak, T.J., 1971. Post-Accident Heat Removal in

LMFBRs. In: Vessel Considerations, ANL-7859, Argonne National Laboratory,

Argonne, USA.

Koide, K., Yasuda, T., Iwamoto, S., Fukuda, E., 1983. Critical gas velocity required for

complete suspension of solid particles in solid-suspended bubble columns. J.

Chem. Eng. Jpn. 16 (1), 712.

Koide, K., Horibe, K., Kawabata, H., Ito, S., 1984. Critical gas velocity required for

complete suspension of solid particles in solid-suspended bubble column with

draught tube. J. Chem. Eng. Jpn. 17 (4), 368374.

Magallon, D., Hohmann, H., Schins, H., 1992. Pouring of 100-kg-scale molten UO2into sodium. Nucl. Technol. 98 (1), 7990.

Nakai, R., Suzuki, T., Yamano, H., Seino, H., Ishikawa, H., Kamiyama, K., Koyama, K.,

Morita, K.,2009. Development of severe accident evaluation technology (Level 2

PSA) for sodium-cooled fast reactors (1) Overview of evaluation methodology

development. In: Proc. of 2009 International Congress on Advances in Nuclear

Power Plants (ICAPP 09), Tokyo, Japan, May 1014, 2009.

Nakai, R., Suzuki, T., Yamano, H., Seino, H., Ishikawa, H., Kamiyama, K., Koyama, K.,

Morita, K., 2010. Development of Level 2 PSA methodology for sodium-cooled

fast reactors (1) Overview of evaluation technology development. In: Proc. of

8th International Topical Meeting on Nuclear Thermal-Hydraulics, Operation

and Safety (NUTHOS-8), Shanghai, China, October 1014, 2010.

Tentner, A.M., Parma, E., Wei, T., Wigeland, R., 2010. Evaluation of Design Measures

for Severe Accident Prevention and Consequence Mitigation. ANL-GENIV-128,

Argonne National Laboratory, Argonne, USA.

Tobita, Y., Kondo, S., Yamano, H., Morita, K., Maschek, W., Coste, P., Cadiou, T., 2006.

The development of SIMMER-III, an advanced computer program for LMFR

safety analysis, and its application to sodium experiments. Nucl. Technol. 153

(3), 243263.

Waltar, A.E., Reynolds, A.B., 1981. Fast Breeder Reactors. Pergamon Press, New York,

USA.

Zhang, B., Harada, T., Hirahara, D., Matsumoto, T., Morita, K., Fukuda, K., Yamano, H.,Suzuki, T., Tobita, Y., 2008. Experimental study of self-leveling behavior in

debris bed. In: Proc. of 6th Japan-Korea Symposium on Nuclear Thermal

Hydraulics and Safety (NTHAS6), Okinawa, Japan, November 2427, 2008.

Zhang, B., Harada, T., Hirahara, D., Matsumoto, T., Morita, K., Fukuda, K., Yamano, H.,

Suzuki, T., Tobita, Y., 2009. Criteria for occurrence of self-leveling in the debris

bed. In: Proc. of 13th International Topical Meeting on Nuclear Reactor

Thermal-Hydraulics (NURETH-13), Kanazawa, Japan, September 27 October

2, 2009.


Suzuki, T., Tobita, Y., 2010. Self-leveling onset criteria in debris beds. J. Nucl. Sci.

Technol. 47 (4), 384395.


Suzuki, T., Tobita, Y., 2011. Experimental investigation on self-leveling behavior

in debris beds. Nucl. Eng. Des. 241 (1), 366377.

Zhang, B., Matsumoto, T., Morita, K., Yamano, H., Tagami, H., Suzuki, T., Tobita, Y.,

2012. Numerical simulation of the self-leveling phenomenon by modified

SIMMER-III. In: Proc. of 20th International Conference on Nuclear Engineering

collocated with ASME 2012 Power Conference (ICONE20-POWER2012),

Anaheim, California, USA, July 30 August 3, 2012.

http://refhub.elsevier.com/S0306-4549(13)00405-2/h0005http://refhub.elsevier.com/S0306-4549(13)00405-2/h0005http://refhub.elsevier.com/S0306-4549(13)00405-2/h0005http://refhub.elsevier.com/S0306-4549(13)00405-2/h0005http://refhub.elsevier.com/S0306-4549(13)00405-2/h0010http://refhub.elsevier.com/S0306-4549(13)00405-2/h0010http://refhub.elsevier.com/S0306-4549(13)00405-2/h0010http://refhub.elsevier.com/S0306-4549(13)00405-2/h0010http://refhub.elsevier.com/S0306-4549(13)00405-2/h0015http://refhub.elsevier.com/S0306-4549(13)00405-2/h0015http://refhub.elsevier.com/S0306-4549(13)00405-2/h0015http://refhub.elsevier.com/S0306-4549(13)00405-2/h0015http://dx.doi.org/10.5516/NET.02.2012.068http://dx.doi.org/10.5516/NET.02.2012.068http://refhub.elsevier.com/S0306-4549(13)00405-2/h0025http://refhub.elsevier.com/S0306-4549(13)00405-2/h0025http://refhub.elsevier.com/S0306-4549(13)00405-2/h0025http://refhub.elsevier.com/S0306-4549(13)00405-2/h0030http://refhub.elsevier.com/S0306-4549(13)00405-2/h0030http://refhub.elsevier.com/S0306-4549(13)00405-2/h0030http://refhub.elsevier.com/S0306-4549(13)00405-2/h0035http://refhub.elsevier.com/S0306-4549(13)00405-2/h0035http://refhub.elsevier.com/S0306-4549(13)00405-2/h0035http://refhub.elsevier.com/S0306-4549(13)00405-2/h0035http://refhub.elsevier.com/S0306-4549(13)00405-2/h0040http://refhub.elsevier.com/S0306-4549(13)00405-2/h0040http://refhub.elsevier.com/S0306-4549(13)00405-2/h0040http://refhub.elsevier.com/S0306-4549(13)00405-2/h0040http://refhub.elsevier.com/S0306-4549(13)00405-2/h0045http://refhub.elsevier.com/S0306-4549(13)00405-2/h0045http://refhub.elsevier.com/S0306-4549(13)00405-2/h0045http://refhub.elsevier.com/S0306-4549(13)00405-2/h0045http://refhub.elsevier.com/S0306-4549(13)00405-2/h0050http://refhub.elsevier.com/S0306-4549(13)00405-2/h0050http://refhub.elsevier.com/S0306-4549(13)00405-2/h0050http://refhub.elsevier.com/S0306-4549(13)00405-2/h0055http://refhub.elsevier.com/S0306-4549(13)00405-2/h0055http://refhub.elsevier.com/S0306-4549(13)00405-2/h0055http://refhub.elsevier.com/S0306-4549(13)00405-2/h0060http://refhub.elsevier.com/S0306-4549(13)00405-2/h0060http://refhub.elsevier.com/S0306-4549(13)00405-2/h0060http://refhub.elsevier.com/S0306-4549(13)00405-2/h0060http://refhub.elsevier.com/S0306-4549(13)00405-2/h0060http://refhub.elsevier.com/S0306-4549(13)00405-2/h0060http://refhub.elsevier.com/S0306-4549(13)00405-2/h0060http://refhub.elsevier.com/S0306-4549(13)00405-2/h0055http://refhub.elsevier.com/S0306-4549(13)00405-2/h0055http://refhub.elsevier.com/S0306-4549(13)00405-2/h0055http://refhub.elsevier.com/S0306-4549(13)00405-2/h0050http://refhub.elsevier.com/S0306-4549(13)00405-2/h0050http://refhub.elsevier.com/S0306-4549(13)00405-2/h0045http://refhub.elsevier.com/S0306-4549(13)00405-2/h0045http://refhub.elsevier.com/S0306-4549(13)00405-2/h0045http://refhub.elsevier.com/S0306-4549(13)00405-2/h0045http://refhub.elsevier.com/S0306-4549(13)00405-2/h0040http://refhub.elsevier.com/S0306-4549(13)00405-2/h0040http://refhub.elsevier.com/S0306-4549(13)00405-2/h0035http://refhub.elsevier.com/S0306-4549(13)00405-2/h0035http://refhub.elsevier.com/S0306-4549(13)00405-2/h0035http://refhub.elsevier.com/S0306-4549(13)00405-2/h0030http://refhub.elsevier.com/S0306-4549(13)00405-2/h0030http://refhub.elsevier.com/S0306-4549(13)00405-2/h0030http://refhub.elsevier.com/S0306-4549(13)00405-2/h0025http://refhub.elsevier.com/S0306-4549(13)00405-2/h0025http://refhub.elsevier.com/S0306-4549(13)00405-2/h0025http://dx.doi.org/10.5516/NET.02.2012.068http://dx.doi.org/10.5516/NET.02.2012.068http://refhub.elsevier.com/S0306-4549(13)00405-2/h0015http://refhub.elsevier.com/S0306-4549(13)00405-2/h0015http://refhub.elsevier.com/S0306-4549(13)00405-2/h0015http://refhub.elsevier.com/S0306-4549(13)00405-2/h0015http://refhub.elsevier.com/S0306-4549(13)00405-2/h0010http://refhub.elsevier.com/S0306-4549(13)00405-2/h0010http://refhub.elsevier.com/S0306-4549(13)00405-2/h0010http://refhub.elsevier.com/S0306-4549(13)00405-2/h0010http://refhub.elsevier.com/S0306-4549(13)00405-2/h0005http://refhub.elsevier.com/S0306-4549(13)00405-2/h0005http://refhub.elsevier.com/S0306-4549(13)00405-2/h0005

1-s2.0-s0306454913004052-main

Documents