Melt jet-breakup and fragmentation phenomena in nuclear reactors: A review of experimental works and solidification effects

During severe accidents at Nuclear Power Plants (NPPs), fuel-coolant interaction (FCI) is a critical event in which the melt released from the core region comes into contact with the coolant. The melt may eject in the form of a melt jet and threaten the integrity of the NPP.

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Review

Melt jet-breakup and fragmentation phenomena in nuclear reactors: A

Yuzuru Iwasawaa,∗, Yutaka Abeb

a Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

b Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki, 305-8573, Japan

A R T I C L E I N F O

Keywords:

Nuclear reactor

Severe accident

Fuel-coolant interaction

Jet-breakup

Fragmentation

Solidification effects

A B S T R A C T

During severe accidents at Nuclear Power Plants (NPPs), fuel-coolant interaction (FCI) is a critical event in which the melt released from the core region comes into contact with the coolant The melt may eject in the form of a melt jet and threaten the integrity of the NPP Therefore, fragmentation of the melt jet and quenching of par-ticulate fragments from the melt jet are invaluable from the viewpoint of safety assessment To assess the in-tegrity of an NPP, melt fragmentation phenomena that affects quenching and sustainable cooling of the debris bed are important factors that must be predicted and evaluated precisely The present review summarizes ex-perimental works on the FCI phenomenon, especially, fragmentation of a melt jet during a severe accident in an NPP In addition, special attention is paid to solidification effects Based on the literature survey, we discussed the dominant factors governing the fragmentation mechanisms Furthermore, we discuss the applicability of various models for estimating these phenomena

1 Introduction

For stabilization and termination of a severe accident in a Nuclear

Power Plants (NPP), investigating the risks and the progression of the

severe accident is important (Sehgal, 2006, 2012) During a severe

accident in an NPPs, fuel-coolant interaction (FCI), critical event in

which the melt released from the core region comes into contact with

the coolant, needs to be assessed for ensuring NPP integrity The melt

may be injected in the form of a melt jet and threaten the integrity of

NPPs such as Light Water Reactors (LWRs) (Ma et al., 2016;Sehgal and

Bechta, 2016) and Sodium-cooled Fast Reactors (SFRs) (Suzuki et al.,

2014; Tobita et al., 2016) Therefore, fragmentation of the melt jet

(called as the jet-breakup), which means a coherent jet disappears in

this paper, and quenching of the particulate fragments from the melt jet

are invaluable from the viewpoint of safety assessment For the safety

assessment, it is important to predict and evaluate precisely the

char-acteristic values of the jet-breakup and the fragmentation phenomena

that affects the quenching and sustainable cooling of the debris bed

(Dinh et al., 1999)

If a melt jet directly hits the internal structures without jet-breakup,

it may threaten the integrity of a reactor vessel and, consequently,

threaten the integrity of a containment vessel Hence, the jet-breakup

length, which refers to as the distance from the liquid (coolant) surface

to the location where a coherent melt jet disappears (Chu et al., 1995;

Matsuo et al., 2008;Iwasawa et al., 2015a;Li et al., 2017), is important

In addition,fine fragmentation of a melt jet may lead to vapor explo-sion, which threaten the integrity of the NPP Even if vapor explosion does not occur, molten fragments may threaten the integrity of the NPP, when they directly hit the internal structures without quenching In addition,fine fragmentation of a melt affects debris bed formation and decay heat removal Therefore, it is important to estimate and evaluate fragment size from the viewpoint of safety assessment

FCI phenomena of a melt jet, such as jet-breakup and fragmentation

is known to be complex, mainly because of two interactions that occur simultaneously: hydrodynamic (e.g., interfacial instability at two-phase interface and liquid entrainment or stripping from interface), and thermal (e.g., coolant boiling and solidification of a melt surface) (Chu

et al., 1995;Sugiyama et al., 1999;Nishimura et al., 2010;Manickam

et al., 2017) Many experiments have been carried out using various combinations of melt and coolant In addition to large-scale experi-ments using actual fuels, scoping experiexperi-ments focusing on the funda-mental processes of the FCI phenomena have also been carried out to investigate each interaction and the dominant factors governing the FCI phenomena

The present review article summarizes experimental works on the FCI phenomena, especially, jet-breakup and fragmentation of a melt jet during a severe accident in NPPs In addition, special attention is paid

to solidification effects Based on the literature survey, this article

https://doi.org/10.1016/j.pnucene.2018.05.009

Received 6 August 2017; Received in revised form 21 March 2018; Accepted 11 May 2018

∗ Corresponding author.

E-mail address: iwasawa.yuzuru.xu@alumni.tsukuba.ac.jp (Y Iwasawa).

Available online 05 June 2018

0149-1970/ © 2018 The Authors Published by Elsevier Ltd This is an open access article under the CC BY-NC-ND license

(http://creativecommons.org/licenses/BY-NC-ND/4.0/)

T

discusses dominant the factors governing jet-breakup and

fragmenta-tion Furthermore, this article discusses the applicability of various

models for estimating these phenomena

The remainder of this is organized as follows InChapter 2,

pre-vious experiments on FCI, including jet-breakup and fragmentation, are

reviewed and summarized These review and summary are presented in

terms of melt and coolant composition InChapter 3, the dominant

factors governing the jet-breakup of a melt jet are discussed based on

the literature survey In addition, existing models for estimating the

jet-breakup length are presented based on their applicability InChapter 4,

the dominant factors governing the fragmentation of a melt jet are

discussed based on the literature survey In addition, existing models

for estimating the fragment size are presented based on their

applic-ability InChapter 5, the solidification effects of the FCI phenomena

are reviewed and summarized A model for estimating the fragment size

considering the solidification effects is presented Chapter 6 concludes

this article

2 Previous experiments on FCI phenomena The following sections will summarize the previous experiments on the FCI phenomena in terms of melt and coolant composition Given that the focus of this review article is on the jet-breakup and the frag-mentation phenomena of a melt jet, the experiments considered herein are those involving injected melts weighing several hundred grams to several hundred kilograms (injected melt jets not melt droplets)

2.1 Oxide/sodium system

This section summarizes the previous experiments on the FCI phe-nomena involving oxide melt and sodium, which mainly target SFRs They are summarized inTable 1

In the M-Series experiments conducted in the Argonne National Laboratories (ANL) (Johnson et al., 1975;Sowa et al., 1979) and the FLAG experiments conducted in the Sandia National Laboratories (SNL) (Chu, 1982), uranium oxide melt was injected, with a focus on vapor explosion.Zagorul'ko et al (2008)conducted the experiment using the

Nomenclature

d characteristic length

D bending stiffness

Dj jet diameter

E Young's modulus

E0 entrainment coefficient

Fr Froude number

g gravitational acceleration

Lbrk jet-breakup length

Ti initial interfacial temperature

ΔTc coolant subcooling

u fluctuating velocity in horizontal direction

U uniform velocity in horizontal direction

v fluctuating velocity in vertical direction

V uniform velocity in vertical direction

vj jet velocity

vrel relative velocity

x horizontal direction

y vertical direction

Greek symbol

δ crust thickness

ε Poisson's ratio

γt temporal growth rate

γy spatial growth rate

ϕ velocity potential

η displacement of interface

κ thermal conductivity

λn neutral-stable wavelength

λm most-unstable wavelength

σ interfacial tension or surface tension

ω angular frequency Subscript

j, 1 melt jet

c, 2 coolant

Table 1

Previous experiments on FCI phenomena conducted using oxide/sodium system

Organization

(Test facility or program)

ANL

(M-Series)

UO 2 -Mo, UO 2 -ZrO 2 -SS/

Sodium

Johnson et al (1975) Sowa et al (1979) SNL

(FLAG)

Fe-Al 2 O 3 , UO 2 -ZrO 2 -SS/

Sodium

Chu (1982) JRC

(BETULLA)

Schins (1984) Schins et al (1984 , 1986) Schins and Gunnerson (1986) JRC

(FARO/TERMOS)

JAEA

(FR Tests)

2015b , 2016) IPPE

(Pluton)

189

melt of thermite mixture in the Pluton test facility at the Institute for

Physics and Power Engineering (IPPE) In the experiments conducted at

the BETULLA facility in the Joint Research Centre (JRC) (Holtbecker

et al., 1977; Schins, 1984; Schins et al., 1984, 1986; Schins and

Gunnerson, 1986), uranium oxide and alumina melts were injected The

JRC-based research group discussed differences in the fragmentation

phenomena between oxide melt and metallic melt into sodium In the

large-scale experiments conducted at the FARO/TERMOS facility in

JRC (Magallon et al., 1992), 100 kg of uranium oxide was injected

Because the conditions and the scale of these experiments were

com-parable to those of an actual SFR undergoing a severe accident,Suzuki

et al (2014)referred to this experiment to evaluate safety assessment

procedures Recently, Japan Atomic Energy Agency (JAEA) conducted

experiments involving the injection of alumina melt into sodium as FR

tests (Matsuba et al., 2012, 2015a, 2015b, 2016) to develop design

criteria for next-generation SFRs (Ichimiya et al., 2007;Kotake et al.,

2010;Aoto et al., 2011)

2.2 Metal/sodium system

This section summarizes the previous experiments on the FCI

phe-nomena conducted using metallic melt and sodium, which mainly

target SFRs They are listed inTable 2

In the experiments conducted at the BETULLA facility in JRC (Benz

and Schins, 1982;Schins, 1984;Schins and Gunnerson, 1986;Schins

et al., 1986), stainless steel and copper melts were injected The ANL

conducted the experiments in which they injected metallic melt into

sodium (Gabor et al., 1988).Gabor et al (1988)visualized the

frag-ments at the bottom of the test section using a radiograph Central

Research Institute of Electric Power Industry (CRIEPI) conducted an

experiment involving metallic fuels (Nishimura et al., 2002, 2005,

2010) for SFRs They focused on how the solidification effects influence

the FCI phenomena JAEA conducted an experiment in which

alu-minum melt was injected into sodium (Matsuba et al., 2016) The melt

jet in sodium was visualized using X-rays

2.3 Oxide/water system

This section summarizes the previous experiments on the FCI

phe-nomena conducted using oxide melt and water, which mainly target

LWRs They are listed inTable 3

The FITS experiments conducted at SNL (Mitchell et al., 1981;

Corradini, 1981), the CCM experiments conducted at ANL (Spencer

et al., 1994), the MIXA experiments conducted at United Kingdom

Atomic Energy Authority (UKAEA) (Denham et al., 1994), the ALPHA

program at Japan Atomic Energy Research Institute (JAERI) (Yamano

et al., 1995), and the ECO experiment conducted at Forschungszentrum

Karlsruhe (FZK) (Cherdron et al., 2005) involved injecting oxide melt

by means of the thermite reaction.Zagorul'ko et al (2008)conducted

the experiment using the melt of thermite mixture in the TVMT

installation at IPPE The ZREX experiments conducted at ANL (Cho

et al., 1997,1998) focused on hydrogen production upon the injection

of zirconia melt The experiments conducted at the KROTOS facility in JRC (Hohmann et al., 1995; Huhtiniemi et al., 1997a, 1997b; Huhtiniemi and Magallon, 2001), those at FARO/TRERMOS and FARO/ FAT facility in JRC (Magallon and Hohmann, 1995; Magallon et al.,

1997, 1999; Magallon and Huhtiniemi, 2001), and the PREMIX ex-periments conducted in the FZK (Huber et al., 1996;Schütz et al., 1997; Kaiser et al., 1997,1999,2001) involved injecting uranium oxide-zir-conia (so-called corium) or alumina melt The results of these experi-ments provided an important database and significant knowledge on FCI phenomena in actual reactors JAERI conducted a series of ex-periments called GPM (Moriyama et al., 2005), which involved in-jecting alumina-zirconia and stainless-carbon melts.Moriyama et al (2005)investigated a method for estimating the jet-breakup length and fragment size The MIRA experiments conducted at Royal Institute of Technology (KTH) (Haraldsson and Sehgal, 1999; Haraldsson, 2000) involved injecting various oxide melts The DEFOR experiments (Kudinov et al., 2008,2010;2013,2015;Karbojian et al., 2009) were also conducted at KTH In this experiment, various oxide melts were also injected to investigate the agglomeration of particulate fragments from a melt jet The French Alternative Energies and Atomic Energy Commission (CEA) conducted experiments at the KROTOS facility, and the TROI facility, which is in the Korea Atomic Energy Research In-stitute (KAIRI), under the OECD/NEA SERENA program This program focused on vapor explosion (Hong et al., 2013) Also, the Access to Large Infrastructures for Severe Accidents (ALISA) project between European and Chinese research institutions in the area of severe acci-dent research is underway (Cassiaut-Louis et al., 2017) In this program, the experiments for the study of FCI was conducted using the KROTOS facility on the PULINIUS platform (Bouyer et al., 2015) In KAIRI, the experiments at the TROI facility (Park et al., 2001,2008,2013;Song

et al., 2002a,2002b,2003a,2003b,2016,2017;Kim et al., 2003,2004,

2005,2008,2011;Song and Kim, 2005;Hong et al., 2013,2015,2016;

Na et al., 2014,2016) involved injecting corium melt to investigate vapor explosions Recently, this research group also focused on In-Vessel Corium Retention External Reactor Cooling (IVR-ERVC) Na

et al (2014, 2016), Hong et al (2016), and Song et al (2017) con-ducted experiments in which corium melt was injected without free fall Furthermore, experiments conducted at the MISTEE-jet and the JEBRA facility in KTH involved injecting oxide and metallic melt (Manickam

et al., 2014,2016,2017) This research group discussed the difference

in fragmentation between oxide melt and metallic melt

2.4 Metal/water system

This section summarizes the previous experiments on the FCI phe-nomena conducted using metallic melt and water coolant, which mainly target LWRs or SFRs They are listed inTable 4

These experiments are focused on fundamental processes of the FCI

Table 2

Previous experiments on FCI phenomena conducted using metal/sodium system

Organization (Test facility or program)

Schins (1984) Schins and Gunnerson (1986)

Schins et al (1986)

Sodium

Gabor et al (1988)

2005 , 2010)

phenomena (Spencer et al., 1986;Cho et al., 1991;Schins et al., 1992;

Hall and Fletcher, 1995; Dinh et al., 1999;Haraldsson, 2000) A few

research groups conducted experiments involving visualizing a melt jet

Hall and Fletcher (1995)conducted the experiment of single nozzle and

multi nozzle geometry at Berkeley Technology Centre (BNL) Moreover,

the experiments conducted at the ANL (Gabor et al., 1992, 1994),

JAERI (Sugiyama et al., 1999;Sugiyama and Yamada, 2000;Sugiyama

and Iguchi, 2002), Korean Maritime University (KMU) (Bang et al.,

2003;Kim and Bang, 2016;Bang and Kim, 2017), University of

Tsu-kuba (UT) (Abe et al., 2004,2005;2006;Matsuo et al., 2008;Iwasawa

et al., 2015a,2015b), JAEA (Matsuba et al., 2013), KTH (Manickam

et al., 2014,2017), and Shanghai Jiao Tong University (SJTU) (Li et al.,

2017) measured the fragment size and shape Experiments conducted

from several viewpoints are summarized in this section The experiment

conducted at Power Reactor and Nuclear Fuel Development

Corpora-tion (PNC) using the MELT-II facility (Kondo et al., 1995) and the

ex-periment conducted at Pohang University of Science and Technology

(POSTEC) (Jung et al., 2016) focused on vapor generation around a

melt jet.Matsuba et al (2013)conducted the experiments focused on

the fundamental processes using up to 400 kg melt They measured

temperature distribution along a column of melt in water by installing

thermocouples on the central axis of the nozzle The experiment con-ducted at Chongqing University (CH) focused on vapor explosions (Lu

et al., 2016) The experiment conducted at Indira Gandhi Centre for Atomic Research (IGCAR) (Mathai et al., 2015) and that conducted at Indian Institute of Technology (IIT) (Pillai et al., 2016) focused on agglomeration Recently, an experiment was conducted at Tokyo In-stitute of Technology (TIT) using simulant metal to develop a method for sealing NPPs (Takahashi et al., 2015;Secareanu et al., 2016) The experiments conducted at University of Tokyo used simulant metal to investigate the effects of internal structures such as Control Rod Guide Tubes in Boiling Water Reactors (BWRs) on the jet-breakup and the fragmentation phenomena (Wei et al., 2016)

2.5 Experiment with other simulant materials This section summarizes the previous experiments on the FCI phe-nomena using other simulant materials, mainly targeting LWRs or SFRs They are listed inTable 5

The experiments conducted at PNC using the JET-I facility (Saito

et al., 1998) and the experiment conducted at ANL under the MFSBS program (Schneider et al., 1992; Schneider, 1995) used volatile

Table 3

Previous experiments on FCI phenomena conducted using oxide/water system

Organization (Test facility or program)

SNL (FITS)

Corradini (1981) UKAEA

(MIXA)

ANL (CCM)

JAERI (ALPHA)

Al 2 O 3 -FeO,

Al 2 O 3 -Fe 2 O 3 /Water

Yamano et al (1995) ANL

(ZREX)

JRC/CEA (KROTOS)

Al 2 O 3 , UO 2 -ZrO 2 /Water Hohmann et al (1995)

Huhtiniemi et al (1997a , 1997b) Huhtiniemi and Magallon (2001) Hong et al (2013)

Bouyer et al (2015) Cassiaut-Louis et al (2017) JRC

(FARO/TERMOS, FAT)

Magallon and Huhtiniemi (2001) Magallon et al (1997 , 1999) Magallon (2006)

FZK (PREMIX)

Schütz et al (1997) Kaiser et al (1997 , 1999 , 2001) FZK

(ECO)

JAERI (GPM)

Al 2 O 3 -ZrO 2 , SS-C/Water Moriyama et al (2005)

KTH (MIRA)

CaO-B 2 O 3 , MnO 2 -TiO 2 ,

WO 3 -CaO/Water

Haraldsson and Sehgal (1999) Haraldsson (2000) IPPE

(Pluton)

KTH (DEFOR)

CaO-B 2 O 3 , WO3-CaO, MnO-TiO 2 , WO 3 -TiO 2 ,

Bi 2 O 3 -TiO 2 , Bi 2 O 3 -CaO,

Bi 2 O 3 -WO 3 , WO 3 -ZrO 2 /Water

Kudinov et al (2008 , 2010 , 2013 , 2015) Karbojian et al (2009)

KAERI (TROI)

UO 2 -ZrO 2 -Zr, UO 2 -ZrO 2 , ZrO 2 -Zr, ZrO 2 , Al 2 O 3

/Water

Park et al (2001 , 2008 , 2013) Song et al ( 2002a , 2002b , 2003a , 2003b ,

2016 , 2017 ) Kim et al (2003 , 2004 , 2005 , 2008 , 2011) Kim et al (2008 , 2011)

Song and Kim (2005) Hong et al (2013 , 2015 , 2016)

Na et al (2014 , 2016) KTH

(MISTEE-jet/JEBRA)

WO 3 -Bi 2 O 3 , WO 3 -ZrO 2 /Water

Manickam et al (2014 , 2016 , 2017)

191

coolants such as nitrogen and freon They investigated the effects of

vapor generation on the jet-breakup and the fragmentation phenomena

Dinh et al (1999)conducted an experiment to investigate the effects of

several variables such as physical properties and phase-change heat

transfer.Saito et al (1988)proposed a semi-empirical correlation for

estimating the jet-breakup length The details of the semi-empirical

correlation will be described in the next section

3 Jet-breakup phenomena

The following sections summarize the jet-breakup length obtained

from the previous experiments The obtained values will be compared

with those obtained using existing methods, and the dominant factors

governing the jet-breakup phenomena will be discussed

3.1 Existing models and methods

This section briefly presents the existing methods for estimating the

jet-breakup length and the fragment size.Saito et al (1988)andEpstein

and Fauske (2001) proposed these correlations, which are re-presentative and widely used

Based on experimental results,Saito et al (1988)pointed out that the important factors governing jet-breakup were the force balance among the inertia forces of a melt jet, buoyancy force owing to density difference, and the forces resulting from hydrodynamic and thermal interactions Then, they proposed the following semi-empirical correlation:

⎝

⎞

⎠

L D

ρ ρ

brk j

j

c

0.5 0.5

(1)

= v

gD

2

where Lbrkdenotes the jet-breakup length, Djdenotes the inlet diameter of

a melt jet, vjdenotes the velocity of a melt jet,ρ denotes the density of fluid, and Fr denotes the Froude number defined bySaito et al (1988), respectively Subscripts j and c denote the jet and the coolant, respectively Epstein and Fauske (2001)proposed a semi-empirical correlation

Table 4

Previous experiments on FCI phenomena conducted using metal/water system

Organization (Test facility or program)

Berg et al (1994) Bürger et al (1995)

PNC (MELT-II)

Haraldsson (2000)

Sugiyama and Yamada (2000) Sugiyama and Iguchi (2002)

KMU (COLDJET)

Bang and Kim (2017)

Matsuo et al (2008) Iwasawa et al (2015a , 2015b)

Glycerol

Pillai et al (2016)

Water

Takahashi et al (2015) Secareanu et al (2016)

MATE (POSTEC)

KTH (MISTEE-jet/JEBRA)

Sn, Wood’ metal/

Water

Manickam et al (2014 , 2017)

SJTU (METRIC)

Table 5

Previous experiments on FCI phenomena using experiment other simulant materials

Organization (Test facility or program)

PNC (JET-I)

ANL (MFSBS)

Schneider (1995)

Paraffin oil, Salt

Dinh et al (1999)

based on previous works by Ricou and Splading (1961) Epstein and

Fauske (2001) introduced the tuning parameter E0 for adjusting the

difference between simple modeling and actual phenomena Their

correlation is given by below:

⎝

⎞

⎠

L

ρ

ρ

1

brk

j

0.5

(3) where E0denotes the tuning parameter called“the entrainment

coef-ficient”, and its values range 0.05 and 0.1 This type of the correlation is

also called a“Taylor type” correlation (Taylor, 1963) We can recognize

that the correlation proposed bySaito et al (1988)depends on vj By contrast, the correlation proposed byEpstein and Fauske (2001)is in-dependent of vj

3.2 Experimental data on jet-breakup length Fig 1 shows the jet-breakup length Lbrk obtained from previous experiments organized by Froude number Fr InFig 1, the vertical axis represents the normalized Lbrk obtained using a jet diameter Djand density ratio of melt to coolantρj/ρc, and the horizontal axis represents Table 6

Previous experiments conducted under nearly saturated or saturated water conditions

Organization (Test facility or program)

FZK (PREMIX)

JAERI (GPM)

Al 2 O 3 -ZrO 2 , SS-C/Water Moriyama et al (2005)

MATE (POSTEC)

Fig 1 Normalized jet-breakup length obtained from previous experiments are organized by Froude number Fr The values obtained using the correlations proposed

bySaito et al (1998)andEpstein and Fauske (2001)are compared with the measured jet-breakup length

193

Fr The open plots indicate the Lbrkobtained in the experiments using water, and thefilled plots indicate the Lbrkobtained in the experiments using sodium Note that the legend inFig 1shows the organization where the experiments were carried out, the test facility or program, melt-coolant composition, and related references The dashed-dotted line indicates the correlation for estimating Lbrkproposed bySaito et al (1988), and the dashed line indicates the correlation for estimating Lbrk

proposed byEpstein and Fauske (2001) Several methods were used to measure Lbrkbecause of the limita-tions of the experiments In the middle- or large-scale experiments, thermocouples were set in the test facility to measure Lbrk from the temperature history (e.g., KROTOS, FARO/TERMOS, FAT, PREMIX, TROI) Alternatively, wired meshes were set up in the test facility to detect the jet-breakup position (e.g., FARO/TERMOS, FR tests) In several experiments, melt jets in the coolant were visualized using high-speed video cameras, and Lbrk was measured using the visualized images (Abe et al., 2006;Matsuo et al., 2008;Iwasawa et al., 2015a;Li

et al., 2017) In previous experiments (Moriyama et al., 2005; Abe

et al., 2006;Matsuo et al., 2008;Iwasawa et al., 2015a;Li et al., 2017),

Lbrkwas measured as the distance from liquid surface (coolant) where the tip velocity of a melt jet decreases rapidly This article summarizes the experiments focused on vapor explosion, and the experiments without jet-breakup in which a melt jet hit bottom of the test facility

Fig 2 Effects of coolant subcooling on jet-breakup length obtained from

pre-vious experiments The results obtained using the correlation proposed by

Epstein and Fauske (2001)are shown for reference

Fig 3 Normalized fragment sizes (MMDs) obtained from previous experiments are organized based on Weber number The critical Weber number theory is presented for reference

directly (Magallon, 2006) In these experiments, the jet-breakup length

could not be measured Therefore, we excluded these experimental

results fromFig 1

FromFig 1, we can recognize that the Lbrkvalues obtained from the

previous experiments show two trends: Lbrkincreases as Froude number

increases, and Lbrkremains almost constant in spite of some variations

Moreover, we can see that the Lbrkvalues obtained from the previous

experiments targeting LWRs and SFRs have no significant differences,

regardless of the experimental scales Almost all of the Lbrkvalues are

close to those obtained using the correlation proposed byEpstein and

Fauske (2001) However, the Lbrkvalues obtained from the experiments

using a volatile liquid such as freon and nitrogen and from those using

nearly saturated or saturated water as a coolant are close to the values

obtained using the correlation proposed bySaito et al (1988)

In previous works, Moriyama et al (2005) proposed criteria for

determining the applicability of the correlation for estimating Lbrkby

using the Bond number; Lbrk follows the correlation by Saito et al

(1988)when the Bond number is small (< 50), and Lbrkfollows the

correlation by Epstein and Fauske (2001) when the Bond number is

large (> 50) The criteria can be applied in the range of Bond number

from 10 to 100, and the range of Froude number from 100 to 500

However,Jung et al (2016)pointed out that the criteria cannot explain

the experimental results obtained byAbe et al (2006)because the Lbrk

measured by them followed the correlation by Epstein and Fauske

(2001)even in the small Bond number.Abe et al (2006)conducted the

experiments using low melting point metal in the subcooled condition

Most of the experimental results conducted byJung et al (2016)

fol-lowed the correlation bySaito et al (1988)except the condition in a

highly subcooled water and a low melt superheat.Jung et al (2016)

considered that the subcooled conditions result in a short jet-breakup

length by hindered the vapor generation and the results agreed with the

correlation byEpstein and Fauske (2001) Therefore,Jung et al (2016)

focused the vapor generation on the jet-breakup and the fragmentation

phenomena, and conducted an experiment at the MATE facility to

verify the criteria They focused on the effects of vapor generation on

the jet-breakup and the fragmentation phenomena In the next section,

we will discuss the dominant factors governing Lbrk and the

applic-ability of the correlations

3.3 Dominant factors affecting jet-breakup length

InTable 6, we summarize the experiments in which nearly saturated

or saturated water was used as the coolant and where the Lbrkvalued

obtained were close to those yielded by the correlation proposed by

Saito et al (1988) In the experiments summarized inTables 5 and 6, a

significant vapor film was generated and sustained around a melt jet

Saito et al (1988)pointed out that coolant vapor was generated at the

tip of a melt jet, and it immediately surrounded a melt jet as a vapor

film They also pointed out that a vapor film disturbed the direct

con-tact between a melt jet and the coolant, and promoted penetration of

the melt jet into the coolant Similarly,Schneider et al (1992)pointed

out that significant vapor generation around a melt jet tends to disturb

fragmentation owing to interfacial instability From the theoretical

viewpoint, Epstein and Fauske (1985) confirmed that a vapor film

suppresses interfacial instability

Therefore, we can consider that a melt jet tends to penetrate further

into the coolant when significant coolant vapor is formed around the

melt jet, which leads to suppression of fragmentation owing to

inter-facial instability Consequently, the Lbrkvalues may agree with those

obtained using the correlation proposed by Saito et al (1988) By

contrast, we can consider that intensive fragmentation occurs due to

interfacial instability under the conditions in which it is difficult for the

vaporfilm to be formed and sustained, which leads to the intensive

jet-breakup Consequently, the Lbrkvalues may agree with those obtained

using the correlation proposed byEpstein and Fauske (2001)

To investigate the effects of vapor generation on Lbrk, we focused on

the previous experiments inTable 6in which the coolant temperature was varied as a test condition Then, we organized the Lbrkvalues in Table 6in terms of the coolant subcoolingΔTcinFig 2 InFig 2, the vertical axis represents the normalized Lbrk, as inFig 1, and the hor-izontal axis representsΔTc The dashed line indicates the correlation for estimating Lbrkproposed byEpstein and Fauske (2001)for reference

InFig 2, highΔTcmeans the coolant temperature is low, and low

ΔTc means the coolant temperature is nearly saturated or saturated Hence, we can interpret that at highΔTc, coolant vapor may condense easily, that is, a stable vaporfilm would be difficult to form

FromFig 2, we can recognize that asΔTcincreases, Lbrktends to be slightly short However, owing to the lack of adequate number of the experimental results, we cannot make a clear conclusion.Jung et al (2016)started an experiment focusing on the effects of vapor genera-tion on the jet-breakup and the fragmentagenera-tion phenomena This pro-gram now is in progress Therefore, they may provide further knowl-edge and clear conclusion in future works Also, we need to verify not only effects of coolant subcooling but also other integral effects in-cluding melt solidification/oxidation on the Lbrk The authors consider that this issue needs to be investigated The research groups of Manickam et al (2017)may report in the future works

4 Fragmentation phenomena The following sections summarize the fragment sizes obtained in the previous experiments The obtained values are compared with those obtained using existing methods, and the dominant factors governing the fragmentation phenomena are discussed

4.1 Existing modeling schemes and methods

There are several classical theories for estimating fragment size such

as Kelvin-Helmholtz instability (KHI) and the critical Weber number theory (CWT) These classical theories include only hydrodynamic in-teractions Previous works (Dinh et al., 1999;Abe et al., 2006;Bang

et al., 2003;Matsuo et al., 2008;Iwasawa et al., 2015a,2015b;Li et al.,

2017) have pointed out that these classical theories mostly pertain to fragment size, although the actual interface phenomena involves com-plex and non-linear deformation

The classical KHI in two-dimensions (JSME, 1995) is a linear sta-bility theory that considers the balance between interfacial tension force and pressure difference due to the velocity difference between the two-phases Then, we can obtain the characteristic wavelengths of the KHI expressed as follows:

ρ ρ v

1 2 rel 2

(4)

ρ ρ v

whereλKHnandλKHmdenote the characteristic wavelengths called the neutral-stable and the most-unstable wavelengths, respectively (Itoh

et al., 2004;Matsuo et al., 2008;Iwasawa et al., 2015b) Detailed de-scriptions of the physical meanings of these wavelengths will be pre-sented in Chapter 5 Here, ρ denotes density, σ denotes interfacial tension, and vreldenotes the relative velocity between the two-phases Previous works (Matsuo et al., 2008; Iwasawa et al., 2015a,2015b) employed vjof a melt jet as vrelunder the assumption that the ambient coolant was stationary

The critical Weber number is used as the criteria for determining the breakup of a liquid drop The Weber number considers the hydro-dynamic force that deforms a droplet and the interfacial force that helps

a droplet retains its shape, and it is expressed as follows:

=

σ

rel2

(6)

195

where d denotes the characteristic length If the Weber number exceeds

the critical value, a droplet breaks up into smaller and more stable

droplets As critical values, for example, 12 (Pilch and Erdman, 1987;

Uršič et al., 2010,Uršič and Leskovar, 2011) or 18 (Moriyama et al.,

2005; Matsuo et al., 2008; Iwasawa et al., 2015b; Manickam et al.,

2016,2017) are used

4.2 Experimental data on fragment size

Fig 3 shows the fragment sizes obtained in the previous

experi-ments In Fig 3, the fragment sizes are organized based on Weber

number Nishimura et al (2010) suggested that the fragment sizes

could be correlated with the Weber number expressed by Eq.(6) As the

characteristic length d, the inlet diameter Djof a melt jet is used instead

of droplet diameter

InFig 3, the vertical axis represents the fragment sizes expressed by

the mass median diameter (MMD) normalized in terms of Djand the

horizontal axis presents the Weber number In many previous works,

MMD is used as the index of fragment size measured using sieves The

open plots indicate the MMDs obtained in the experiments using water,

and the filled plots indicate the MMDs obtained in the experiments

using sodium Note that the legend in Fig 3shows the organization

where the experiments were carried out, test facility or program,

melt-coolant composition, and related references Also, the CWT is shown

and compared with the MMDs for reference

InFig 3, overall, the MMDs obtained in the previous experiments

decrease as the Weber number increases The increase in vj, which

in-duces fragmentation of a melt jet, may play an important role, although

the experimental conditions employed in the previous experiments

differ We can see that the CWT, which is based only on the

hydro-dynamic interactions, can be used to estimate the MMDs when the

Weber number is low (almost of the order of 101-102i.e when the jet

diameter is of the order of a few critical diameters) At high Weber

numbers (almost of the order of 103-105), however, the MMDs obtained

in the previous experiments related to LWRs (i.e using water) shows a

weak tendency against the Weber number In addition, the MMDs

ob-tained from in the previous experiments targeting SFRs (i.e using

so-dium coolant) are smaller than those obtained in the previous

experi-ments targeting LWRs Fig 3 includes the MMDs obtained in the

different melt superheat and coolant subcooling for water and sodium

coolant Therefore, the variation of the MMDs indicates the influence of

melt superheat and coolant subcooling Even if there is the variation of

the MMDs due to melt superheat and coolant subcooling, we can

identify the influence of coolant variation on the MMDs at high Weber

number

The jet-breakup and the fragmentation phenomena involve not only

hydrodynamic interactions but also thermal interactions Therefore, we

should verify whether the model (CWT) is applicable In addition, we

need to consider and investigate the effects of the thermal interactions

4.3 Dominant factors affecting fragment size

In this section, we discuss the dominant factors governing the

fragmentation phenomena from the viewpoint of thermal interactions

Schins and Gunnerson (1986)discussed the difference in the

fragmen-tation phenomena based on an experiment in which oxide and metallic

was injected melt into sodium They pointed out that the fragments

obtained from the experiments in which metallic melt was injected into

sodium coolant were smooth and round-shaped: the fragments obtained

in the experiments in which oxide melt was injected into sodium

coolant had a cracked shape and were brittle and fragile, with only a

few fragments being smooth and round-shaped Moreover, Tyrprekl

et al (2014) discussed the fragmentation phenomena based on

mor-phology measurements conducted using metallographic, analytical, and

microscopic techniques for the fragments obtained in the experiment in

which oxide and metallic were injected melt into water They pointed

out that the oxide and the metallic melt differed significantly in shape: the oxide melt gained an almost angular shape unlike the metallic melt Recently,Manickam et al (2017)reported the same results from their experiments

Schins and Gunnerson (1986)andTyrpekl et al (2014)mentioned that differences in the fragmentation phenomena between the oxide and the metallic melt They mentioned that the effects of 1 (as follows) are dominant in both oxide and metallic melt

1 Hydrodynamic fragmentation due to prompt boiling of the coolant This leads to prompt fragmentation and generates smooth spherical fragments

Schins and Gunnerson (1986)andTyrpekl et al (2014)also men-tioned that the effects of 2 and 3 (as follows) are present in the oxide melt

2 Thermal fragmentation due to thermal stress acting on the crust of the melt surface This leads to shrinking and cracks the crust This occurs after hydrodynamic fragmentation

3 Coolant ingression inside the shrunken and cracked crust plays an important role in generating cracked and angular fragments

On the other hand, in the metallic melt, Schins and Gunnerson (1986)andTyrpekl et al (2014)also pointed out that thermoelasticity

of metal disturbs the cruck because the thermal stress does not exceed the material strength of the crust Therefore, hydrodynamic fragmen-tation becomes dominant in the metallic melt Consequently, mainly smooth spherical fragments were formed in the experiment involving metallic melt

Based on the previous works mentioned above, we can infer the two reasons for the differences in the MMDs between the oxide/sodium and the oxide/water system as follows:

1 In the case of oxide melt, the crust tends to be cracked owing to the thermal stress caused by the temperature gradient in the crust compared to the case of metallic melt (Schins and Gunnerson, 1986; Tyrprekl et al., 2014)

2 Sodium has large effusivity than water The effusivity determines interfacial temperature between melt and coolant temperature to a lower value for sodium coolant, which affects crust formation and fragmentation phenomena (Schins and Gunnerson, 1986)

At this time, we need to note that the difference of opaque and semi-transparent melt mentioned byDombrovsky and Dinh (2008): in case of opaque melt such as corium, radiative heat transfer from the melt surface controls rapid crust formation from the melt surface On the other hand, in case of semi-transparent melt such as alumina, con-vective heat transfer controls crust formation although radiative heat transfer from melt volume controls rapid solidification of the melt Then, we can suppose that the MMDs obtained from the previous experiments for SFRs are smaller than those obtained from the previous experiments for LWRs at high Weber number because of the difference

in the thermal stress that breaks the curst owing to the difference in the effusivity of the coolant in addition to differences in the shrinkage and the coolant ingression into the crust on the melt surface

We can recognize that the solidification and the subsequent cracking of the crust on the melt surface are important factors Investigation of the solidification effects on the jet-breakup and the fragmentation phenomena in NPPs is important, but it is given the complexity of the phenomena Therefore, investigating the solidifica-tion effects separately is an effective approach

5 Solidification effects on FCI phenomena The following section will summarize the experimental works on the FCI phenomena with a focus on the solidification effects In SFRs and LWRs, the influence of solidification effects on FCI is important

In SFRs, stable film boiling could not be formed around a melt

(Kondo et al., 1995;Suzuki et al., 2014;Vanderhaegen and Belguet,

2014) because the melt and the coolant were partly in direct contact

Fauske et al (2002)pointed out that solidification of the melt surface

occurs during FCI in SFRs Previous works (Bürger et al., 1985,1986)

have pointed out that the solidification effects could suppress the

fragmentation phenomena However,Magallon et al (1992)reported

that intensive fragmentation occurred in the experiment at the FARO/

TERMOS facility, and the size of the fragments obtained from the

ex-periment were of the order of 103∼101μm Therefore, the solidification

effects on the fragmentation phenomena are required to be investigated

from the viewpoint of debris coolability

In LWRs, the solidification could also occur (Dombrovsky and Dinh,

2008; Uršič et al., 2012) The solidification effects are important,

especially with regard to the fragmentation phenomenon, which may

lead to vapor explosion (Bürger et al., 1985,1986;Uršič et al., 2010,

2011;Uršič and Leskovar, 2011,2012,2015).Dombrovsky and Dinh

(2008),Uršič et al (2010,2011),Uršič and Leskovar, 2011andUršič

and Leskovar (2012)developed a model to calculate the temperature

involved in the solidification effects on a melt droplet, andUršič et al

(2015)reflected the model into an integrated code for evaluating vapor

explosion

5.1 Experimental works on solidification effects

This section summarizes the previous experiments on the FCI

phe-nomena that focused on the solidification effects They are listed in

Table 7 The previous experiments include in which several grams to

several hundred kilograms of melt were injected, that is, ranging from

melt droplets to melt jets Although the experiments with the simulant

melt were summarized inTable 7, there are the study investigate the

solidification effects in the experiments with corium melt using

simu-lation (Uršič et al., 2012;Uršič and Leskovar, 2012)

In the previous works, solidification of the melt surface has been

re-ferred to by specific terminology: surface freezing (Fauske et al., 2002) and

surface solidification (Yang and Bankoff, 1987;Cao et al., 2002;Iwasawa

et al., 2015a,2015b) The crust formed on the melt surface leads to shrink

and crack due to thermal stress in the experiments conducted using oxide

melt (Schins and Gunnerson, 1986;Tyrpekl et al., 2014) Investigating the

influence of the solidification effects on the jet-breakup and the

frag-mentation phenomena in NPPs is difficult, and investigating the

solidifi-cation effects separately is one of the effective approaches

We have supplementarily mentioned that the cracking subsequent

to curst formation has been researched widely and extensively

(Cronenberg et al., 1974; Cronenberg and Fauske, 1974; Knapp and

Todreas, 1975;Ladisch, 1977;Corradini and Todreas, 1979;Cao et al.,

2002;Dombrovsky, 2009) Because details of these works are beyond

the scope of this article, we have omitted detailed description of these

significant works

InTable 7, Bürger et al (1985, 1986) from IKE and Yang and Bankoff (1987)from Northwestern University (NU) conducted experi-ments in which they observed the fragmentation phenomena More-over, they measured the shape and size of the fragments by injecting a melt droplet into streaming water.Li et al (1998)andHaraldsson et al (2001)from KTH, Nishimura et al (2002)from CRIEPI, and Zhang

et al (2009)andZhang and Sugiyama (2010,2011,2012)from Hok-kaido University (HU) conducted experiments in which they observed the fragmentation phenomena and measured the shape and size of the fragments by injecting melt droplets into static water Then, Bürger

et al (1985, 1986)pointed out that fragmentation and solidification were competitive processes and classified various fragmentation modes based on observation results and fragment shape Li et al (1998) pointed out that the eutectic melt experience deeper fragmentation than the non-eutectic melt Also,Li et al (1998)mentioned that non-eutectic melt in the mushy zone (a mixture of liquid melt andfine solid particles in the preceding cooling process) will become increasingly viscous, and will prevents the fragmentation, especially when the melt superheat is small Yang and Bankoff (1987) and Haraldsson et al (2001) proposed the criteria under which a melt droplet breaks up based on the work ofEpstein (1977).Nishimura et al (2002),Zhang

et al (2009), andZhang and Sugiyama (2010,2011,2012)pointed out that fragment size increases owing to the solidification effects and proposed an empirical correlation for estimating the fragment size Sugiyama et al (1999)conducted an experiment in which they in-jected a simulant melt in the form of a melt jet and reported that the sediments obtained in the experiment were cylindrical, which indicates that the crust could be formed by solidifying the melt surface before the jet-breakup Moreover, the previous works (Nishimura et al., 2005,

2010;Iwasawa et al., 2015b) reported that sheet- andfilament-shaped fragments were formed in addition to the cylindrical sediments The previous works (Nishimura et al., 2010; Iwasawa et al., 2015a) also reported that a melt jet breaks up under the condition that vj and coolant temperature are relatively high, despite the solidification ef-fects At this time,Iwasawa et al (2015a)concluded that the correla-tion proposed byEpstein and Fauske (2001)can be applied to the es-timation of Lbrk Moreover,Nishimura et al (2010) proposed that an empirical correlation for estimating fragment size under high Weber number, which refers to a scenario in which hydrodynamic interactions become dominant In these works (Nishimura et al., 2005, 2010; Iwasawa et al., 2015a,2015b), the condition that solidification effects become dominant is defined as the point when the initial interfacial temperature Ti(Fauske, 1973) is lower than the melting point of a melt

in an initial condition Under the condition that the solidification effects become dominant, however, few works have investigated and con-structed a mechanistic model for estimating the size of particulate fragments from a melt jet In the next section, an up-to-date model for estimating fragment size, including the influence of the solidification

effects on a melt jet, will be presented

Table 7

Previous experiments on the FCI phenomena focused on solidification effects

Water

Droplet Injection

Bürger et al (1985 , 1986)

Water

Droplet Injection

Yang and Bankoff (1987)

Water

Jet Injection

Sugiyama et al (1999)

Injection

Li et al (1998) Haraldsson et al (2001)

Injection

Nishimura et al (2002 , 2005 , 2010)

Injection

Zhang et al (2009) Zhang and Sugiyama (2010 , 2011 , 2012)

197