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.

Progress in Nuclear Energy 108 (2018) 188–203 Contents lists available at ScienceDirect Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene Review Melt jet-breakup and fragmentation phenomena in nuclear reactors: A review of experimental works and solidification effects T Yuzuru Iwasawaa,∗, Yutaka Abeb a b Graduate School of Systems and Information Engineering, University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki, 305-8573, Japan Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1, Tennodai, Tsukuba, Ibaraki, 305-8573, Japan A R T I C LE I N FO A B S T R A C T Keywords: Nuclear reactor Severe accident Fuel-coolant interaction Jet-breakup Fragmentation 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 Therefore, fragmentation of the melt jet and quenching of particulate fragments from the melt jet are invaluable from the viewpoint of safety assessment To assess the integrity 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 experimental 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 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 characteristic 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 explosion, 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 experiments using actual fuels, scoping experiments focusing on the fundamental 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 Corresponding author E-mail address: iwasawa.yuzuru.xu@alumni.tsukuba.ac.jp (Y Iwasawa) https://doi.org/10.1016/j.pnucene.2018.05.009 Received August 2017; Received in revised form 21 March 2018; Accepted 11 May 2018 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/) Progress in Nuclear Energy 108 (2018) 188–203 Y Iwasawa, Y Abe Nomenclature Greek symbol d D Dj E E0 Fr g k Lbrk P t Ti ΔTc u U v V vj vrel x y δ ε γt γy ϕ η κ λ λn λm ρ σ ω characteristic length bending stiffness jet diameter Young's modulus entrainment coefficient Froude number gravitational acceleration wave number jet-breakup length pressure time initial interfacial temperature coolant subcooling fluctuating velocity in horizontal direction uniform velocity in horizontal direction fluctuating velocity in vertical direction uniform velocity in vertical direction jet velocity relative velocity horizontal direction vertical direction crust thickness Poisson's ratio temporal growth rate spatial growth rate velocity potential displacement of interface thermal conductivity wavelength neutral-stable wavelength most-unstable wavelength density interfacial tension or surface tension angular frequency Subscript j, c, s w initial melt jet coolant sodium water Previous experiments on FCI phenomena discusses dominant the factors governing jet-breakup and fragmentation Furthermore, this article discusses the applicability of various models for estimating these phenomena The remainder of this is organized as follows In Chapter 2, previous 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 In Chapter 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 jetbreakup length are presented based on their applicability In Chapter 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 applicability In Chapter 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 concludes this article 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 fragmentation 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 phenomena involving oxide melt and sodium, which mainly target SFRs They are summarized in Table 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 Table Previous experiments on FCI phenomena conducted using oxide/sodium system Organization (Test facility or program) Melt/Coolant References ANL (M-Series) SNL (FLAG) JRC (BETULLA) UO2-Mo, UO2-ZrO2-SS/ Sodium Fe-Al2O3, UO2-ZrO2-SS/ Sodium UO2, Al2O3/Sodium Johnson et al (1975) Sowa et al (1979) Chu (1982) JRC UO2/Sodium (FARO/TERMOS) JAEA (FR Tests) IPPE (Pluton) Al2O3/Sodium ZrO2- Fe/Sodium 189 Holtbecker et al (1977) Schins (1984) Schins et al (1984, 1986) Schins and Gunnerson (1986) Magallon et al (1992) Matsuba et al (2012, 2015a, 2015b, 2016) Zagorul'ko et al (2008) Progress in Nuclear Energy 108 (2018) 188–203 Y Iwasawa, Y Abe 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 experiments conducted in the FZK (Huber et al., 1996; Schütz et al., 1997; Kaiser et al., 1997, 1999, 2001) involved injecting uranium oxide-zirconia (so-called corium) or alumina melt The results of these experiments provided an important database and significant knowledge on FCI phenomena in actual reactors JAERI conducted a series of experiments called GPM (Moriyama et al., 2005), which involved injecting 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 Institute (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 accident 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 InVessel Corium Retention External Reactor Cooling (IVR-ERVC) Na et al (2014, 2016), Hong et al (2016), and Song et al (2017) conducted 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 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 comparable 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 phenomena conducted using metallic melt and sodium, which mainly target SFRs They are listed in Table 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 fragments 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 aluminum 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 phenomena conducted using oxide melt and water, which mainly target LWRs They are listed in Table 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 2.4 Metal/water system This section summarizes the previous experiments on the FCI phenomena conducted using metallic melt and water coolant, which mainly target LWRs or SFRs They are listed in Table These experiments are focused on fundamental processes of the FCI Table Previous experiments on FCI phenomena conducted using metal/sodium system Organization (Test facility or program) Melt/Coolant References JRC (BETULLA) SS, Cu/Sodium ANL CRIEPI U, U-Zr, U-Fe/ Sodium Ag, Cu/Sodium Benz and Schins (1982) Schins (1984) Schins and Gunnerson (1986) Schins et al (1986) Gabor et al (1988) JAEA Al/Sodium 190 Nishimura et al (2002, 2005, 2010) Matsuba et al (2016) Progress in Nuclear Energy 108 (2018) 188–203 Y Iwasawa, Y Abe Table Previous experiments on FCI phenomena conducted using oxide/water system Organization (Test facility or program) Melt/Coolant References SNL Al2O3-Fe/Water UO2-Mo/Water Mitchell et al (1981) Corradini (1981) Denham et al (1994) UO2-ZrO2-SS/Water Spencer et al (1994) Al2O3-FeO, Al2O3-Fe2O3/Water ZrO2, Zr/Water Yamano et al (1995) (FITS) UKAEA (MIXA) ANL (CCM) JAERI (ALPHA) ANL (ZREX) JRC/CEA (KROTOS) JRC Cho et al (1997, 1998) Al2O3, UO2-ZrO2/Water Al2O3-Fe/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) Magallon and Hohmann (1995) Magallon and Huhtiniemi (2001) Magallon et al (1997, 1999) Magallon (2006) Huber et al (1996) Schütz et al (1997) Kaiser et al (1997, 1999, 2001) Cherdron et al (2005) Al2O3-ZrO2, SS-C/Water Moriyama et al (2005) CaO-B2O3, MnO2-TiO2, WO3-CaO/Water ZrO2- Fe/Sodium Haraldsson and Sehgal (1999) Haraldsson (2000) Zagorul'ko et al (2008) CaO-B2O3, WO3-CaO, MnO-TiO2, WO3-TiO2, Bi2O3-TiO2, Bi2O3-CaO, Bi2O3-WO3, WO3-ZrO2 /Water UO2-ZrO2-Zr, UO2-ZrO2, ZrO2-Zr, ZrO2, Al2O3 /Water Kudinov et al (2008, 2010, 2013, 2015) Karbojian et al (2009) UO2-ZrO2/Water (FARO/TERMOS, FAT) FZK Al2O3-Fe/Water (PREMIX) FZK (ECO) JAERI (GPM) KTH (MIRA) IPPE (Pluton) KTH (DEFOR) KAERI (TROI) KTH (MISTEE-jet/JEBRA) WO3-Bi2O3, WO3-ZrO2 /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) Manickam et al (2014, 2016, 2017) thermocouples on the central axis of the nozzle The experiment conducted 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 Institute 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) 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 Tsukuba (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 Corporation (PNC) using the MELT-II facility (Kondo et al., 1995) and the experiment 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 2.5 Experiment with other simulant materials This section summarizes the previous experiments on the FCI phenomena using other simulant materials, mainly targeting LWRs or SFRs They are listed in Table 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 191 Progress in Nuclear Energy 108 (2018) 188–203 Y Iwasawa, Y Abe Table Previous experiments on FCI phenomena conducted using metal/water system Organization (Test facility or program) Melt/Coolant References ANL IKE Wood’ metal/Water Wood’ metal/Water JRC ANL BNL PNC (MELT-II) KTH Wood’ metal/Water Al, Al-U/Water Tin/Water Wood’ metal/Water Spencer et al (1986) Cho et al (1991) Berg et al (1994) Bürger et al (1995) Schins et al (1992) Gabor et al (1992, 1994) Hall and Fletcher (1995) Kondo et al (1995) JAERI Zn, Sn, Cu/Water KMU KMU (COLDJET) UT Wood’ metal/Water Wood’ metal/Water JAEA IGCAR CH IIT Wood’ metal/Water Wood’ metal/Water Al, Pb, Bi/Water Pb, Al/Water, Glycerol Wood’ metal, Ga/ Water Wood’ metal/Water Wood’ metal/Water TIT UT MATE (POSTEC) KTH (MISTEE-jet/JEBRA) SJTU (METRIC) Wood’ metal/Water Dinh et al (1999) Haraldsson (2000) Sugiyama et al (1999) Sugiyama and Yamada (2000) Sugiyama and Iguchi (2002) Bang et al (2003) Kim and Bang (2016) Bang and Kim (2017) Abe et al (2004, 2005, 2006) Matsuo et al (2008) Iwasawa et al (2015a, 2015b) Matsuba et al (2013) Mathai et al (2015) Lu et al (2016) Pillai et al (2016) Wood’ metal/Water Takahashi et al (2015) Secareanu et al (2016) Wei et al (2016) Jung et al (2016) Sn, Wood’ metal/ Water Sn/Water Manickam et al (2014, 2017) Li et al (2017) Table Previous experiments on FCI phenomena using experiment other simulant materials Organization (Test facility or program) Melt/Coolant References PNC (JET-I) ANL (MFSBS) KTH Water/Nitrogen, Freon Saito et al (1988) Wood’ metal/Freon Schneider et al (1992) Schneider (1995) Dinh et al (1999) Water, Salt, Wood’ metal/ Paraffin oil, Salt 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 and Fauske (2001) proposed these correlations, which are representative 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: Jet-breakup phenomena ρj 0.5 Lbrk = 2.1 ⎜⎛ ⎟⎞ Fr 0.5 Dj ⎝ ρc ⎠ 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 Fr = (1) vj2 gDj (2) where Lbrk denotes the jet-breakup length, Dj denotes the inlet diameter of a melt jet, vj denotes the velocity of a melt jet, ρ denotes the density of fluid, and Fr denotes the Froude number defined by Saito et al (1988), respectively Subscripts j and c denote the jet and the coolant, respectively Epstein and Fauske (2001) proposed a semi-empirical correlation 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) and Epstein 192 Progress in Nuclear Energy 108 (2018) 188–203 Y Iwasawa, Y Abe Fig Normalized jet-breakup length obtained from previous experiments are organized by Froude number Fr The values obtained using the correlations proposed by Saito et al (1998) and Epstein and Fauske (2001) are compared with the measured jet-breakup length 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: that the correlation proposed by Saito et al (1988) depends on vj By contrast, the correlation proposed by Epstein and Fauske (2001) is independent of vj 0.5 Lbrk ⎛ ρj ⎞ = ⎜ ⎟ Dj 2E0 ⎝ ρc ⎠ 3.2 Experimental data on jet-breakup length (3) Fig shows the jet-breakup length Lbrk obtained from previous experiments organized by Froude number Fr In Fig 1, the vertical axis represents the normalized Lbrk obtained using a jet diameter Dj and density ratio of melt to coolant ρj/ρc, and the horizontal axis represents where E0 denotes the tuning parameter called “the entrainment coefficient”, 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 Table Previous experiments conducted under nearly saturated or saturated water conditions Organization (Test facility or program) Melt/Coolant References ANL FZK (PREMIX) JAERI (GPM) MATE (POSTEC) Wood’ metal/Water Al2O3-Fe/Water Spencer et al (1986) Kaiser et al (2001) Al2O3-ZrO2, SS-C/Water Moriyama et al (2005) Wood’ metal/Water Jung et al (2016) 193 Progress in Nuclear Energy 108 (2018) 188–203 Y Iwasawa, Y Abe Fr The open plots indicate the Lbrk obtained in the experiments using water, and the filled plots indicate the Lbrk obtained in the experiments using sodium Note that the legend in Fig shows 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 Lbrk proposed by Saito et al (1988), and the dashed line indicates the correlation for estimating Lbrk proposed by Epstein and Fauske (2001) Several methods were used to measure Lbrk because of the limitations 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 highspeed 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), Lbrk was 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 Effects of coolant subcooling on jet-breakup length obtained from previous experiments The results obtained using the correlation proposed by Epstein and Fauske (2001) are shown for reference Fig Normalized fragment sizes (MMDs) obtained from previous experiments are organized based on Weber number The critical Weber number theory is presented for reference 194 Progress in Nuclear Energy 108 (2018) 188–203 Y Iwasawa, Y Abe the previous experiments in Table in which the coolant temperature was varied as a test condition Then, we organized the Lbrk values in Table in terms of the coolant subcooling ΔTc in Fig In Fig 2, the vertical axis represents the normalized Lbrk, as in Fig 1, and the horizontal axis represents ΔTc The dashed line indicates the correlation for estimating Lbrk proposed by Epstein and Fauske (2001) for reference In Fig 2, high ΔTc means the coolant temperature is low, and low ΔTc means the coolant temperature is nearly saturated or saturated Hence, we can interpret that at high ΔTc, coolant vapor may condense easily, that is, a stable vapor film would be difficult to form From Fig 2, we can recognize that as ΔTc increases, Lbrk tends 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 generation on the jet-breakup and the fragmentation phenomena This program now is in progress Therefore, they may provide further knowledge and clear conclusion in future works Also, we need to verify not only effects of coolant subcooling but also other integral effects including 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 directly (Magallon, 2006) In these experiments, the jet-breakup length could not be measured Therefore, we excluded these experimental results from Fig From Fig 1, we can recognize that the Lbrk values obtained from the previous experiments show two trends: Lbrk increases as Froude number increases, and Lbrk remains almost constant in spite of some variations Moreover, we can see that the Lbrk values obtained from the previous experiments targeting LWRs and SFRs have no significant differences, regardless of the experimental scales Almost all of the Lbrk values are close to those obtained using the correlation proposed by Epstein and Fauske (2001) However, the Lbrk values 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 by Saito et al (1988) In previous works, Moriyama et al (2005) proposed criteria for determining the applicability of the correlation for estimating Lbrk by using the Bond number; Lbrk follows the correlation by Saito et al (1988) when the Bond number is small (< 50), and Lbrk follows 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 by Abe 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 by Jung et al (2016) followed the correlation by Saito 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 by Epstein 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 applicability of the correlations 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 interactions 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 complex and non-linear deformation The classical KHI in two-dimensions (JSME, 1995) is a linear stability 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: 3.3 Dominant factors affecting jet-breakup length In Table 6, we summarize the experiments in which nearly saturated or saturated water was used as the coolant and where the Lbrk valued obtained were close to those yielded by the correlation proposed by Saito et al (1988) In the experiments summarized in Tables 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 contact 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 interfacial instability Consequently, the Lbrk values 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 vapor film to be formed and sustained, which leads to the intensive jetbreakup Consequently, the Lbrk values may agree with those obtained using the correlation proposed by Epstein and Fauske (2001) To investigate the effects of vapor generation on Lbrk, we focused on λKHn = λKHm = 2πσ (ρ1 + ρ2 ) ρ1 ρ2 vrel (4) 3πσ (ρ1 + ρ2 ) ρ1 ρ2 vrel (5) where λKHn and λKHm denote 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 descriptions of the physical meanings of these wavelengths will be presented in Chapter Here, ρ denotes density, σ denotes interfacial tension, and vrel denotes the relative velocity between the two-phases Previous works (Matsuo et al., 2008; Iwasawa et al., 2015a, 2015b) employed vj of a melt jet as vrel under 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 hydrodynamic force that deforms a droplet and the interfacial force that helps a droplet retains its shape, and it is expressed as follows: We = 195 ρvrel d σ (6) Progress in Nuclear Energy 108 (2018) 188–203 Y Iwasawa, Y Abe 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) and Tyrpekl et al (2014) mentioned that differences in the fragmentation phenomena between the oxide and the metallic melt They mentioned that the effects of (as follows) are dominant in both oxide and metallic melt 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 Hydrodynamic fragmentation due to prompt boiling of the coolant This leads to prompt fragmentation and generates smooth spherical fragments Fig shows the fragment sizes obtained in the previous experiments 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 Dj of a melt jet is used instead of droplet diameter In Fig 3, the vertical axis represents the fragment sizes expressed by the mass median diameter (MMD) normalized in terms of Dj and 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 shows the organization where the experiments were carried out, test facility or program, meltcoolant composition, and related references Also, the CWT is shown and compared with the MMDs for reference In Fig 3, overall, the MMDs obtained in the previous experiments decrease as the Weber number increases The increase in vj, which induces 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 hydrodynamic interactions, can be used to estimate the MMDs when the Weber number is low (almost of the order of 101-102 i.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 obtained from in the previous experiments targeting SFRs (i.e using sodium coolant) are smaller than those obtained in the previous experiments targeting LWRs Fig 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 Schins and Gunnerson (1986) and Tyrpekl et al (2014) also mentioned that the effects of and (as follows) are present in the oxide melt 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 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) and Tyrpekl 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 fragmentation 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: 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) 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 semitransparent melt mentioned by Dombrovsky 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, convective 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 solidification effects separately is an effective approach 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 fragmentation 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 morphology 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 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 196 Progress in Nuclear Energy 108 (2018) 188–203 Y Iwasawa, Y Abe Table Previous experiments on the FCI phenomena focused on solidification effects Organization Melt/Coolant Experiment References IKE CRIEPI Cu/Sodium HU Cu/Sodium Droplet Injection Droplet Injection Jet Injection Droplet Injection Droplet/jet Injection Droplet Injection Bürger et al (1985, 1986) KTH Wood’ metal/ Water Wood’ metal/ Water Sn, Tin/ Water Pb-Bi/Water NU JAERI 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 experiment were of the order of 103∼101 μm 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, 2011 and Uršič and Leskovar (2012) developed a model to calculate the temperature involved in the solidification effects on a melt droplet, and Uršič et al (2015) reflected the model into an integrated code for evaluating vapor explosion Yang and Bankoff (1987) Sugiyama et al (1999) Li et al (1998) Haraldsson et al (2001) Nishimura et al (2002, 2005, 2010) Zhang et al (2009) Zhang and Sugiyama (2010, 2011, 2012) In Table 7, Bürger et al (1985, 1986) from IKE and Yang and Bankoff (1987) from Northwestern University (NU) conducted experiments in which they observed the fragmentation phenomena Moreover, they measured the shape and size of the fragments by injecting a melt droplet into streaming water Li et al (1998) and Haraldsson et al (2001) from KTH, Nishimura et al (2002) from CRIEPI, and Zhang et al (2009) and Zhang and Sugiyama (2010, 2011, 2012) from Hokkaido 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 noneutectic melt in the mushy zone (a mixture of liquid melt and fine 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 of Epstein (1977) Nishimura et al (2002), Zhang et al (2009), and Zhang 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 injected 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- and filament-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 effects At this time, Iwasawa et al (2015a) concluded that the correlation proposed by Epstein and Fauske (2001) can be applied to the estimation 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 constructed 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 5.1 Experimental works on solidification effects This section summarizes the previous experiments on the FCI phenomena that focused on the solidification effects They are listed in Table 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 in Table 7, there are the study investigate the solidification effects in the experiments with corium melt using simulation (Uršič et al., 2012; Uršič and Leskovar, 2012) In the previous works, solidification of the melt surface has been referred 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 fragmentation phenomena in NPPs is difficult, and investigating the solidification 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 197 Progress in Nuclear Energy 108 (2018) 188–203 Y Iwasawa, Y Abe ∂v ∂v ∂P +V =− +g ∂t ∂y ρ ∂y (9) where P denotes pressure, and g denotes gravitational acceleration Eqs (7)–(9) are applied to the melt jet and the coolant Note that the nonlinear term is neglected from the Euler equations because of the assumption that the interface fluctuation is small enough This assumption also means that the interface displacement is small enough and can be expressed as follows: η (t , y ) = η0 ei (ωt − ky) (10) From Eq (10), we can recognize that a constant-amplitude wave with no decrease travels except if ω and k have positive imaginary parts In the present model, the interface fluctuation induces the fluctuated velocities u and v The relationship between the fluctuated velocity u and the interface displacement η is expressed as follows: u= Fig Schematic of linear stability model, including solidification effects Crust formation at the melt jet-coolant interface (Iwasawa et al., 2015b) D The following section presents a mechanistic model for estimating fragment size, including the influence of the solidification effects on a melt jet, proposed by Iwasawa et al (2015b) The detailed description and derivations are presented in the following sections The present model is based on previous works (Epstein, 1977; Haraldsson et al., 2001) ∂ 2η ∂ 4η − σ = P1 − P2 ∂y ∂y (12) where σ denotes interfacial tension, and D denotes bending stiffness In Eq (12), the first term on the left-hand side denotes the elastic force due to the mechanical strength of the crust, and the second term on the left-hand side denotes the interfacial force acting on the crust Note that σ is defined as σ = σ1+σ2 (Epstein, 1977): σ1 refers to the interfacial force between the melt jet and the crust, and σ2 refers to the interfacial force between the coolant and the crust Iwasawa et al (2015b) used the measured values in air as an alternative because estimation or measurement of the exact values of σ1 and σ2 is difficult The crust may be formed on the melt jet-coolant interface during the jet-breakup and the fragmentation phenomena Therefore, the physical meaning and the value of D may be different from those of D considered and measured in solid material According to potential flow, the fluctuated velocities u, v are expressed using the velocity potential ϕ: 5.2.1 Modeling assumptions and governing equations This section describes the assumptions and the governing equations of the present model The present model employs a linear stability theory to calculate the growth of fluctuation at a melt jet-coolant interface based on previous works (Epstein, 1977; Haraldsson et al., 2001) and assumes that the melt jet-coolant interface extends infinitely along the vertical, as shown in Fig 4, for simplification The simplified system shown in Fig considers interfacial instability with the crust, which has a certain thickness δ Subscripts and denote the melt jet and the coolant, respectively In Fig 4, Cartesian coordinates are employed: the x-direction is along to the horizontal, and the y-direction is along the vertical Fluid (region x < 0) with density ρ1 flows along with the vertical with uniform velocity V1, and fluid (region x < 0) with density ρ2 flows along the vertical with uniform velocity V2 In addition, following assumptions are applied: u=− ∂ϕ ∂ϕ , v=− ∂y ∂x (13) In addition, ϕ satisfies the following boundary conditions and the continuity equation expressed as Eqs (14) and (15) ∂ϕ1 ∂ϕ2 (t , −∞, y ) = 0, (t , ∞, y ) = ∂y ∂y (1) Viscosity is assumed to be negligible compared to interfacial tension and crust stiffness (2) Crust is thin enough, so inertia is neglected Moreover, interface fluctuation is small enough, so the linear stability theory can be applied (3) Melt jet and coolant are assumed to be incompressible and irrotational Therefore, the present model assumes potential flow (4) The crust has no edge, that is, infinite size, and a constant thickness Also, thermal stress due to temperature gradient can be neglected ∂ 2ϕ ∂x + ∂ 2ϕ ∂y =0 (14) (15) 5.2.2 Derivation of interface growth rate In this section, we derive the growth rate of the interface displacement to calculate the characteristic wavelengths based on the linear stability theory The temporal growth rate γt and the spatial growth rate γy are employed They are expressed as follows using Eq (10) (Itoh et al., 2004; Matsuo et al., 2008): Based on the above assumptions, the present model employs the continuity and the Euler equations in two dimensions as follows: ∂u ∂u ∂P +V =− ∂t ∂y ρ ∂x (11) To include the solidification effects, the modified Laplace law can be employed and expressed as follows (Epstein, 1977; Haraldsson et al., 2001): 5.2 Model for estimating fragment size (Iwasawa et al., 2015b) ∂u ∂v + =0 ∂x ∂y ∂η ∂η dη +V = ∂y ∂t dt (7) (8) dη ⎞ γt ≡ Re ⎜⎛ ⎟ = Re(iω) = − ωi ⎝ η dt ⎠ (16) dη ⎞ γy ≡ Re ⎜⎛ ⎟ = Re(ik ) = − k i ⎝ η dy ⎠ (17) From Eqs (16) and (17), we derive the relationship between 198 Progress in Nuclear Energy 108 (2018) 188–203 Y Iwasawa, Y Abe Iwasawa et al (2015b) assumed that only the temporal growth rate γt could be considered, that is, the spatial growth rate γy could be ignored when calculating the characteristic wavelengths According to the assumption, we can obtain γy = 0, that is, - ki = from Eq (17) This means that the k in the fluctuation has no imaginary part; then, the first term of the left-hand side in Eq (24) has real parts From Eq (16), Eq (24) needs to have an imaginary part to ensure temporal growth of the fluctuation Therefore, the second term of the left side in Eq (24) needs to be imaginary Consequently, we can obtain γt, expressed as follows, by using the relationship k = 2/λ: angular frequency ω and wave number k (dispersion relation) of the fluctuation To derive the dispersion relation, Eq (8) is rewritten as Eq (18) by integrating along the x-direction and replacing u and v using ϕ: P=ρ ∂ϕ ∂ϕ + ρV ∂t ∂y (18) Now, we assume that ϕ is independent of the space x, y and the time t, and it fluctuates periodically with time In addition, we assume that the interface fluctuation prevails only along the forward y-direction and satisfies the boundary condition expressed by Eq (14) Then, we can rewrite ϕ as Eq (19) ϕ1 (t , x , y ) = ϕ01 e kx ei (ωt − ky), ϕ2 (t , x , y ) = ϕ02 e−kx ei (ωt − ky) ρ ρ (V1 − V2)2 2π σ 2π D 2π ⎛ ⎞ − ⎛ ⎞ − ⎛ ⎞⎤ γt = ⎡ 2 ⎢ (ρ + ρ ) ρ1 + ρ2 ⎝ λ ⎠ ρ1 + ρ2 ⎝ λ ⎠ ⎥ ⎝ λ ⎠ ⎣ ⎦ (19) where ϕ01 and ϕ02 denote unknown constants We substitute Eqs (10) and (19) into Eq (18), and compute the difference related to the P of each phase (melt jet and coolant) to obtain Eq (20) (25) On the right-hand side of Eq (25), the first term refers to the destabilizing effects caused by a dynamic pressure drop owing to the velocity deference between each phase (melt jet and coolant), second term refers to the stabilizing effects of interfacial tension, and the third term refers to the stabilizing effects of the elastic force due to mechanical strength of the crust The interface becomes unstable when the term in the square root of Eq (25) has positive parts, which is the case when first term is larger than the last two terms Note that if the third term is negligible (D = 0), we can easily introduce the KHI (Haraldsson et al., 2001; Iwasawa et al., 2015b) P1 − P2 = ϕ01 ρ1 (ω − kV1) ie kx ei (ωt − ky) − ϕ02 ρ2 (ω − kV2) ie−kx ei (ωt − ky) (20) Next, we substitute Eq (10), Eq (13), and Eq (19) into Eq (11) to obtain Eq (21) ϕ01 ke kx = −η0 (ω − kV1) i, ϕ02 ke−kx = η0 (ω − kV2) i (21) Furthermore, we obtain Eq (22) by substituting Eq (10) into Eq (12) Dk + σk 2η0 ei (ωt − kx ) = P1 − P2 5.2.3 Solidification effects on interfacial instability This section presents the influence of the solidification effects on interfacial instability Fig 5(a) shows the calculated relationship between γt and λ from Eq (25) under the condition V1 - V2 = 1.0 m/s and D = Note that the previous work (Iwasawa et al., 2015b) employed the values of physical properties from the previous experiments (Iwasawa et al., 2015a) In the experiment, Iwasawa et al (2015a) employed low melting point alloy (Bi-Sn eutectic) In Fig 5(a), the third term on the left-hand side of Eq (25) is zero, that is, D = This means that each phase is in direct-mechanical contact (no crust), and the KHI can be calculated From Fig 5(a), if λ is large and of a certain length, the temporal growth rate γt starts to increase abruptly from zero This indicates that the interface becomes unstable and starts to grow The value of λ at which the interface becomes unstable is called neutralstable wavelength λn (Itoh et al., 2004; Matsuo et al., 2008; Iwasawa et al., 2015b) Furthermore, from Fig 5(a), if λ is lager than λn and a certain length, γt is maximized This indicates that the interface is as unstable (22) Finally, we obtain Eq (23), which is the dispersion relation in the present model, by substituting Eq (20) into Eq (22) and eliminating e ± ky using Eq (21) Note that Eq (23) is arranged about ω (ρ1 + ρ2 ) ω2 − 2k (ρ1 V1 + ρ2 V2) ω − Dk − σk + (ρ1 V12 + ρ2 V22) k = (23) This equation can be solved easily for ω because Eq (23) is a quadratic equation on ω Therefore, we can obtain the dispersion relation in the present model as follows: ω= (ρ1 V1 + ρ2 V2) k ± ρ1 + ρ2 ρ ρ (V1 − V2)2k Dk σk + − ρ1 + ρ2 ρ1 + ρ2 (ρ1 + ρ2 )2 (24) Iwasawa et al (2015b) used MMD as an index of fragment size They pointed out that the spatial effects on the jet-breakup and the fragmentation phenomena are averaged by using MMD Therefore, Fig Calculated temporal growth rate against wavelength: (a) Kelvin-Helmholtz instability, (b) solidification effects (Iwasawa et al., 2015b) 199 Progress in Nuclear Energy 108 (2018) 188–203 Y Iwasawa, Y Abe Fig Calculated variations in wavelength against relative velocity, and effects of bending stiffness (Nm) (Iwasawa et al., 2015b) as it can be The wavelength λ at which the two-phase interface becomes as unstable as it can be is called the most-unstable wavelength λm (Itoh et al., 2004; Matsuo et al., 2008; Iwasawa et al., 2015b) Note that we can easily calculate λn and λm from γt = and dγt/dt = 0, respectively Hence, we confirm that the present model can estimate the growth rate and the wavelength of the fluctuation Fig 5(b) show the calculated relationship between γt and λ from Eq (25) under the condition of V1 - V2 = 1.0 m/s, D = 0, and D = 1.0 Nm From Fig 5(b), we can recognize that γt and λ are smaller when D = 1.0 Nm than that when D = According to the calculated results, we can recognize that in the present model, the crust significantly shifts the interfacial instability Fig shows the calculated results of the characteristic wavelengths, λn, and λm, by varying D to investigate sensitivity In Fig 6, the values of λn and λm calculated from the present model are compared with those calculated from the KHI and the fragment diameter d calculated based on the CWT Note that the bending stiffness D is varied from 10−7 to 10−4 Nm From Fig 6, we can recognize that the λn and λm calculated using the present model are larger than those calculated without the crust In addition, we can recognize that as D increases, λn and λm increase According to Fig 6, the present model significantly shifts the interfacial instability as D increases, that is, the solidification effects 5.2.4 Comparison with experimental data This section presents the results of comparison between the characteristic wavelengths and the MMDs obtained in the previous experiment (Iwasawa et al., 2015b) and discuss the applicability of the present model In the previous work (Iwasawa et al., 2015b), spherical, filament-, and sheet-shaped fragments were obtained in an experiment in which a melt jet was injected; this experiment focused on solidification effects Iwasawa et al (2015a, 2015b) used Ti to determine the initial conditions of the experiments If Ti decreases to a value lower than the melting point of the melt, the solidification effects could be dominant (called surface solidification condition) By contrast, if Ti increases to be higher than the melting point of the melt, the solidification effects could be less dominant (called liquid-liquid contact condition) Fig 7(a) shows a comparison between the results of MMD measurement base only on the spherical fragments and the characteristic wavelengths based on KHI, as well as fragment size based on the CWT In Fig 7, the red-open symbols denote the MMDs obtained under the liquid-liquid contact condition, and the blue-closed symbols denote the MMDs obtained under the surface solidification From Fig 7(a), we can recognize that the KHI and the CWT can be applied to estimate the fragment size of spherical fragments Fig 7(b) shows a comparison Fig Comparison of MMDs and the classical theories (KHI and CWT): (a) MMDs of spherical fragments, (b) MMDs of filament- and sheet-shaped fragments (Iwasawa et al., 2015b) between the results of MMD measurement based on filament- and sheetshaped fragments and the characteristic wavelengths based on the KHI, as well as the fragment size based on CWT From Fig 7(b), by contrast, the KHI and CWT cannot be applied for estimating the size of filament-, and sheet-shaped fragments Iwasawa et al (2015b) pointed out that filament-, and sheet-shaped fragments were generated under the condition that the solidification effects become dominant Therefore, they pointed out that a model considering the solidification effects was necessary to estimate the size of filament- and sheet-shaped fragments Fig shows a comparison between the results of MMD measurement based on filament-, and sheet-shaped fragments and the 200 Progress in Nuclear Energy 108 (2018) 188–203 Y Iwasawa, Y Abe of a melt jet during a severe accident in NPPs In addition, we focused on the solidification effects Much progress has been made in terms of understanding the jet-breakup and the fragmentation phenomena over the past few decades Based on a literature survey, in this article, we presented the data obtained from the experimental works on jetbreakup length and fragment size In addition, we discussed dominant factors governing the jet-breakup and the fragmentation phenomena Furthermore, we discussed models for estimating the jet-breakup and the fragmentation phenomena The influence of the solidification effects on the FCI phenomena were summarized, and an up-to-date model including the solidification effects for estimating the fragment size was presented Acknowledgements This work was supported by JSPS KAKENHI Grant Number 261960 Y I is grateful to A Kaneko (University of Tsukuba) and K Koyama (Mitsubishi FBR Systems, Inc.) for helpful discussions References Abe, Y., Kizu, T., Arai, T., Nariai, H., Chitose, K., Koyama, K., 2004 Study on thermalhydraulic behavior during molten material and coolant interaction Nucl Eng Des 230, 277–291 Abe, Y., Kizu, T., Nariai, H., Chitose, K., Koyama, K., 2005 Study on the quench behavior of molten fuel material jetted into coolant Transactions of the Japan Society of Mechanical Engineers, Series B 71, 947–953 (in Japanese) Abe, Y., Matsuo, E., Arai, T., Nariai, H., Chitose, K., Koyama, K., Itoh, K., 2006 Fragmentation behavior during molten material and coolant interactions Nucl Eng Des 236, 1668–1681 Aoto, K., Uto, N., Sakamoto, Y., Ito, T., Toda, T., Kotake, S., 2011 Design study and R&D progress on Japan sodium-cooled fast reactor J Nucl Sci Technol 48, 463–471 Bang, K.H., Kim, H.T., 2017 Experiment and Modeling of Jet Breakup in Fuel-coolant Interactions In: Proceedings of the 8th European Review Meeting on Severe Accident Reaserch (ERMSAR-2017), pp 1–14 Warsaw, Poland Bang, K.H., Kim, M.J., Kim, D.H., 2003 Experimental study of melt jet breakup in water J Nucl Sci Technol 40, 807–813 Benz, R., Schins, H., 1982 Boiling fragmentation of moltn stailess steel and copper in sodium Nucl Eng Des 72, 429–437 Berg, E.V., Bürger, M., Cho, S.H., Schatz, A., 1994 Modeling of the breakup of melt jets in liquids for LWR safety abalysis Nucl Eng Des 149, 419–429 Bouyer, V., Cassiaut-Louis, N., Fouquart, P., Piluso, P., 2015 PLINIUS prototypic corium experimental platform: major results and future works In: Proceedings of the 16th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-16), Chicago, IL, USA, 1–14 Bürger, M., Cho, S.H., Kim, D.S., Carachalios, C., Müller, K., Fröhlich, G., 1985 Effect of Solid Crust on the Hydrodynamic Fragmentation of Melt Droplets Institut für Kernenergetik und Energiesysteme der Universitat Stuttgart Report No IKE TF-74 Bürger, M., Cho, S.H., Carachalios, C., Müller, K., Unger, H., Jacobs, H., 1986 Effect of Solid Crusts on the Hydrodynamic Fragmentation of Melt Drops Sicence and Technology of Fast Reactor Safety BNES, London, pp 503–508 Bürger, M., Cho, S.H., Berg, E.V., Schatz, A., 1995 Breakup of melt jets as pre-condition for premixing: modeling and experimental verification Nucl Eng Des 155, 215–251 Cao, X., Tobita, Y., Kondo, S., 2002 A thermal fragmentation model induced by surface solidification J Nucl Sci Technol 39, 628–636 Cassiaut-Louis, N., Brayer, C., Chikhi, N., Fouquart, P., Piluso, P., Journeau, C., Zhou, W., Liao, Y., 2017 Experiments linked to fuel coolant interaction within the Euro-Chinese project ALISA In: Proceedings of the 17th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-17), Xi’an, China, 1–12 Cherdron, W., Huber, F., Kaiser, A., Schütz, W., 2005 ECO Steam Explosion Experimentsdocumentation and Evaluation of Experimental Data FZKA-7011 Cho, S.H., Berg, E.V., Bürger, M., Schatz, A., 1991 Experimental investigations with respect to the modelling of fragmentation in parallel shear flows of liquids In: Proceedings of the Sprays and Aerosols Conference, pp 165–169 Guildford, UK Cho, D.H., Armstrong, D.R., Gunther, W.H., Basu, S., 1997 Experiments on interactions between zirconium-containing melt and water (ZREX): hydrogen generation and chemical augmentation of energetics In: Proceedings of the OECD/CNSI Specialists Meeting on Fuel-coolant Interactions pp 595–608 Tokai-mura, Japan Cho, D.H., Armstrong, D.R., Gunther, W.H., 1998 Experiments on Interactions between Zirconium-containing Melt and Water NUREG/CR-5372 Chu, T.Y., 1982 Fragmentation of molten-core material by sodium In: Proceedings of the International Topical Meeting on LMFBR Safety, pp 487–499 Lyon, France Chu, C.C., Sienicki, J.J., Spencer, B.W., Frid, W., Löwenhielm, G., 1995 Ex-vessel meltcoolant interactions in deep water pool: studies and accident management for Swedish BWRs Nucl Eng Des 155, 159–213 Corradini, M.L., 1981 Phenomenological modeling of the triggering phase of small-scale steam explosion experiments Nucl Sci Eng 78, 154–170 Corradini, M.L., Todreas, N.E., 1979 Prediction of minimum UO2 particle size based thermal stress initiated fracture model Nucl Eng Des 53, 105–116 Cronenberg, A.W., Fauske, H.K., 1974 UO2 solidification phenomena associated with rapid cooling in liquid sodium J Nucl Mater 52, 24–32 Fig Comparison of MMDs of filament- and sheet-shaped fragments and linear instability theory, including solidification effects (Iwasawa et al., 2015b) characteristic wavelengths obtained using the present model, the KHI, and fragment size based on CWT Note that Iwasawa et al (2015b) set D as the fitting value because it is difficult to estimate D during the jetbreakup and the fragmentation phenomena From Fig 8, we can recognize that the characteristic wavelengths calculated from the present model agree well with the MMDs measured based on filament- and sheet-shaped fragments at D = 10−6 to 10−5 Nm Fig shows that the present model can estimate the MMDs measured from filament- and sheet-shaped fragments, which cannot be estimated by the KHI and CWT We can estimate δ based on the fitted values of D The previous works (Epstein, 1977; Haraldsson et al., 2001; Iwasawa et al., 2015b) employed the relationship between D and δ in the case of a solid plate derived based on the material dynamics expressed as follows (JSME, 2007): D= Eδ 12(1 − ε 2) (26) where E denotes Young's modulus, and ε denotes Poisson's ratio The previous works (Iwasawa et al., 2015b) obtained δ = 6.7–15 mm from a comparison of the MMDs measured based on filament- and sheet-shaped fragments and the characteristic lengths calculated using the present model These fragments may be generated in a state where a crust of a certain thickness exists on the melt jetcoolant interface From the above results and discussions, the present model considering the solidification effects is useful for estimating the MMDs measured based on the filament- and sheet-shaped fragments, which cannot be estimated using the KHI and CWT, by setting D properly Note that the linear stability theory can only explain the interfacial instability and cannot consider the complex and non-linear deformation of the interface Also, the effect of the vapor film is neglected both in the KHI and the present model These should be future works Conclusions In the present review article, we summarized experimental works on FCI phenomena, especially jet-breakup and fragmentation phenomena 201 Progress in Nuclear Energy 108 (2018) 188–203 Y Iwasawa, Y Abe formation in the DEFOR test facility Nucl Eng Des 239, 1653–1659 Kim, H.T., Bang, K.H., 2016 Composition of jet breakup in fully-flooded and partiallty flooded reactor cavity In: Proceedings of the 11th International Topical Meetig on Nuclear Reactor Thermal Hydraulics, Operation and Safety (NUTHOS-11), pp 1–10 Gyeongju, Korea Kim, J.H., Park, I.K., Min, B.T., Hong, S.W., Shin, Y.S., Song, J.H., Kim, H.D., 2003 An experimental study on intermediate steam explosions experiments with molten zirconia and corium in the TROI facilities In: Proceedings of the 10th International Conference on Nuclear Thermal Hydraulics (NURETH-10), pp 1–6 Seoul, Korea Kim, J.H., Park, I.K., Min, B.T., Hong, S.W., Song, J.H., Kim, H.D., 2004 An efficient of corium composition varuations on occurrence of a spontaneous steam explosion in the TROI experiments In: Proceedings of the 6th International Topical Meetig on Nuclear Reactor Thermal Hydraulics, Operation and Safety (NUTHOS-6), pp 1–13 Nara, Japan Kim, J.H., Park, I.K., Min, B.T., Hong, S.W., Kim, H.Y., Song, J.H., Kim, H.D., 2005 Triggered steam explosion experiments in the TROI facility In: Proceedings of the 2005 International Congress on Advances in Nuclear Power Plants (ICAPP’05), pp 223–231 Seoul, Korea Kim, J.H., Park, I.K., Hong, S.W., Min, B.T., Hong, S.H., Song, J.H., Kim, H.D., 2008 Steam explosion experiments using nuclear reactor materials in the TROI facilities Heat Tran Eng 29, 748–756 Kim, J.H., Min, B.T., Park, I.K., Hong, S.W., 2011 Triggered steam explosion with corim melts of various compositions in a two-dimensional interaction vessel in the TROI facility Nucl Technol 176, 372–386 Knapp, R.B., Todreas, N.E., 1975 Thermal stress initiated fracture as a fragmentation mechanism in the UO2-sodium fuel-coolant interaction Nucl Eng Des 35, 69–85 Kondo, S., Konishi, K., Isozaki, M., Imahori, S., Furutani, A., Brear, D.J., 1995 Experimental study on simulated molten jet-coolant interactions Nucl Eng Des 155, 73–84 Kotake, S., Sakamoto, Y., Mihara, T., Kubo, S., Uto, N., Kamishima, Y., Ato, K., Toda, M., 2010 Development of advanced loop-type fast reactor in Japan Nucl Technol 170, 133–147 Kudinov, P., Karbojian, A., Ma, W., Dinh, T.N., 2008 An experimental study on debris formation with corium simulant materials In: Proceedings of the 2008 International Congress on Advances in Nuclear Power Plants (ICAPP’08), pp 1–9 CA, USA Kudinov, P., Karbojian, A., Ma, W., Dinh, T.N., 2010 The DEFOR-S experimental study of debris formation with corium simulant materials Nucl Technol 170, 219–230 Kudinov, P., Karbojian, A., Tran, C.T., Villanueva, W., 2013 Agglomeration and size distribution of debris in DEFOR-A experiments with Bi2O3-WO3 corium simulant melt Nucl Eng Des 263, 284–295 Kudinov, P., Grishchenko, D., Konovalenko, A., Karbojian, A., 2015 Experimental investigation of debris bed agglomeration and particle size distribution using WO3-ZrO2 melt In: Proceedings of the 16th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-16), pp 1–9 Chicago, IL, USA Ladisch, R., 1977 Comment on fragmentation of UO2 by thermal stress and pressurization Nucl Eng Des 43, 327–328 Li, H.X., Haraldsson, H.Ó., Dinh, T.N., Green, J.A., Sehgal, B.R., 1998 Fragmentation behaviour of melt drop in coolant; effect of melt solidification In: Proceedings of the 3rd International Conference on Multiphase Flows (ICMF3), (Lyon, France) Li, Y., Wang, W., Lin, M., Zhong, M., Zhou, Y., Yang, Y., 2017 Experimental studies on breakup and fragmentation behavior of molten tin and coolant interaction Science and Technology of Nuclear Installations 2017, 1–14 Lu, Q., Chen, D., Li, C., 2016 Visual investigation on the breakup of high superheated molten metal during FCI process Appl Therm Eng 98, 962–975 Ma, W., Yuan, Y., Sehgal, B.R., 2016 In-vessel melt retention of pressurized water reactors: historical review and future research needs Engineering 2, 103–111 Magallon, D., 2006 Characteristics of corium debris bed generated in large-scale fuelcoolant interaction experiments Nucl Eng Des 236, 1998–2009 Magallon, D., Hohmann, D., 1995 High pressure corium melt quenching tests in FARO Nucl Eng Des 155, 253–270 Magallon, D., Huhtiniemi, I., 2001 Corium melt quenching tests at low pressure and subcooled water in FARO Nucl Eng Des 204, 369–376 Magallon, D., Hohmann, H., Schins, H., 1992 Pouring of 100-kg-scale molten UO2 into sodium Nucl Technol 98, 79–90 Magallon, D., Huhtiniemi, I., Hohmann, D., 1997 Experimental investigation of 150-kgsxale corium melt jet quenching in water Nucl Eng Des 177, 321–337 Magallon, D., Huhtiniemi, I., Hohmann, D., 1999 Lessons learnt from FARO/TERMOS corium melt quenching experiments Nucl, Eng Des 189, 223–238 Manickam, L., Thakre, S., Ma, W., Bechta, S., 2014 Simultaneous visual acquisition of melt jet breakup in water by high speed videography and Radiography In: Proceedings of the 10th International Topical Meetig on Nuclear Reactor Thermal Hydraulics, Operation and Safety (NUTHOS-10), pp 1–13 Okinawa, Japan Manickam, L., Kudinov, P., Ma, W., Bechta, S., Grishchenko, D., 2016 On the influence of water suncooling and melt jet parameters on denris formation Nucl Eng Des 309, 265–276 Manickam, L., Bechta, S., Ma, W., 2017 On the fragmentation characteristics of melt jets quenched in water Int J Multiphas Flow 91, 262–275 Mathai, A.M., Sharma, A.K., Anandan, J., Malarvizhi, B., Das, S.K., Nashine, B.K., Chellapandi, P., 2015 Investigation of fragmentation phenomena and debris bed formation during core meltdown accident in SFR using simulated experiments Nucl Eng Des 292, 87–97 Matsuba, K., Kamiyama, K., Konishi, K., Toyooka, J., Sato, I., Zuev, V.A., Kolodeshnikov, A.A., Vasilyev, Y.S., 2012 Experimental study on material relocation during core disruptive accident sodium-coolant fast reactors -results of a series of fragmentation tests for molten oxide discharge into a sodium pool- In: Proceedings of the 8th JapanKorea Symposium on Nuclear Thermal Hydraulics and Safety (NTHAS8), pp 1–7 Beppu, Japan Matsuba, K., Isosaki, M., Kamiyama, K., Tobita, Y., Suzuki, T., 2013 Fundamental experiment on the distance for fragmentation of molten core material during core disruptive accidents in sodium-cooled fast reactors Nuclear Safety and Simulation 4, Cronenberg, A.W., Chawla, T.C., Fauske, H.K., 1974 A thermal stress mechanism for the fragmentation of molten upon contact with sodium coolant Nucl Eng Des 30, 434–443 Denham, M.K., Tyler, A.P., Fletcher, D.F., 1994 Experiments on the mixing of molten uranium dioxide with water and initial comparison with CHYMES code calculations Nucl Eng Des 146, 97–108 Dinh, T.N., Bui, V.A., Nourgaliev, J.A., Green, J.A., Segal, B.R., 1999 Experimental and analytical studies of melt jet-coolant interactions: a synthesis Nucl Eng Des 189, 299–327 Dombrovsky, L.A., 2009 Approximate model for breakup-of solidifiying melt particles due to thermal stress in surface crust layler Int J Heat Mass Tran 52, 582–587 Dombrovsky, L.A., Dinh, T.N., 2008 The effect of thermal radiation on the solodification dynamics of metal oxide melt droplet Nucl Eng Des 238, 1421–1429 Epstein, M., 1977 Stability of a submerged frozen crust J Heat Tran 99, 527–532 Epstein, M., Fauske, H.K., 1985 Steam film instability and the mixing of core-melt jets and water In: ANS Proceedings of National Heat Transfer Conference, pp 277–284 Colorado, USA Epstein, M., Fauske, H.K., 2001 Applications of the turbulent entrainment assumption to immiscible gas-liquid and liquid-liquid systems Chem Eng Res Des 79, 453–462 Fauske, H.K., Koyama, K., Kubo, S., 2002 Assessment of the FBR core disruptive accident (CDA): the role and application of general behavior principles (GBPs) J Nucl Sci Technol 39, 615–627 Fauske, H.K., 1973 On the mechanism of uranium dioxide-sodium explosive interactions Nucl Sci Eng 51, 95–101 Gabor, J.D., Purviance, R.T., Aeschimann, R.W., Spencer, B.W., 1988 Breakup and quench of molten metal fuel in sodium In: Proceedings of the International Top Meetigs on Safety of Next Generation Power Reactors, pp 839–843 Seattle, USA Gabor, J.D., Purviance, R.T., Cassulo, J.C., Spencer, B.W., 1992 Molten aluminum alloy fuel fragmentation experiments In: Proceedings of the 5th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-5), pp 1–16 Salt Lake City, Utah, USA Gabor, J.D., Purviance, R.T., Cassulo, J.C., Spencer, B.W., 1994 Molten aluminum alloy fuel fragmentation experiments Nucl Eng Des 146, 195–206 Hall, R.W., Fletcher, D.F., 1995 Validation of CHYMES: simulant studies Nucl Eng Des 155, 97–114 Haraldsson, H.Ó., 2000 Breakup of Jet and Drops during Premixing Phase of Fuel Coolant Interactions Ph.d thesis The Royal Institute of Technology, Sweden Haraldsson, H.Ó., Li, H.X., Yang, Z.L., Dinh, T.N., Sehgal, B.R., 2001 Effect of solidification on drop fragmentation in liquid-liquid media Heat Mass Tran 37, 417–426 Haraldsson, H.Ó., Sehgal, B.R., 1999 Breakup of high temperature oxide jet in water In: Proceedings of the 9th International Topical Meeting on Nuclear Reactor Thermal Hydraulics (NURETH-9), pp 1–11 San Francisco, California, USA Hohmann, D., Magallon, D., Schins, A., Yerkess, 1995 FCI experiments in the alumina oxide/water system Nucl Eng Des 155, 391–403 Holtbecker, H., Schins, H., Jorzik, E., Klein, K., 1977 Sodium-fuel Interaction: Dropping Experiments and Subassembly Commission of the European Communities Report EUR 5854 Hong, S.W., Piluso, P., Leskovoar, M., 2013 Status of the OECD-SERENA project for the resolution of ex-vessel J Energy Power Eng 7, 423–431 Hong, S.W., Min, B.T., Hong, S.H., 2015 An investigation on size distribution and physical characteristics of debris in TROI FCI tests Nucl Technol 191, 122–135 Hong, S.W., Na, Y.S., Hong, S.H., Song, J.S., 2016 Fuel-coolant interaction test results under different cavity conditions Nucl Technol 196, 538–552 Huber, F., Kaiser, A., Steinbück, M., Will, H., 1996 PREMIX, Doucumentation of the Results of Experiments PM01 to PM06 FZKA-6370 Huhtiniemi, I., Magallon, D., 2001 Insigh into steam explosion with corium melts in KROTOS Nucl Eng Des 204, 391–400 Huhtiniemi, I., Hohmann, D., Magallon, D., 1997a FCI experiments in the corium/water system Nucl Eng and Des 177, 339–349 Huhtiniemi, I., Magallon, D., Hohmann, D., 1997b Results of recent KROTOS FCI tests: alimina versu corium melts Nucl Eng Des 189, 379–389 Ichimiya, M., Mizuno, T., Kotake, S., 2007 A next generation sodium-cooled fast reactor concept and its R&D program Nucl Eng Technol 39, 171–186 Itoh, H., Nakamura, H., Kumamaru, H., Kukita, Y., 2004 Internal-shear mode instabilities on high-speed liquid jet, (1) characteristics of linear solutions J Nucl Sci Technol 41, 802–808 Iwasawa, Y., Abe, Y., Matsuo, E., Koyama, K., 2015a Jet breakup behavior with surface solidification Transactions of the JSME 81, 1–15 (in Japanese) Iwasawa, Y., Abe, Y., Matsuo, E., Koyama, K., 2015b Effects of surface solidification on fragmentation behavior of molten material jet Transactions of the JSME 81, 1–20 (in Japanese) Johnson, T.R., Pavlik, J.R., Baker, L., 1975 Post accident Heat Removal: Large-scale Molten-fuel-sodium Interaction Experiments ANL-75–12 The Japan Society of Mechanical Engineers (JSME), 1995 Progress in Heat Transfer New Series, vol Yokendo-publishing Co Ltd, pp 28–34 (in Japanese) The Japan Society of Mechanical Engineers (JSME), 2007 JSME Mechanical Engineer's Handbook: Fundamentals a.3: Strength of Materials Maruzen-publishing Co Ltd., pp 46–58 (in Japanese) Jung, H.W., Moriyama, K., Park, H.S., 2016 Experimental revisit of melt jet breakup length correlations for fuel-coolant interactions In: Proceedings of the 11th International Topical Meetig on Nuclear Reactor Thermal Hydraulics, Operation and Safety (NUTHOS-11), pp 1–13 Gyeongju, Korea Kaiser, A., Schütz, W., Will, H., 1997 Melt water interaction tests (PREMIX tests PM10 and PM11) In: Proceedings of the OECD/CNSI Specialists Meeting on Fuel-coolant Interactions, pp 646–657 Tokai-mura, Japan Kaiser, A., Schütz, W., Will, H., 1999 PREMIX Tests PM12, PM13, and PM14 Documentation and Evaluation of Experimental Data FZKA-6370 Kaiser, A., Schütz, W., Will, H., 2001 PREMIX Experiments PM12-pm18 to Investigate the Mixing of a Hot Melt with Water FZKA-6380 Karbojian, A., Ma, W.M., Kudinov, P., Dinh, T.N., 2009 A scoping study of debris bed 202 Progress in Nuclear Energy 108 (2018) 188–203 Y Iwasawa, Y Abe Song, J.H., Park, I.K., Chang, Y.J., Shin, Y.S., Kim, J.H., Min, B.T., Hong, S.W., Kim, H.D., 2002a Experiments on the interactions of molten ZrO2 with water using TROI facility Nucl Eng Des 213, 97–110 Song, J.H., Park, I.K., Shin, Y.S., Kim, J.H., Hong, S.W., Min, B.T., Kim, H.D., 2002b Spontaneous steam explosion observed in the fuel coolant interactions using reactor materials Journal of the Korean Nuclear Society 33, 344–357 Song, J.H., Hong, S.W., Kim, J.H., Chang, Y.J., Shin, Y.S., Min, B.T., Kim, H.D., 2003a Insights from the recent steam explosion experiments in TROI J Nucl Sci Technol 783–795 Song, J.H., Park, I.K., Shin, Y.S., Hong, S.W., Min, B.T., Kim, H.D., 2003b Fuel coolant interaction experiments in TROI using a UO2/ZrO2 mixture Nucl Eng Des 222, 1–15 Song, J.H., Kim, Y.H., Hong, S.W., An, S., 2016 A use of prototypic material for the investigation of severe accident progression Prog Nucl Energy 93, 297–305 Song, J.H., Na, Y.S., Hong, S.W., Hong, S.H., 2017 Effect of melt water interaction configuration on the process of steam explosion J Nucl Sci Technol 54, 47–57 Sowa, E.S., Gabor, J.D., Pavlik, J.R., Cassulo, J.C., Cook, C.J., Baker, L., 1979 Molten core debris-sodium interactions: M-series experiments In: Proceedings of the ANS/ENS International Meeting on Fast Reactor Safety Technology, (Seattle, Washington) Spencer, B.W., Gabor, J.D., Cassulo, J.C., 1986 Effect of boiling regime on melt stream breakup in water In: Proceedings of the 4th Miami International Symposium on Multi-phase Transport and Particulate Phenomena, (Miami, USA) Spencer, B.W., Wang, S.K., Blomquist, C.A., McUmber, L.M., Schneider, J.P., 1994 Fragmentation and Quench Behavior of Corium Melt Stream in Water NUREG/CR6133, ANL-93/32 Sugiyama, K., Iguchi, K., 2002 Research on the Fundamental Process of Thermal-hydraulic Behaviors in Severe Accident -breakup and Cooling of Molten Material Jets Japan Atomic Energy Research Institute, JAERI-Tech, pp 2002–2010 Sugiyama, K., Yamada, T., 2000 A breakup mechanism of high-temperature melt jets (observation in a molten tin jet) Transactions of the Japan Society of Mechanical Engineers, Series B 66, 1507–1513 (in Japanese) Sugiyama, K., Sotome, F., Ishikawa, M., 1999 Thermal interaction in crusted melts jets with large-scale structures Nucl Eng Des 189, 329–336 Suzuki, T., Kamiyama, K., Yamano, H., Kubo, S., Tobita, Y., Nakai, R., Koyama, K., 2014 A scenario of core disruptive accident for Japan sodium-cooled fast reactor to achieve invessel retention J Nucl Sci Technol 51, 493–513 Takahashi, M., Secareanu, R., Mihalache, M., Chapelat, A., 2015 Fundamental study on heavy meyal freezing behavior for stop of water leakage form LWE containment vessel Prog in Nucl Energy 82, 184–190 (x) Taylor, G.I., 1963 The dispersion of jets of metals at low melting point in water In: Batchelor, G.K (Ed.), The Scientific Papers of Sir Geoffrey Ingram Taylor vol Cambridge University Press, pp 304–305 Tobita, T., Kamiyama, K., Tagami, H., Matsuba, K., Suzuki, T., Isozaki, M., Tamano, H., Morita, K., Guo, L.C., Zhang, B., 2016 Development of the evaluation methodology for the material relocation behavior in the core disruptive accident of sodium-cooled fast reactors J Nucl Sci Technol 53, 698–706 Tyrprekl, V., Piluso, P., Bakardjieva, S., Dugne, O., 2014 Material effect in the nuclear fuel-coolant interaction: analysis of prototypic melt fragmentation and solidification in the KROTOS facility Nucl Technol 186, 527–532 Uršič, M., Leskovar, M., 2011 Fine fragmentation of melt droplets In: Proceedings of 20th International Conference Nuclear Energy for New Europe, pp 1–8 Bovec, Slovenia Uršič, M., Leskovar, M., 2012 Temperature profile modelling in fuel-coolant interaction codes Int J Heat Mass Tran 55, 5350–5356 Uršič, M., Leskovar, M., Mavko, B., 2010 Material properties' influence in fuel-coolant interaction codes J Eng Gas Turbines Power 132, 1–7 Uršič, M., Leskovar, M., Mavko, B., 2011 Improved solidification influence modelling for Eulerian fuel-coolant interaction codes Nucl Eng Des 241, 1206–1216 Uršič, M., Leskovar, M., Mavko, B., 2012 Simulations of KROTOS alumina and corium steam explosion experiments: applicability of the improved solidification influence modelling Nucl Eng Des 246, 163–174 Uršič, M., Leskovar, M., Meignen, R., 2015 Eulerian modelling of melt solidification impact during fuel-coolant interaction Ann Nucl Energy 78, 130–139 Vanderhaegen, M., Belguet, A.L., 2014 A review on sodium boiling phenomena in reactor systems Nucl Sci Eng 176, 115–137 Wei, H., Erkan, N., Okamoto, K., 2016 Experimental investigation of the effect of control rod guide tubes on the breakup of a molten metal jet in the lower plenum of a boiling water reactor under isothermal conditions J Visual 19, 1–12 Yamano, N., Maruyama, Y., Kudo, T., Hidaka, A., Sugimoto, J., 1995 Phenomenologocal studies on melt-coolant interactions in the ALPHA program Nucl Eng Des 177, 369–389 Yang, J.W., Bankoff, S.G., 1987 Solidification effects of the fragmentation of molten metal drops behind a pressure shock wave J Heat Tran 109, 226–231 Zagorul’ko, Y.I., Zhmurin, V.G., Volov, A.N., Kovalev, Y.P., 2008 Experimental investigation of thermal interaction between corium and coolant Therm Eng 55, 235–244 Zhang, Z.G., Sugiyama, K., 2010 Fragmentation of a single molten metal droplet penetrating sodium pool II stainless stell and the relationship with copper droplet J Nucl Sci Technol 47, 169–175 Zhang, Z.G., Sugiyama, K., 2011 Fragmentation of a single molten metal droplet penetrating into sodium pool: thermal and hydrodynamic effects on fragmentation in stainless steel Nucl Technol 175, 619–627 Zhang, Z.G., Sugiyama, K., 2012 Fragmentation of a single molten metal droplet penetrating into sodium pool IV thermal and hydrodynamic effects on fragmentation in copper J Nucl Sci Technol 49, 602–609 Zhang, Z.G., Sugiyama, K., Itagaki, W., Nishimura, S., Kinoshita, I., Narabayashi, T., 2009 Fragmentation of a single molten metal droplet penetrating sodium pool I copper droplet and the relationship with copper jet J Nucl Sci Technol 46, 453–459 272–277 Matsuba, K., Kamiyama, K., Toyooka, J., Tobita, Y., Zuev, V.A., Kolodeshnikov, A.A., Vasilyev, Y.S., 2015a Experimental discussion on fragmentation mechanism of molten oxide discharged into a sodium pool In: Proceedings of the 23th International Conference on Nuclear Engineering (ICONE-23), pp 1–6 Chiba, Japan Matsuba, K., Isozaki, M., Kamiyama, K., Tobita, Y., 2015b Distance for fragmentation of a simulated molten-core material discharged into a sodium pool J Nucl Sci Technol 52, 707–712 Matsuba, K., Kamiyama, K., Toyooka, J., Tobita, Y., Zuev, V.A., Kolodeshnikov, A.A., Vasilyev, Y.S., 2016 Experimental discussion on fragmentation mechanism of molten oxide discharged into a sodium pool Mechanical Engineering Journal 3, 1–8 Matsuo, E., Abe, Y., Chitose, K., Koyama, K., Itoh, K., 2008 Study on jet breakup behavior at core disruptive accident for fast breeder reactor Nucl Eng Des 238, 1996–2004 Mitchell, D.E., Corradini, M.L., Tarbell, W.W., 1981 Intermediate Scale Steam Explosion Phenomena: Experiments and Analysis NUREG/CR-2145, SAND81–0124 Moriyama, K., Maruyama, Y., Usami, T., Nakamura, H., 2005 Coarse break-up of a stream of oxide and steel melt in a water pool JAERI-Research 2005–2017 Na, Y.S., Hong, S.H., Song, J.H., Hong, S.W., 2014 Pre-mixing visualization in fuelcoolant interaction without a free fall of the corium melt In: Proceedings of the 9th Japan-Korea Symposium on Nuclear Thermal Hydraulics and Safety (NTHAS9), (Buyeo, Korea) Na, Y.S., Hong, S.H., Song, J.H., Hong, S.W., 2016 Fuel-coolant interaction visualization test for in-vessel corium retention external reactor vessel cooling (IVR-ERVC) condition Nucl Eng Technol 48, 1–8 Nishimura, S., Kinoshita, I., Sugiyama, K., Ueda, N., 2002 Thermal fragmentation of a molten metal jet dropped into a sodium pool at interface temperatures below its freezing point J Nucl Sci Technol 39, 752–758 Nishimura, S., Kinoshita, I., Sugiyama, K., Ueda, N., 2005 Thermal interaction between molten metal jet and sodium pool: effect of principal factors governing fragmentation of the jet Nucl Technol 149, 189–199 Nishimura, S., Sugiyama, K., Kinoshita, I., Itagaki, W., Ueda, N., 2010 Fragmentation mechanism of a single molten copper jet penetrating a sodium pool -transition from thermal to hydrodynamic fragmentation in instantaneous contact interface temperatures below its freezing point- J Nucl Sci Technol 47, 219–228 Park, I.K., Chang, Y.J., Shin, Y.S., Kim, C.H., Min, B.T., Hong, S.W., Song, J.H., Kim, H.D., 2001 Stem explosion experiments in the “Test for Real cOrium Interaction with water (TROI) In: Transactions of the International Conference on Structual Mechanics in Reactor Technology, pp 1–8 Washington DC, USA Park, I.K., Kim, J.H., Hong, S.H., Min, B.T., Hong, S.W., Song, J.H., Kim, H.D., 2008 An investigation of the particle size responses for various fuel-coolant interactions in the TROI experiments Nucl Technol 161, 45–56 Park, I.K., Kim, J.H., Min, B.T., Hong, S.W., 2013 Thermal-hydraulic aspects of FCI in TROI corium/water interaction tests Nucl Eng Des 263, 419–430 Pilch, M., Erdman, C.A., 1987 Use of breakup time data and velocity history data to predict the maximum size of stable fragments for acceleration-induced breakup of a liquid drop Int J Multiphas Flow 13, 741–757 Pillai, D.S., Vigmesh, R., Sudha, A.J., Pushpavanama, S., Sundararajan, T., Nashine, B.K., Selvaraj, P., 2016 Experimental simulation of fragmentation and stratification of core debris on the core catcher of a fast breeder reactor Nucl Eng Des 301, 39–48 Ricou, F.B., Spalding, D.B., 1961 Measurements of entrainment of axisymmetrical turbulent jets J Fluid Mech 11, 21–32 Saito, M., Sato, K., Imahori, S., 1988 Experimental study on penetration behaviors of water jet into Freon-11 and liquid nitrogen In: ANL Proceedings: National Heat Transfer Conference, pp 173–183 Schins, H., 1984 A new interpretation on formation of UO2 PAHR particulate in sodium In: Proceedings of 6th International Meeting on Debris Coolability, pp 1–10 Los Angeles, USA Schins, H., Gunnerson, F.S., 1986 Boiling and fragmentation behavior during fuel-sodium interactions Nucl Eng Des 91, 221–235 Schins, H., Lamain, L., Biasi, L., 1984 Breakup time of fragmenting-solidifying UO2 spheres when quenched in sodium Nucl Eng Des 80, 19–25 Schins, H., Magallon, D., Giuliani, S., Gunnerson, F.S., 1986 Pouring of molten UO2, UC and Al2O3 in sodium: interactions and debris; theoretical analysis European Applied Research Reports 7, 577–672 Schins, H., Hohmann, H., Bürger, M., Berg, E.V., Cho, S.H., 1992 Breakup of melts jets in a water pool as a key process for analysis of lower PRV-head failure during core melt accidents in LWR In: Proceedings of the Annual Meeting on Nuclear Technology ’92 (Jahrestagung Kerntechnik ’92), pp 159–251 Karlsruhe, Germany Schneider, J.P., 1995 Breakup of Metal Jets Penetrating a Volatile Liquid Ph.d thesis University of Illinois, USA Schneider, J.P., Marciniak, J.M., Jones, B.G., 1992 Breakup of metal jets penetrating a volatile liquid In: Proceedings of the 5th International Conference on Nuclear Thermal Hydraulics (NURETH-5), pp 437–449 Salt Lake City, USA Schütz, W., Huber, F., Kaiser, A., Will, H., 1997 PREMIX an experimental approach to investigate the mixing behavior of a hot melt being poured into water In: Proceedings of 2nd International Meeting on Advanced Reactor Safety, pp 887–894 Orland, USA Secareanu, R., Mereu, R., Takahashi, M., Inzoli, F., Prisecaru, I., 2016 Experimental and numerical study of freezing and flow characteristics of Wood's Metal injection in a water pool Appl Therm Eng 103, 1261–1277 Seghal, B.R., 2012 Nuclear Safety in Light Water Reactors Severe Accident Phenomenology Academic Press, Elsevier Sehgal, B.R., 2006 Stabilization and termination of severe accidents in LWRs Nucl Eng Des 236, 1941–1952 Sehgal, B.R., Bechta, S., 2016 Severe accident progression in the BWR lower plenum and the modes of vessel failure Ann Nucl Energy 93, 28–34 Song, J.H., Kim, J.H., 2005 The effect of the UO2/ZrO2 composition on fuel coolant interaction Nucl Technol 149, 309–323 203 ... Phenomena: Experiments and Analysis NUREG/CR-2145, SAND81–0124 Moriyama, K., Maruyama, Y., Usami, T., Nakamura, H., 2005 Coarse break-up of a stream of oxide and steel melt in a water pool JAERI-Research... 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) and Tyrpekl et al (2014) also pointed... conducted a series of experiments called GPM (Moriyama et al., 2005), which involved injecting alumina-zirconia and stainless-carbon melts Moriyama et al (2005) investigated a method for estimating