Investigation on upper bounds of recriticality energetics of hypothetical core disruptive accidents in sodium cooled fast reactors

Investigation on upper bounds of recriticality energetics of hypothetical core disruptive accidents in sodium cooled fast reactors

Nuclear Engineering and Design 326 (2018) 392–402 Contents lists available at ScienceDirect Nuclear Engineering and Design journal homepage: www.els...

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Nuclear Engineering and Design 326 (2018) 392–402

Contents lists available at ScienceDirect

Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes

Investigation on upper bounds of recriticality energetics of hypothetical core disruptive accidents in sodium cooled fast reactors

T



Werner Mascheka, , Rui Lia, Claudia Matzerath Boccaccinia, Fabrizio Gabriellia, Koji Moritab a b

Karlsruhe Institute of Technology (KIT), Campus North, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany Kyushu University, Department of Applied Quantum Physics and Nuclear Engineering, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan

A B S T R A C T One key research goal for GEN-IV systems is an enhanced safety compared to the former Sodium Cooled Fast Reactor concepts. A key issue is built-in safety and the capability to prevent accidents and to demonstrate that their consequences do not violate aimed-at safety criteria. From the beginning of SFR development the Core Disruptive Accident (CDA) has played an outstanding role in the safety assessment. Under core disruptive accident conditions with core melting the fuel might compact, prompt criticality might be achieved and a severe nuclear power excursion with mechanical energy release might be the consequence. Numerous safety analyses accompanied the development and the licensing procedures of past fast reactor projects. A central issue of all analyses was the assessment of a realistic upper bound of energetics especially related to recriticalities in disrupted core configurations. Striving for an even higher safety level for next generation reactors a new strategy focused on the development and introduction of preventive and mitigative measures both to reduce the chance for a severe accident development and to mitigate its energetics. For assessing the effectiveness of these measures the knowledge of the CDA behavior is essential. In this context and on basis of new code developments, new experimental insights and extended studies for many reactor types of different power classes over the recent years, the issue of a realistic upper bound of energetics of the late core melt phases is again of relevance. Of special interest is the identification of natural and intrinsic mechanisms that limit the escalation of energetics. The current paper deals with these issues and tries to add supportive facts on the limits of CDA energetics. The evaluation of results of mechanistic SIMMER-II and SIMMER-III/IV analyses performed for various core designs and power classes and specific model case studies in 2D and 3D geometry indeed supports the idea of a limit of recriticality energetics. Intrinsic mechanisms exist, which limit the escalation energetics even in case of a strong blockage confinement suppressing any fuel discharge and allowing on-going sloshing recriticalities. In the light of the available information and taking into account relevant scientific publications and studies by the international community on the subject, one could conclude that an upper bound for energetics in the range given in the paper can be deduced.

1. Introduction The Sodium-Cooled Fast Reactor (SFR) as advanced reactor concept has the highest technical maturity level among Generation IV systems. It has been built already in large, commercial scale and operated for many years. Extensive experience exists in the full range of design, licensing, operation and handling of incidents and accidents. A key research goal of GEN-IV systems is an enhanced safety compared to the former SFR concepts (Gif IV Technology Roadmap, 2002). In particular, the achievement of a robust architecture against abnormal situations and the robustness of the safety demonstrations should result in clearly demonstrable safety improvements. The defense in depth concept is the



key to achieve the robustness in safety (Fiorini, 2009). A key issue is built-in safety and the capability to prevent accidents and to demonstrate that their consequences do not violate aimed-at safety criteria. However, from the beginning of SFR development in the 1950s, the Core Disruptive Accident (CDA), also coined ‘Bethe-Tait’ Accident, has played an outstanding role in the safety assessment, as the SFR core is not designed in the most neutronically reactive configuration. Under core disruptive conditions with core melting the fuel might compact, prompt criticality might be achieved and a severe nuclear power excursion with mechanical energy release might be the consequence. The following list of literature (Bohl, 1979; Maschek and Asprey, 1983; Kondo et al., 1985; Theofanous and Bell, 1984; Gouriou et al., 1982)

Corresponding author. E-mail address: [email protected] (W. Maschek).

https://doi.org/10.1016/j.nucengdes.2017.11.002 Received 6 June 2017; Received in revised form 25 October 2017; Accepted 2 November 2017 Available online 29 December 2017 0029-5493/ © 2017 Elsevier B.V. All rights reserved.

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has to be expected. Therefore, it is of interest, if under such conditions natural and intrinsic mitigating effects exist that limit the energetics. The issue of an upper bound of energetics of a CDA and of connected recriticalities was a permanent point of discussion in the safety assessment of fast reactors (Bohl, 1979; Maschek and Asprey, 1983; Kondo et al., 1985; Theofanous and Bell, 1984; Risikoorientierte Analyse, 1982; Nakai, 2010). Special focus was on ‘bottled-up’ whole core pools, where fuel could only be discharged after recriticalities which melted away the blockages or broke them up mechanically. In the current paper, we therefore focus on mitigating phenomena of recriticalities triggered by sloshing fuel motions (Maschek et al., 1992a) in case of a large core-wide melt pool. Sloshing recriticalities have to be expected in the so-called transition phase of a CDA when core exits are blocked by fuel and steel blockages and insufficient fuel has been discharged from the core region (Maschek et al., 1992a,b). The fuel motion is triggered by gravity, pressure sources or by the neutronic power profile itself. The Transition Phase (TP) is characterized by a progressive core disruption where local multi-phase fuel/steel pools grow radially after hexcan destruction. The early transition phase is characterized by incoherent fuel motion within intact hexcan structure. The occurrence of high reactivity ramp rates to lead to an energetic disassembly is considered to be fairly unlikely. In the early transition phase due to the low temperature and pressure levels no rapid and sufficient material discharge can be expected for reactors without special material discharge provisions. Phenomena are driven by strong feedback effects and strong nonlinearities exist. A ‘competition’ between fuel losses and material motion exists deciding over the energetics potential of the transition phase. The formation of larger connected fuel pools with inherent neutronic and thermal–hydraulic instabilities, meaning that it does not exist a stable boiled-up pool, can finally result in a large-scale and coherent sloshing motion, a global fuel compaction and a recriticality with a nuclear power excursion. This power excursion finally disassembles the core and might lead to a mechanical load of the vessel structures (Flad et al., 2017). This coherent large scale fuel motion is a phenomenon which therefore needs the highest attention (Maschek et al., 1992a,b). In general, two different outcomes from the TP can be envisioned. One outcome is the above described route via severe recriticalities and a core disassembly. The disassembly leads to re-melting of blockages or their mechanical destruction including the above core structures. The other route is a non-energetic route directly into the Post Accident Heat Removal Phase (PAHR) in case sufficient fuel can be unloaded from the core during the later melt-down phase. The discharge is enabled by a remelting of existing blockages and opening fuel discharge paths directly through the subassembly subchannels, the hexcan gaps or via the Control Rod Guide Tube (CRGTs) channels. The findings on the transition phase are mainly based on calculations with the SIMMER code family. Starting even with SIMMER-II (Bohl and Luck, 1990), which has been applied for TP analyses of intermediate size and large size reactors projected and built in the 70s and 80s of the last century. Due to weaknesses of SIMMER-II it was necessary to develop a new code generation, just named for continuity also SIMMER, namely the SIMMER-III and SIMMER-IV codes (Kondo et al., 1992, 1999; Yamano et al., 2003, 2008, 2012). SIMMER-III is a two-dimensional (2D), SIMMER-IV a three-dimensional (3D), multivelocity-field, multi-phase, multi-component, Eulerian, fluid-dynamics code system coupled with a structure model for fuel-pins, hexcans and general structures, and a space-, time- and energy-dependent transport theory neutron dynamics model. The new SIMMER codes are capable of representing the important physical phenomena in detail and include a comprehensive consideration of multidimensional effects and address the multidisciplinary nature of reactor accidents with complex interactions between different phenomena. The accident scenario is followed ‘mechanistically’, including all different phenomena and complex interactions with state of the art modeling and parameter ranges. The newly developed ASTERIA code (Ishizu et al., 2012), belongs into

reflects some work and the analyses performed in the past for oxide fuel cores. A central issue of all analyses was the assessment of a realistic upper bound of energetics especially related to recriticalities in the disrupted core configuration. The analyses showed some potential for energetics in the core melt phases. Striving for an even higher safety level for next generation reactors a new strategy focused on the development and introduction of preventive and mitigative measures both to reduce the chance for a severe accident development and to mitigate its energetics. The first focus of prevention and mitigation of energetics was by optimizing and reducing the sodium void worth of the cores, such controlling the energetics of the early accident phases. This however led to the detrimental effect to shift the energetics problem to the later core melt phases and the recriticality problem in large molten fuel pools. In the recent years one also concentrates on getting controllability of the later accident phases by measures coined ‘Controlled Material Relocation’ (CMR) (Ieda et al., 1994; Maschek, 1995; Endo et al., 2002; Sato et al., 2009). These measures are under investigation and one wants to identify their effectiveness to minimize the consequences of CDAs. For assessing the effectiveness of these measures the knowledge of the general CDA behavior is essential. With new code developments, new experimental insights and extended studies for many reactor types of different power classes over the recent years, one could now again try to investigate the problem of a realistic upper bound of energetics of the late core melt phases and identify natural and intrinsic mechanisms that limit the escalation of energetics. The current paper deals with these issues and tries to add supportive facts on the limits of CDA energetics. 2. Mitigating measures and mechanisms We mostly concentrate on mitigation effects in oxide fueled cores in case a CDA e.g. caused by an Unprotected Loss of Flow accident (ULOF) could not be prevented. In the past, safety research has been focused mainly in obtaining a sort of controllability of the early accident phases, especially by optimizing the core reactivity coefficients as e.g. the sodium void worth. This has now achieved a satisfactory level of optimization as reported in Vasile (2015), guaranteeing either a prevention of core degradation or at least eliminating any energetics. As described, new work concentrates on gaining ‘controllability’ of the later accident phases with their potential of extensive core melting and recriticalities. The objective is to mitigate or eliminate any severe energetics development. One key measure to obtain control is via introducing adequate design measures to guarantee a timely and sufficient fuel discharge from the core, a ‘Controlled Material Relocation’ (CMR) (Ieda et al., 1994; Maschek, 1995; Endo et al., 2002; Sato et al., 2009; Tobita et al., 1999) to achieve a neutronically subcritical core configuration. The idea of a recriticality free core promoted mainly in Japan is realized via CMR measures on the subassembly level before enlarging the molten region. Special Fuel Assemblies with Inner DUct Structure (FAIDUS) are the adopted concept that allows a large fuel escape path in case of local fuel melting (Sato et al., 2009; Tobita et al., 1999). In the CAPRA project (Languille et al., 1995; Maschek and Struwe, 2000) aiming at burning Plutonium and Minor Actinides the reactor core had a very high PU-enrichment. To cope with the recriticality problem it was proposed to modify and use the numerous diluents in the core for fuel discharge (Maschek and Struwe, 2000). As each diluent was surrounded by 6 fuel elements, a timely and sufficient fuel discharge via accessing the diluents (basically an empty tube) could be envisioned in case of a core melt accident. For the French ASTRID reactor again CMR measures are proposed that work via an empty tube structure named Mitigating Transfer Tubes (TT-DCS-M) (Bachrata et al., 2015). Some tubes are positioned in the inner core zone with most of the tubes surrounding the second core zone. If the designed mitigating measures for fuel discharge are not effective within the time-slot of core melting, a nuclear power excursion 393

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have later been recommended as a test for general fluid-dynamics codes (Pigny, 2010) and have also been used in many different other fields for validation purposes (Buruchenko and Crespo, 2014; Martel et al., 1998; Henderson and Miles, 1994; Guelfi et al., 2007; Lakehal et al., 2002; Guo et al., 2012). Though sloshing motions in the usual technical environment are not of the centralized type, the experiments can serve as a good test for code validation. A general point of interest is that the centralized inward sloshes from the converging water waves are highly unstable and can be strongly disturbed by structures in the flow. These effects have also been investigated and results are reported. The sloshing experiments naturally do not include the neutronic feedback from the fluid-motion. From the mechanistic SIMMER simulations and the model case studies shown in the next chapter it can be seen that the neutronic feedback makes the sloshing process significantly more chaotic. The local fuel accumulation itself carries the dominating neutronic worth profile and drives the sloshing process.

the same code category. The investigations on limits of energy release by recriticalities in case a large fuel pool has been formed which is confined in blockages, focuses on the assessment of the following issues: 1) Do intrinsic phenomena exist that might mitigate and limit the energetics of severe recriticalities by sloshing fuel motions? 2) Do phenomena exist that might not be covered by the usual 2D accident simulations, but need a 3D resolution? The first issue investigated more deeply concerns the special recriticality and power excursion behavior in confined pools, observed in mechanistic SIMMER calculations and also confirmed in accompanying model case studies. Obviously after some recriticality events with energy increase in the pool, a saturation level of the internal energy is reached and the sloshing activity is strongly hampered and levels off. The second issue investigated is connected to the limitation of the mechanistic and model case simulations which were performed in the framework of past reactor safety studies (Bohl, 1979; Maschek and Asprey, 1983; Kondo et al., 1985; Theofanous and Bell, 1984; Gouriou et al., 1982). In the past at FZK/KIT mostly 2D SIMMER-III simulations have been performed which could not cover asymmetric sloshing geometries or singular obstacles in the pool region as control or shut-down rods. In a new study with SIMMER-IV 3D simulations of model cases have been performed which close this knowledge gap and which are described in the current paper. The aim of these investigations was to check if phenomena not seen in 2D might be observed in 3D. The assessment of intrinsic mitigating mechanisms takes into account the information provided by numerous ‘mechanistic’ accident simulations performed for reactor cores of different power classes, specific ‘model case’ studies for individual accident phenomena and state of the art experimental knowledge which is fed into the input parameters required by the mechanistic simulations. In addition, a critical review of relevant scientific publications and studies by the international community in this field, which are devoted to high mechanical energy releases in case of a CDA, were analyzed and evaluated.

4. Limitation of energetics in confined bottled-up pools In the following, mechanistic simulations in real reactor geometry with all structural details and idealized model case studies are presented to describe the findings on recriticality behavior in bottled-up fuel-steel pools. 4.1. Limitation of energetics by pool pressurization The typical trace of the nuclear power and energetics development from mechanistic SIMMER simulations describing different control rod conditions (position and sodium temperature) is given in Fig. 3 for ULOF simulations of the CP-ESFR Working Horse (WH) core (Flad et al., 2013). The CP-ESFR WH core with 3600 MWth power is composed of 453 fuel subassemblies (SAs) subdivided into two zones in order to flatten the core power profile in the equilibrium cycle. The average Pu content is 14.5% wt. for the inner zone and 16.9% wt. for the outer zone. The core active height is 100 cm. Above the active zone, an upper axial blanket, an upper gas plenum and a Na plenum zone are placed. In the ULOF simulation, after some excursions with re-melting of blockages and ongoing fuel discharge, finally enough fuel has been relocated outside of the core and nuclear shut-down is achieved. The nuclear energy development shows an interesting feature as after the first 10 s, where the core is still blocked and confined one still encounters recriticalities and power excursions, but the energetics curve of deposited nuclear energy shows some saturation. This phenomenon has been observed in nearly all the past mechanistic simulations (Fig. 3) and as examples the ULOF simulations of the transition phase of CPESFR are shown (Flad et al., 2013). One reason finally ending the excursion activity is that the energy level reached in the core and the energy deposition in the blockages and surrounding structures is so high that blockages re-melt, are pushed forward and some fuel can leave the core region. Finally, enough fuel is discharged to leave the core subcritical (Fig. 3). Another reason for the obvious ‘saturation’ behavior can be better observed in so-called ‘model cases’, where a pool is confined by rigid smooth walls, not allowing any fuel discharge. A local perturbation e.g. by a dropping fuel mass in the pool center initiates the sloshing motion in this case. The model cases chosen were for an intermediate size core as e.g. the former SNR-300 (Maschek and Asprey, 1983; Risikoorientierte Analyse, 1982). For the model case studies, a smaller core size compared to a large core as in Fig. 3 has been chosen for reducing computation costs. The goal of the study is to deduce general findings on transition phase behavior independent of core parameters as e.g. core size. To remember the core size of such an intermediate size core as SNR-300 was ∼2 m in diameter and 0.96 m in height with an average Pu enrichment of 27.5%. In Fig. 4 the power and energy trace are given and in Fig. 5 it can be observed that the violent fuel motion

3. The centralized sloshing phenomenon The mechanistic SIMMER simulations of a typical CDA as the ULOF indicate the formation of a large core-wide fuel-steel pool if the core melt and disruption process cannot be stopped by early fuel discharge. The pool is confined by axial and radial blockages preventing an effective discharge. Due to gravity, local pressure sources, instabilities and neutronic effects sloshing motions can be triggered and fuel compaction leads to a nuclear power transient. Characteristically, liquid fuel is driven away from the core center towards the core peripheries and then returns by a spring-back effect and moves inward toward the center of the core again. This centralized slosh can then initiate a recriticality with a subsequent nuclear power excursion. Simply the nuclear power profile in a pool can trigger this motion. In Maschek et al. (1992b), a schematic picture is given which illustrates this centralized motion and is repeated here (Fig. 1). For a better understanding of the underlying motion patterns and phenomenology and especially for code validation sloshing experiments have been performed (Maschek et al., 1992a,b). In a cylindrical vessel both dam-break and water-step geometrical set-ups have been designed with and without disturbances of the flow by asymmetries, structures and particle beds. A typical example of a centralized sloshing motion is given in Fig. 2. As sloshing recriticalities need a high precision simulation, the experiments have also been extensively used to validate the SIMMER-III (Kondo et al., 1992, 1999) and SIMMER-IV codes (Yamano et al., 2003, 2008, 2012). In addition, the alternative methods as the SPH formalism (SIMSPH code, (Vorobyev et al., 2011)) have been applied to analyze details of the converging and piling up fluid masses. The experiments 394

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Fig. 1. Schematic representation of liquid fuel sloshing in an ideal cylindrical pool.

nuclear energy deposition (Fig. 6) is still going on in this model case simulation and the pool temperature and pressure increase but the energy deposited is generated via decay heat and does no more result from sloshing recriticalities. The amount of the reactivity reducing effect of the axial pool expansion has also been checked for various core sizes with neutronic calculations by ERANOS (Ruggieri et al., 2006) and has been confirmed. As to be expected the reactivity effect is reduced in cores with larger radial dimensions. There are three main conclusions which can be drawn from the simulation for the bottled-up pool configurations:

dies out at the end of the calculation. As can be seen in the integrated power traces, two phases during the sloshing process can be identified as:

• An initial phase (1) with a strongly increasing energy deposition and a steep gradient; • A second phase (2) showing a strong saturation tendency with a flat gradient

To further confirm this specific behavior the model case has been run up to 80 s. Fig. 6 shows the power end energy development and the leveling out of energy increase. In Fig. 7 the motion pattern is displayed and it can be observed that at a time of ∼10 s the sloshing motions become rather restricted and at the end of the calculation one observes an axially expanded fuel pool subcritical with about −23$. The height of the pool has grown by ∼12 cm, still single phase, but expanded by the temperature increase and thermal expansion. The

1. The sloshing motion is triggered by a creation of vapor. This can be the result of a fuel or steel vaporization by nuclear energy deposition in the pool or e.g. a Fuel Coolant Interaction (FCI) with sodium evaporation. The former phenomenon can be observed in Fig. 5. 2. In case of a confined pool, the energy deposition within the pool leads to a continuous increase of temperature and pressure and

Fig. 2. Sloshing motions in a dam-break geometry (Maschek et al., 1992).

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1e+15

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Fig. 3. Typical nuclear power and deposited nuclear energy of the transition phase ULOF simulation with multiple recriticalities and power excursions (CP-ESFR case) (Flad et al., 2013).

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finally suppresses any further vaporization process and consequently the sloshing motion dies out. This means that no more energetic recriticality has to be expected and also no increasing power surges. 3. The temperature increase in the pool leads to a density reduction, fuel expansion and increase of the pool height introducing negative reactivity. One obviously observes a self-limiting behavior which is very important for the assessment of recriticality energetics (Figs. 3–7).

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Besides the investigated phenomena described before, focusing on the mitigation effects in a confined pool region, the following other phenomena contribute to the mitigation of recriticalities by disturbing efficient sloshing motions.

• Fuel discharge from the core to reach subcriticality is the main

mechanism to prevent and mitigate recriticalities and their nuclear power excursions. Analyses (Maschek et al., 2011, 1999) show that if 40% of the core fuel has been discharged, the reactivity level in the core drops significantly and a severe recriticality becomes very unlikely. A small contribution of ∼2–3% of fuel loss can be attributed to the gap system of blanket or reflector elements surrounding

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the conditions at the end of the calculation seen in Figs. 6 and 7. The pressurized fuel/steel pool is then discharged through the escape paths and the so-called expansion phase is entered.

The phenomenon is of special importance in case of strong blockages and limited or delayed fuel discharge from the core region. There exists an inherent mitigating effect in such bottled-up pools limiting the growth of recriticalities causing secondary power excursions. In the mechanistic simulations with pool configurations with less solid blockages, the temperature increase and pressure build-up in general leads to a thermal and/or mechanical destruction of the blockage structure and/or blanket/reflector structures before reaching

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Fig. 5. Sloshing motion triggered by a fuel mass dropping into the pool (ALPLK1 – fuel volume fraction).

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the enlargement of the pool region and the ingress of coolant with following FCI events play an important role (Guo et al., 2012; Maschek et al., 2011, 1999). The ingress of upper blanket fuel curbs the recriticality risk (Maschek and Asprey, 1983), as the UO2 both reduces the reactivity level and quenches the hot core fuel. However most innovative cores do not have axial blankets. The ingress of absorber material could contribute to reactivity mitigation. However the low density of current absorber material (B4C) leading to buoyancy driven separation might diminish its effect in the late pool phase (Maschek and Asprey, 1983). Eutectic formation with steel may also enhance the steel separation from the fuel pool. Obstacles in the flow retard any sloshing motions and destroy coherency of the fluid motion. Numerical investigations and experiments also show the impact of a rugged lower pool surface to

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the core. Idealized geometrical fuel configurations could still be neutronically critical but are of no relevance for the actual safety assessment. To assure and increase fuel discharge special measures are proposed (Ieda et al., 1994; Maschek, 1995; Endo et al., 2002; Sato et al., 2009; Tobita et al., 1999; Maschek et al., 2011; Maschek et al., 1998; Ishizu et al., 2010) in the new SFR systems, ranging from specially designed subassemblies to large scale tube systems. The fuel discharge through widely open structures might lead to FCI events that could lead to pressure driven recriticalities, as simulated in the current paper. The melting or break-up of blockages surrounding the pool can open discharge paths for the fuel. The core clamping system plays a significant role for the behavior of the upper core structures. Remelting of blockages and pushing them forward is one feature of this scenario. Real blanket structures pose a certain barrier for the fuel discharge, while steel structures are more easily melted away. Here

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Fig. 7. Motion pattern of the extended sloshing calculation (80 s) triggered by a fuel mass dropping into the pool.











Evaluation of the results of mechanistic SIMMER-II and SIMMERIII/IV analyses performed in the past for various core designs and power classes as e.g. CRBR (Bohl, 1979; Theofanous and Bell, 1984), SNR300 (Maschek and Asprey, 1983), MONJU (Kondo et al., 1985), SPX (Gouriou et al., 1982), CP-ESFR (Flad et al., 2017), JSFR (Endo et al., 2002; Sato et al., 2009; Tobita et al., 1999; Nakai, 2010) and ASTRID (Bachrata et al., 2015) reveals limited energetics levels expressed by maximal average bulk fuel temperatures of ∼4500 K, definitely below 5000 K. This corresponds to vapor pressures about ∼1 MPa, so no high energetics level that may cause an energetic expansion phase (Flad et al., 2017). Melting and disruption of blockages that might confine the molten fuel pool region take place during the transient, fuel is discharged and core subcriticality is reached. The physical phenomena listed in 4.2 limit an escalation to higher energetics levels. As shown in 4.1, additionally an intrinsic mechanism exists which also limits the escalation even in case of a strong blockage confinement suppressing any fuel discharge and allowing on-going sloshing recriticalities and fuel temperature increase. The new findings provide a clue, why in the past mechanistic safety analyses for various reactor types, including those with strong axial blankets or reduced fuel discharge, the nuclear energy release and peak fuel temperatures reached in recriticality events stayed under the mentioned limit. In the light of the new available information and findings one could conclude that an upper bound for energetics in transition phase pools can be deduced. A paper is in preparation, describing the probabilistic evaluation of the transition phase energetics by recriticalities based on the Phenomenological Relationship Diagram (PRD) (Tatewaki et al., 2015; Williams et al., 1980), taking into account the above findings and the fore-mentioned review of relevant publications devoted to high mechanical energy releases in case of a CDA. The results of the evaluation confirm the low probability for scenarios with high energetics.

mitigate sloshing and consequential recriticalities. Such a lower pool configuration can be observed in mechanistic code simulations. The mitigating mechanism works via reducing the compaction velocity and the coherency of material motion in case of a recriticality. In the 3D simulations of the following section the obstacle effect is demonstrated. Obstacles with potential of fuel discharge as the Control Rod Guide Tubes (CRGT) can act both in disturbing the flow field and contribute to the fuel discharge option. As long as obstacles are available and not destroyed they significantly mitigate the sloshing motion and the recriticality energetics. After destruction they can serve as efficient fuel discharge paths (Maschek et al., 2011; Maschek et al., 1998; Ishizu et al., 2010). Under optimal conditions, a significant share of the required 30–40% of discharged fuel can be attributed to the CRGT system (Maschek et al., 1998). The rheology of the pool is another important factor. Any particles (fuel or steel), fuel chunks and larger movable structures mitigate the fluid motion in the pool. The incoherency of the pool temperature distribution has a special effect especially on the mixing behavior of the individual core zones (Bohl, 1979; Maschek and Asprey, 1983; Kondo et al., 1985; Theofanous and Bell, 1984; Maschek et al., 2011; Ishizu et al., 2010). Single phase compaction in general mitigates the energy deposition of a power burst as the rapid build-up of single phase pressures leads to a rapid dispersion of the fuel accumulation (Theofanous and Bell, 1984). The compaction of fuel during sloshing leads to the reactivity and power surge. During the compaction process singlephase liquid conditions may develop and the singe phase pressure build-up leads to an efficient disassembly of the fuel and nuclear shut-down. The fuel steel ratio and heat transfer are important for the effectiveness of sloshing. Fuel vaporization drives the motion process in a fuel-rich pool. In a pool with larger steel content the heat transfer between fuel and steel becomes important. Useful information has been gained from out-of-pile and in-pile tests as SCARABEE-N (BF3) and CABRI-RAFT (TPA2) (Yamano et al., 2009). Especially in TPA2 the heat transfer has been shown to be limited by vapor blanketing of steel droplets. The indication of a reduced fuelto-steel heat transfer is an important argument that a less rapid steel vapor pressure buildup takes place mitigating the triggering of rapid core material motion and resultant energetic sloshing recriticalities. The Bell-Plesset instability (Plesset, 1954), a special form of the Rayleigh-Taylor instability (Chen, 1997), is connected to the perturbation of the interface of a converging fluid wave in cylindrical or spherical geometry as observed in the centralized sloshing motion. This type of instability is nicely visible in the sloshing experiments (see Fig. 2). Estimates of the fluid retardation in ideal geometry indicate a range of up to 20% (Li et al., 2016a,b). Experimental investigations on sloshing motions and potentials for other hydraulic disturbances are reported in Morita et al. (2014) and Tatewaki et al. (2015).

5. 3D simulations of sloshing in confined pools SIMMER calculations are presented which overcome the limitation of the mechanistic and model case simulations which were performed in the framework of past reactor safety studies. In the past mostly 2D SIMMER-III simulations have been performed which could not cover asymmetric sloshing geometries or singular obstacles in the pool region as control or shut-down rods. Similarly as in 2D simulations, to initiate sloshing, in 3D, perturbations in the pool have been assumed by a local trigger as e.g. by a dropping fuel mass or by a local pressure sources (FCI). In the following three typical cases are presented in Table 1. First the 2D simulations have been repeated in 3 D geometry to check for consistency of results. In the next step then the main aim of the analyses, investigating the impact of asymmetries, were performed. The 3D SIMMER-IV model cases were based on a similar two-dimensional cylindrical (R-Z) model as described before. The 3D meshes system is composed of 26 × 26 × 24 in the X-Y-Z dimensions (Fig. 8). The first 3D case modeled an asymmetric perturbation by dropping 398

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damping effect of obstacles and the reduction of energetics. The significant impact of structures in the flow field, seen in the simulations (Fig. 12) have already been demonstrated in the sloshing experiments (Maschek et al., 1992a,b), a phenomenon which is known and applied in marine technology. The mitigating impact of obstacles thus can be confirmed by 3D simulations. For mechanistic simulations, therefore the 3D SIMMER option is recommended which both assesses the mitigating impact of obstacles and the potential fuel discharge after their destruction.

Table 1 Summary of 3D simulation conditions. Model case (3D simulations)

Detailed pool set-up

Asymmetric case 1 Asymmetric case 2 Asymmetric case 3

Confined fuel pool + dropping mass right corner Confined fuel pool + local pressure source (FCI) Confined fuel pool + central dropping mass + obstacles

a fuel mass on one side of the pool. Fig. 9 shows an asymmetrically dropping mass case with sloshing. This asymmetric perturbation however represents a globally acting neutronic perturbation via a reactivity ramp rate and as consequence a centralized sloshing motion is triggered. The first small power peak in the simulation of an asymmetric dropping mass takes place earlier than in the case of the central dropping because of an immediate one-sided compaction from the outgoing waves. FCI could be another asymmetric trigger for sloshing. In 3D representation, this is more meaningful, as in 2D, where the FCI process at e.g. the pool bottom or top is acting as in a whole circle and at the radial pool boundary it is acting around the whole circumference. Fig. 10 shows first the sloshing motion when the FCI is assumed in a noncentral bottom location of the fuel pool. The upper pictures represent a central cut through the 3D pool. The asymmetric trigger via a FCI leads to an immediate recriticality with a power excursion. Thus asymmetric configurations still have the potential to produce recriticalities in case sufficient fuel is still in the core. In one of the first 3D SIMMER-IV mechanistic accident simulations of a ULOF (Yamano et al., 2009) one could also observe this tendency. Additional 3D calculations have been performed investigating the impact of obstacles at the pool bottom, as described before. In 2D modeling the obstacles represent rings and like walls that would obstruct the flow. In the 3D calculations, the obstacles can be modeled more realistically and in the shown simulation represents the existing control and shut-down rods in an intermediate size reactor. As example the core & special element structure (control/ shut-down rods and diluents) of the SNR-300 Mark-I core have been chosen. The special elements structures of the Mark-Ia core have been introduced into the pool (Fig. 11) and the sloshing process has been initiated by a centrally dropping fuel mass. A series of snapshots in Fig. 11 clearly show the strong damping effect of obstacles in the pool. No efficient central sloshing can be identified but a formation of individual pool regions, which lead to additional flow incoherencies. In Fig. 12 the power trace and the deposited nuclear energy in the pool with and without obstacles is compared showing the significant

6. Conclusions The objective of the current paper is the investigation of intrinsic phenomena related to the limitation and mitigation of energetics of sloshing recriticalities in confined bottled-up pool configurations. The second objective focusses on the assessment of phenomena not fully investigated in the past because of the restrictions of the 2D modeling of mechanistic and model case studies. For limiting and mitigating recriticality energetics a massive and timely fuel discharge from the confined pool region is the most effective mechanism preventing the escalation of power excursions. The discharge of ∼40% of fuel significantly diminishes or eliminates the recriticality risk. This can be achieved if the pool confining structures are transparent or weak and built-up fuel/steel blockages are incomplete or can be easily destroyed. For advanced reactor designs special elements are foreseen to allow a controlled fuel removal (CMR). In case stronger and more solid blockage formation is experienced, SIMMER simulations show the formation of larger bottled-up fuel pools which allow more coherent sloshing material motions. Several recriticalities and increasing power excursions can be observed. Reaching high energetics levels, the final temperature increase and pressure build-up finally leads to a mechanical destruction of the blockage, a massive fuel discharge and potentially the loading of the vessel structures. The question therefore arises, if mitigating intrinsic phenomena are available which limit the growth of energetics in such a bottled-up pool configuration. The energetics behavior of confined pools is therefore more deeply investigated in the paper based on mechanistic SIMMER calculations and model case studies. It could be confirmed that after some recriticality events with energy increase in the pool a saturation is reached and the sloshing activity is strongly hampered and finally dies out with the result of diminishing of the nuclear power excursions and recriticality energetics. The important findings of the investigations are:

• Also in a bottled-up pool configuration without effective fuel losses from the pool region the nuclear activity finally dies out. Thus an

Fig. 8. Geometrical conditions of the 3D case core (centrally dropping mass).

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Fig. 9. Sloshing motion of the initial phase for the 3D model case ‘Asymmetric case 1’.

Fig. 10. Sloshing motion of the initial phase for 3D model case with FCI (Asymmetric case 2).



important mitigating mechanism is represented by the pressure increase in a confined pool finally suppressing any fuel motion enhancement combined with a thermal pool expansion leading to reactivity loss and subcriticality. Several additional intrinsic mechanisms exist that mitigate the sloshing process, mostly related to the retardation of the flow, disturbance of its coherency and the loss of reactivity by mix-in of neutron absorbing material.



The second part of the paper focuses on new 3D simulations of sloshing pools with SIMMER-IV. In general, for reactor studies in the past mostly 2D SIMMER-III simulations have been performed both for mechanistic and model case studies. For the current study, SIMMER-IV 3D simulations of model cases have been set-up to specifically investigate 3D effects of asymmetries and the impact of singular obstacles in the pool region. Three important findings can be reported:

Evaluating the results of mechanistic SIMMER-II and SIMMER-III/IV analyses performed in the past for various core designs and power classes reveal limited energetics levels expressed by maximal average bulk fuel temperatures significantly below 5000 K. The new findings provide a clue, why in the past mechanistic safety analyses for various reactor types including those with strong axial blankets or reduced fuel discharge, the nuclear energy release and peak fuel temperatures reached in recriticality events stayed under the mentioned limit. In the light of the new available information and findings one could conclude that an upper bound for energetics in transition phase pools can be deduced. With new measures optimizing the core reactivity coefficients and especially with the introduction of Controlled Material Relocation

• The 3D simulations reveal that even with strong flow asymmetries •

central local trigger. Pool motion starts by fuel or steel vaporization in the highest power density location. Obstacles in the flow retard any sloshing motions and effectively destroy coherency of the fluid motion. Depending on the actually existing disturbances a significant reduction in energetics can be expected. The mechanism works via reducing the compaction velocity and the coherency of material motion in case of a recriticality. The obstacles as control rods are finally melted away but then open efficient fuel discharge paths. 3D SIMMER simulations are recommended for mechanistic analyses to realistically profit from mitigating structures in the pool.

recriticalities could be achieved under ideal geometrical pool conditions. In case sufficient fuel is still in the pool region also asymmetric configurations can thus become neutronically critical leading to a nuclear power excursion. Local triggers, connected with neutronics, as the asymmetric drop-in of fuel into the pool, causes nearly the same motion pattern as a

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t=0.00 s

t=0.30 s

t=1.40 s

t=1.80 s

t=2.40 s

t=8.00 s

Fig. 11. Sloshing motion of the 3D ‘Asymmetric case 3’ model case with many obstacles (the right pictures represent a cut through the pool center).

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(CMR) design measures the probability of energetic recriticalities that could jeopardize reactor structures is reduced to a very low level.

3D sloshing simulation with CR + Diluents 3D sloshing simulation without CR + Diluents

Acknowledgements

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The authors would like to express their appreciation for the fruitful discussions with Mrs. Tomoko Ishizu.

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Bachrata, A., Bertrand, F., Lemasson, D., 2015. Unprotected loss of flow simulation on ASTRID CFV-V3 reactor core. In: Proceedings of ICAPP 2015, May 03–06, Nice, France, Paper 15356. Bohl, W.R., Luck, L.B., 1990. SIMMER-II: A Computer Program for LMFBR Disrupted Core Analyses, LA-11415-MS. Bohl, W.R., 1979. Some recriticality studies with SIMMER-II. In: Proc. Int. Mtg. on Fast Reactor Technology, August 19–23, Seattle, USA. Buruchenko, S., Crespo, A., 2014. Validation of the DualSPHysics code for liquid sloshing. In: Proc. Int. Conf. ICCM2014, July 28–30, Cambridge, England. Chen, X.M., 1997. Rayleigh–Taylor instability of cylindrical jets with radial motion. Nucl. Eng. Des. 177, 121–129. Endo, H., Kubo, S., Kotake, S., Sato, I., Kondo, Sa., Niwa, H., Koyama, K., 2002. Elimination of recriticality potential for the Self-consistent nuclear energy system. Prog. Nucl. Energy 40 (3–4), 577–586.

1x109

0

0

1

2

3

4

5

6

7

8

Time (s) Fig. 12. Deposited nuclear energy [J] of 3D simulations with many obstacles and with no obstacles.

401

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W. Maschek et al.

Millenium, vol. 80, Transactions of the American Nuclear Society, June 6–10, Boston, MA. Maschek, W., Roth, A., Kirstahler, M., Meyer, L., 1992a. Simulation Experiments for Centralized Liquid Sloshing Motions, KfK 5090. Kernforschungszentrum Karlsruhe. Maschek, W., Munz, C.D., Meyer, L., 1992b. Investigation of sloshing motions in pools related to recriticalities in liquid-metal fast breeder reactor core meltdown accidents. Nucl. Technol. 98, 27. Maschek, W., Struwe, D., 2000. Accident analyses and passive measures reducing the consequences of a core-melt in CAPRA/CADRA reactor cores. Nucl. Eng. Des. 202, 311. Maschek, W., Flad, M., Matzerath Boccaccini, C., Wang, S., Gabrielli, F., Kriventsev, V., Chen, X.-N., Zhang, D., Morita, K., 2011. Prevention and migration of severe accident developments and recriticalities in advanced fast reactor systems. Prog. Nucl. Energy 53, 835–841. Maschek, W., 1995. In: A Preventive/Mitigative Measure Avoiding Recriticalities in Liquid Metal Reactors, TOPSAFE’95, Budapest, Hungary, September 24–27. Morita, K., Matsumoto, T., Emura, Y., Abe, T., Tatewaki, I., Endo, H., 2014. Investigation on sloshing response of liquid in a 2D pool against hydraulic disturbance. In: NTHAS9: The Ninth Korea–Japan Symposium on Nuclear Thermal Hydraulics and Safety, November 16–19, Buyeo, Korea. Nakai, R., 2010. SFR safety principles & safety approaches for future SFR. In: IAEA-GIF Joint Workshop on Safety Aspects of SFR, June 23–25, Vienna, Austria. Pigny, S.L., 2010. Academic validation of multi-phase codes. Nucl. Eng. Des. 240, 3819–3829. Plesset, M.S., 1954. On the stability of fluid flows with spherical symmetry. J. Appl. Phys. 25, 96–98. Risikoorientierte Analyse zum SNR-300 (Risk-Oriented Study of SNR-300), Gesellschaft für Reaktorsicherheit, GRS-51, 1982. Ruggieri, W.J.M., Tommasi, J., Lebrat, J.F., Suteau, C., Plisson-Rieunier, D., De Saint Jean, C., Rimpault, G., Sublet, J.C., 2006. ERANOS 2.1: International code system for GEN IV fast reactor analysis. In: Proceedings of ICAPP ’06, June 4–8, Reno, NV, USA, Paper 6360. Sato, I., Tobita, Y., Konishi, K., Kamayama, K., Toyooka, J., Nakai, R., Kubo, S., Kotake, S., Komayama, K., Vassiliev, Y., Vurim, A., Zuev, V., 2009. Elimination of severe recriticality events in the core disruptive accident of JSFR aiming at in-vessel retention of the core materials. In: FR’09, Kyoto, Japan, December 7–11. Tatewaki, I., Morita, K., Endo, H., 2015. A study on characteristics of molten pool sloshing in core disruptive accidents. In: ICONE-23, May 17–21, Chiba, Japan. Theofanous, T.G., Bell, C.R., 1984. An Assessment of CRBR Core Disruptive Accident Energetics, NUREG/CR-3225, LA-9716-MS. U.S. Nuclear Regulatory Commission. Tobita, Y., Morita, K., Kawada, K., Niwa, H., Ninokata, N., 1999. Evaluation of CDA energetics in the prototype LMFBR with latest knowledge and tools. In: ICONE-7, Tokyo, Japan. Vasile, A., 2015. The ASTRID project. In: IAEA Forty-Eighth Meeting of the Technical Working Group on Fast Reactors, May 29, IPPE, Russian Federation. Vorobyev, V., Kriventsev, V., Maschek, W., 2011. Simulation of central sloshing experiments with smoothed particle hydrodynamics (SPH) method. Nucl. Eng. Des. 241, 3086–3096. Williams, D.C., et al., 1980. LMFBR Accident Delineation Study: Phase I Final Report, NUREG/CR-1507, SAND80-1267. U.S. NRC. Yamano, H., et al., 2003. SIMMER-IV: A Three-Dimensional Computer Program for LMFR Core Disruptive Accident Analysis. Japan Nuclear Cycle Development Institute JNC TN9400 2003-070. Yamano, H., et al., 2008. Development of a three-dimensional CDA analysis code: SIMMER-IV and its first application to reactor case. Nucl. Eng. Des. 238, 66–73. Yamano, H., Suzuki, T., Tobita, Y., Matsumoto, T., Morita, K., 2012. Validation of the SIMMER-IV severe accident computer code on three-dimensional sloshing behavior. In: Proc. 8th Japan–Korea Symposium on Nuclear Thermal Hydraulics and Safety, N8P1004, December 9–12, Beppu, Japan. Yamano, H., Onoda, Y., Tobita, Y., Sato, I., 2009. Transient heat transfer characteristics between molten fuel and steel with steel boiling in the CABRI-TPA2 test. Nucl. Technol. 165, 145. Yamano, H., Tobita, Y., Fujita, S., Maschek, W., 2009. First 3-D calculation of core disruptive accident in large, sodium-cooled fast reactor. Ann. Nucl. Energy 36, 337–343.

Fiorini, G.L., 2009. The Collaborative Project on European Sodium Fast Reactor (CP ESFR) FISA 2009, 22–24 June, Prague, Czech Republic. Flad, M., et al., 2013. Severe accident analyses with SIMMER-III. In: Int. Conference on Fast Reactors and Related Fuel Cycles: Safe Technologies and Sustainable Scenarios (FR13), Paris, France. Flad, M., Gabrielli, F., Gianfelici, S., Li, R., Maschek, W., Matzerath Boccaccini, C., Vezzoni, B., Rineiski, A., 2017. Quantitative evaluation of the post disassembly energetics of a hypothetical core disruptive accident in a sodium cooled fast reactor. In: International Conference on Fast Reactors and Related Fuel Cycles: Next Generation Nuclear Systems for Sustainable Development (FR17), June 26–29, Yekaterinburg, Russian Federation. Gif IV Technology Roadmap, November 2002. Available from: < http://www.gen-4. org > . Gouriou, A., Francillon, E., Kayser, G., Malenfer, G., Languille, A., 1982. The dynamic behavior of the super-phenix reactor under unprotected transient. In: Proc. of the LMFBR Safety Topical Meetin, July 19–23, Lyon, II-291. Guelfi, A., Bestion, D., Boucker, M., Boudier, P., Fillion, P., Grandotto, M., Hérard, J.-M., Hervieu, E., Péturaud, P., 2007. NEPTUNE: a new software platform for advanced nuclear thermal hydraulics. Nucl. Sci. Eng. 156, 281–324. Guo, L., Zhang, S., Morita, K., Fukuda, K., 2012. Fundamental validation of the finite volume particle method for 3D sloshing dynamics. Int. J. Numer. Methods Fluids 68, 1–17. Henderson, D.M., Miles, J.W., 1994. Surface-wave damping in a circular cylinder with a fixed contact line. J. Fluid Mech. 275, 285–299. Ieda, Y., Niwa, H., Uto, N., Kondo, S., 1994. Assessment of proposed passive prevention and mitigation measures for future fast breeder reactors. In: Proc. Int. Conf. ARS’94, April 17–21, Pittsburgh, USA. Ishizu, Tomoko, Endo, Hiroshi, Tokiwai, Moriyasu, Yokoyama, Tsugio, Ninokata, Hisashi, 2010. Study of the self-controllability for the fast reactor core with high thermal conductivity. J. Nucl. Sci. Technol. 47 (8), 684–697. Ishizu, T., Endo, H., Tatewaki, I., Yamamoto, T., Shirakawa, N., 2012. Development of integrated core disruptive accident analysis code for FBR–ASTERIA-FBR. In: Proceedings of ICAPP ’12, June 24–28, Chicago, USA, Paper 12100. Kondo, Sa., Furutani, A., Ishikawa, M., 1985. SIMMER-II application and validation studies in Japan for energetics accommodation of severe LMFBR accidents. In: Proc. Int. Topl. Mtg. Fast Reactor Safety, vol. I, American Nuclear Society, Knoxville, Tennessee, April 21–25, p. 481. Kondo, S., Morita, K., Tobita, Y., Shirakawa, N., 1992. SIMMER-III: an advanced computer program for lmfbr severe accident analysis. In: ANP'92, Tokyo, Japan. Kondo, S., Tobita, Y., Morita, K., Brear, D.J., Kamiyama, K., Yamano, H., Fujita, S., Maschek, W., Fischer, E.A., Kiefhaber, E., Buckel, G., Hesselschwerdt, E., Flad, M., Coste, P., Pigny, S., 1999. Current status and validation of the SIMMER-III LMFR safety analysis code. In: Proc. 7th International Conference on Nuclear Engineering (ICONE-7), April 19–23, Tokyo, Japan, ICONE-7249. Lakehal, D., Meier, M., Fulgosi, M., 2002. Interface tracking towards the direct simulation of heat and mass transfer in multiphase flows. Int. J. Heat Fluid Flow 23, 242–257. Languille, A., Garnier, J.C., Lo Pinto, P., Na, B.C., Verrier, D., Duplaix, J., Allan, P., Sunderland, R.E., Kiefhaber, E., Maschek, W., Struwe, D., 1995. CAPRA core studies – the oxide reference option. In: GLOBAL ’95, Paris, France. Li, R., Maschek, W., Matzerath Boccaccini, C., Vezzoni, B., Flad, M., Rineiski, A., 2016b. Impact of the Bell-Plesset instability on centralized sloshing in pool geometry. J. Hydrogen Energy 41, 7126–7131. Li, R., Maschek, W., Matzerath Boccaccini, C., Marchetti, M., Kriventsev, V., Rineiski, A., 2016a. Bell-Plesset instability analysis for an inward centralized sloshing. J. Nucl. Eng. Des. 297, 313–319. Martel, C., Nicolas, J.A., Vega, J.M., 1998. Surface-wave damping in a brimful circular cylinder. J. Fluid Mech. 360, 213–228. Maschek, W., Asprey, M., 1983. SIMMER-II recriticality analyses for a homogeneous core of the 300 MWe class. Nucl. Technol. 63, 330. Maschek, W., Morita, K., Flad, M., 1998. SIMMER-III analyses of enhanced fuel removal processes under core disruptive accident conditions. In: 6th International Conference on Nuclear Engineering, ICONE-6, May 10–15. Maschek, W., Fauske, H.K., Kondo, S., 1999. Severe recriticalities, still a concern for future liquid metal reactors? In: 1999 ANS Annual Meeting: The Atom and the Next

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