Fragmentation of continuous molten copper droplets penetrating into sodium pool

The progression of hypothetical core disruptive accidents (CDAs) in metal fuel cores is strongly affected by exclusion of molten metal fuel from the core region due to molten fuel–coolant interaction (FCI). As a basic study of FCI, the present paper focuses on the fragmentation characteristics of continuous molten copper droplets with a total mass from 20 to 50 g penetrating into a sodium pool. The results show that the fragmentation of the continuous molten copper droplets is sensitive to the change of the hydrodynamic and thermal conditions when the instantaneous contact interface temperature (T_i) is lower than the turning point (T_tp) and insensitive at T_i > T_tp. Compared with the fragmentation of a single droplet, the fragmentation of continuous droplets is accelerated and enhanced due to the collision between the droplets and the upward microjets. The present mass median diameter (D_m) or dimensionless mass median diameter (D_m/D₀) of continuous copper droplets shows a distribution with smaller values than those of single copper droplet, and larger values than those of copper jets under similar thermal and hydrodynamic conditions. These results are promising to assure the termination of accidents in CDAs and useful to the core design with enhanced safety in FBRs.     

Fragmentation of a Single Molten Metal Droplet Penetrating Sodium Pool I Copper Droplet and the Relationship with Copper Jet

The progression of hypothetical core disruptive accidents in metallic fuel fast breeder reactors is strongly affected by the fragmentation of molten metallic fuels due to the molten fuel-coolant interaction (FCI). As a basic study of FCI, the present paper focuses on the fragmentation of a single molten copper droplet with mass from 1 to 5 g, whichpenetrated a sodium pool at instantaneous contact interface temperatures (T_i) from 995 to 1,342°C. Intensive fragmentation of a single molten copper droplet was clearly observed even if T_i values are below the melTsing point (1,083°C) of copper besides the higher T_i range. The intensive fragmentation shows that the mass median diameters (D_m) of copper droplets with a fivefold difference in mass or the same mass have little difference, i.e., they are nearly the same. Under the lower T_i condition, the D_m data of droplet fragments of both the same and different masses scatter widely. It is found that the present D_m/D₀ data of mass median diameter normalized by the diameter before touching sodium (D0) give a distribution with larger values than those of molten copper jets with large mass from 20 to 300 g under the lower T_i condition, which were previously reported by the authors, because of the limited amount of heat of droplets. The present Dm=D0 data under the higher T_i condition are found to show an effecTive fragmentation compared with those of molten copper jets with a large mass of 4 kg.     

Thermal Fragmentation of a Molten Metal Jet Dropped into a Sodium Pool at Interface Temperatures below Its Freezing Point

In order to verify the thermal fragmentation of a molten jet dropped into a sodium pool at instantaneous contact interface temperatures below its freezing point, a basic experiment was carried out using molten copper and sodium. Twenty grams of copper was melted in a crucible with an electrical heater and was dropped through a 6 mm nozzle into a sodium pool of 553 K, in the form of a jet column. Thermal fragmentation originating inside the molten copper jet with a solid crust was clearly observed in all runs. It is verified that a small quantity of sodium, which is locally entrapped inside the molten jet due to the organized motion between the molten jet and sodium, is vaporized by the sensible heat and the latent heat of molten copper, and the high internal pressure causes the molten jet with a solid crust to fragment. It is also found that the fragmentation caused in the molten copper-sodium interaction was severer than that in the molten uranium alloy jet-sodium interaction, which was reported by Gabor et al, under the same superheating condition and lower ambient Weber number condition of molten copper.     

UO2 solidification phenomena associated with rapid cooling in liquid sodium

An important safety aspect of fuel meltdown in a liquid-metal fast breeder reactor (LMFBR) is the fragmentation of molten UO₂ into finely divided particles when quenched in sodium coolant, with subsequent coolant vaporization. In order to analyze the mechanics of such fragmentation, a knowledge of the physical state of the UO₂ surface within the breakup period must be known. To accomplish this, the kinetics of crystal formation and growth are investigated and compared with the heat transfer controlled solidification rate to determine whether or not the surface of a UO₂ droplet can remain molten if contact is established during quenching in sodium coolant. Results indicate that although the initial heat transfer rate for perfectly wetted UO₂ is quite rapid, the crystallization process is approximately an order of magnitude greater, with the UO₂-Na contact temperature well below the temperature for homogeneous solidification. Thus, it can be concluded that the freezing of UO₂ in sodium is heat transfer limited such that any fragmentation analysis should account for surface solidification.     

汽膜对熔滴水力学碎化影响的数值模拟

在熔融物与冷却剂相互作用(FCI)过程中,熔滴的水力学碎化对于后续是否产生蒸汽爆炸以及爆炸的强弱程度有着重要影响。传统的熔滴水力学碎化数值研究通常只考虑液液直接接触的两相系统;而堆芯熔化后,熔融物温度在2 500K以上,熔融物周围会迅速产生汽膜,导致熔滴和冷却剂之间的传热和阻力特性发生改变。本文基于PLIC-VOF(piecewise linear interface construction-volume of fluid)界面跟踪方法对有汽膜存在的三相系统中的熔滴水力学碎化过程进行了数值研究,通过分析熔滴在有无汽膜和不同边界速度触发情况下碎化过程中的界面特性,发现熔滴碎化程度随Weber数的增加而加剧,汽膜对熔滴的水力学碎化存在一定的抑制作用。     

Transformation and fragmentation behavior of molten metal drop in sodium pool

In order to clarify the fragmentation mechanism of a metallic alloy (U–Pu–Zr) fuel on liquid phase formed by metallurgical reactions (liquefaction temperature = 650 °C), which is important in evaluating the sequence of core disruptive accidents for metallic fuel fast reactors, a series of experiments was carried out using molten aluminum (melting point = 660 °C) and sodium mainly under the condition that the boiling of sodium does not occur. When the instantaneous contact interface temperature (T_i) between molten aluminum drop and sodium is lower than the boiling point of sodium (T_c,bp), the molten aluminum drop can be fragmented and the mass median diameter (D_m) of aluminum fragments becomes small with increasing T_i. When T_i is roughly equivalent to or higher than T_c,bp, the fragmentation of aluminum drop is promoted by thermal interaction caused by the boiling of sodium on the surface of the drop. Furthermore, even under the condition that the boiling of sodium does not occur and the solid crust is formed on the surface of the drop, it is confirmed from an analytical evaluation that the thermal fragmentation of molten aluminum drop with solid crust has a potential to be caused by the transient pressurization within the melt confined by the crust. These results indicate the possibility that the metallic alloy fuel on liquid phase formed by the metallurgical reactions can be fragmented without occurring the boiling of sodium on the surface of the melt.     

Simulation of the mixing process in FCIs with hydrodynamic fragmentation model

Fuel Coolant Interactions (FCIs) are important issues in nuclear reactor severe accident analysis. In FCIs, fragmentation model of molten droplets is a key factor to estimate degree of possible damage. In this paper, the mixing process in FCIs is studied by the simulation of MIXA experiment with hydrodynamic fragmentation model. The result shows that hydrodynamic fragmentation model underestimates the fragmentation rate of high temperature molten droplets under the condition of low Weber numbers. It is concluded that models based on thermal fragmentation mechanism should be adopted to analyze the FCI process and its consequence.     

Experimental investigation on the bursting of single molten droplet in coolant

An experiment facility for observing low-temperature molten tin alloy droplet into water was es- tablished to investigate mechanisms of vapor explosion occurring in severe accidents of a fission nuclear reactor.The vapor explosion behaviors of the molten material were observed by a high-speed video cam- era and the vapor explosion pressures were recorded by a pressure transducer mounted under the water surface.The results showed that the pressure reached a peak value when the molten metal temperature was 600℃-650℃,and the coolant temperature had an obvious decreasing effect on the droplet breakups.A model for single droplet fuel/coolant interaction is proposed.It considers that in the case of Rayleigh-Taylor instability,the coolant that jets from opposite direction penetrates into the fuel and the vapor explosion occurs because of the rapid evaporation.This model explained the effect of metal droplet temperature and coolant temperature on vapor explosion.     

Fragmentation behavior during molten material and coolant interactions

A safe design for a fast breeder reactor (FBR) requires post-accident heat removal (PAHR) for any potential core disruptive accident (CDA). It is important to ensure that the molten core material solidifies in the sodium coolant in the reactor vessel even if all of the core material has melted. In the present experiment, molten material was injected into water to experimentally obtain the information on the molten material jet entering the coolant and its fragmentation. Visual information was obtained with a high-speed video camera, showing that fragmentation behavior on the side of the jet was different from that on the jet front, and that the injection nozzle diameter significantly influenced the jet breakup length, while the molten jet temperature and the coolant temperature did not influence the jet breakup length. Comparison of the diameters of fragments of the solidified molten material thus obtained with fragmentation theory shows that the median fragment diameter is between the critical Weber number theory and the most-unstable wavelength of the instability theory of surface waves at a gas liquid interface.The quench behavior of the molten jet in coolant was calculated for FBR conditions by using the model that reflects actual fragmentation behavior. It was clarified that the mass of molten material in the coolant pool is related to the fragment diameter under FBR conditions.     

Visualization on the behavior of inert gas jets impinging on a single glass tube submerged in liquid sodium

In order to accurately model sodium–water reaction jets in steam generators of fast breeder reactors, knowledge of size distributions or mean diameters of liquid sodium droplets entrained into the reaction jets is prerequisite. In the present study, argon-gas jet behaviors, without chemical reaction, injected into liquid sodium were successfully visualized using an endoscope and a glass tube, and the size distributions and mean diameters of liquid sodium droplets entrained into the gas jet were also obtained in the bubbling regime. Most of the liquid sodium droplets were observed to be intermittently produced in the vicinity of a gas nozzle in the present study. The droplet size distributions of entrained sodium droplets were found to agree well with the Nukiyama–Tanasawa distribution function when the arithmetic mean diameter was used. The Sauter mean diameters obtained in the present study were also found to be well correlated with an empirical equation proposed by Epstein et al. The present study shows that the existing knowledge, which is based on the results of water experiments, is suitable in terms of accuracy in practice.     

Prediction of minimum UO2 particle size based on thermal stress initiated fracture model

An analytic study was employed to determine the minimum UO₂ particle size that could survive fragmentation induced by thermal stresses in a UO₂---Na fuel-coolant interaction (FCI), based on a brittle fracture mechanics approach. Solid and liquid UO₂ droplets were considered, with perfect wetting by the sodium or finite heat transfer coefficient. The analysis indicated that particles below the range of 50 μm in radius could survive an FCI under the most severe temperature conditions without thermal stress fragmentation, and seemed to verify the experimental observations as to the range of the minimum particle size due to thermal stress fragmentation by FCI. The basic complexities in fracture mechanics make further investigation in this area interesting but not necessarily fruitful for the immediate future.     

Study on fragmentation behavior of liquid lead alloy droplet in water

Fragmentation behavior of molten lead alloys droplet in water was investigated experimentally by releasing liquid LBE (45w%Pb-55w%Bi) and lead droplets into a pool of subcooled water. The fragmentation occurred when the temperature of the interface between a molten droplet and water was higher than the spontaneous nucleation temperature of water and lower than the minimum film boiling temperature. With increasing the droplet temperatures, the peak pressure in fragmentation of LBE droplet increased from 5 to 8 kPa, and for lead, the value remained around 2 kPa. With increasing the water subcooling, the peak pressure in fragmentation remained constant at 5 kPa for LBE droplet and at 2 kPa for lead droplet. The lead alloy fragmentation process in water was numerically simulated by embedding a semi-empirical fragmentation model for droplet fragmentation rate into the computer code of two-phase flow: JASMINE code. The corresponding results, such as pressure history and fragmentation peak pressure, agreed well with the experimental results.     

Fragmentation of molten debris during a molten fuel-coolant interaction

The potential for an energetic molten fuel-coolant interaction (MFCI) during a hypothetical core meltdown accident is of concern in nuclear safety analysis. An important aspect of a MFCI is the fine fragmentation and intermixing of molten core debris with the core coolant. The fragmentation characteristics of the molten debris (a mixture of UO₂ and zircaloy cladding) particles produced during a recent high-energy in-pile experiment are analyzed. The experimental results suggest that two mechanisms contributed to the fragmentation of the molten debris in this experiment, in which an MFCI occured. Phenomenological modelling of these two mechanisms and the effects of the governing parameters are presented.     

A thermal stress mechanism for the fragmentation of molten UO2 upon contact with sodium coolant

An important aspect of fuel-coolant interaction problems relative to various hypothetical LMFBR accidents is the fragmentation of molten oxide fuel on contact with sodium coolant. In order to properly analyze the kinetics of such an event, an understanding of the breakup process and an estimate of the size and dispersion of such fragmented fuel must be known. A thermal stress initiated mechanism for fragmentation is presented using elastic stress theory for the cases of both temperature-dependent and independent mechanical properties. Included is a study of the effect of the choice of surface heat transfer boundary condition and the compressibility of the unsolidified inner core. Results of parametric calculations indicate that the thermal stresses induced in the thin outer shell and the pressurization of the inner molten core are potentially responsible for the fragmentation. For UO₂ in Na the calculated stresses are extremely high, while for aluminum in water they are much smaller and a strong function of the surface heat transfer boundary condition. Qualitatively, these results compare favorably with small scale dropping experiments, that is, molten UO₂ quenched in Na undergoes fragmentation while aluminum in water usually results in little breakup. The experimentally observed increase in breakup with decreasing coolant temperature is also in qualitative agreement with the thermal stress-induced mode of fragmentation.     

A description of a fuel-coolant thermal interaction model with application in the interpretation of experimental results

A coherent thermo- and hydrodynamic model to explain molten fuel-coolant interactions in the CORECT II experimental facility is described. The effects of heat losses to the surroundings, mass entrainment, two-phase frictional losses and non-condensable gases are taken into account for the coolant modelization, while a solidification-controlled fragmentation model is proposed for the fuel behavior. Interpretation of two significant experiments in the CORECT II facility permit verification of the consistency of the formulation for the behavior of the fuel-coolant couple. The interpretations allow a generalized interaction scenario in this facility to be proposed, illustrate the importance of understanding the mechanisms underlying the prefragmentation and mixing phase preceding the thermal interaction, and confirms the hypothesis that the process of solidification in the fuel is a major factor governing fuel fragmentation.     

Study on thermal-hydraulic behavior during molten material and coolant interaction

In a core disruptive accident (CDA) of a Fast Breeder Reactor, the post accident heat removal (PAHR) is crucial for the accident mitigation. The molten core material should be solidified in the sodium coolant in the reactor vessel. The material, being fragmented while solidification and forming debris bed, will be cooled in the coolant.

In the experiment, molten material jet is injected into water to experimentally obtain the visualized information of the fragmentation and boiling phenomena during PAHR in CDA. The experiment shows that the break up of the molten material into fine fragments is observed at the front, side and middle part of the jet during very short time interval. The distributed particle behavior of the molten material jet is observed with high-speed video camera. And the visual data is analyzed with Particle Imaging Velocimetry (PIV).

The experimental results are compared with the existing theories. Consequently, the marginal wavelength on the surface of a water jet is close to the value estimated based on the Rayleigh–Taylor instability. Moreover, the fragmented droplet diameter obtained from the interaction of molten material and water is close to the value estimated based on the Kelvin–Helmholtz instability.     

The tandem mirror hybrid reactor

A tandem-mirror fusion reactor was designed to produce fissile fuel for conventional fission-power reactors. The tandem-mirror concept lends itself to the development of an excellent hybrid reactor because of its cylindrical geometry and steady-state nature. Different coolant technology, fuel cycles, and physics operating modes were considered. The four technologies distinguished by coolant type are: (1) gas, either helium or steam, (2) water, (3) liquid metal, and (4) molten salt. Four physics operating modes were considered: (1) the two-component, (2) Kelley, (3) thermal and (4) thermal barrier. The thermal-barrier mode was finally chosen because of its simultaneous high Q and low beam, and magnet technologies gave superior performance. The design described, however, uses the Q 2 thermal mode because the thermal barrier concept was invented toward the end of the study. The neutral-beam injectors are of the negative-ion type operated at 400 keV. The magnet technology under consideration is based on Nb₃Sn conductor operated at 12–15 T. The plasma exhaust is converted at 50% efficiency to electricity in a one-stage, direct-energy converter.We set the size of the commercial plant at 4000 MW nuclear and placed primary emphasis on ²³³U production. We dropped water as a coolant option because of poor breeding resulting from neutron moderation. Liquid metal was dropped because of its safety-related fire-hazard and MHD-design problems, which resulted in some drop in breeding. After a more thorough study of molten salt and helium, we judged the molten salt case we studied to require too much development with too great a risk of not finding solutions to problems such as fabrication of molybdenum structures. The helium-cooled, Th-metal blanket performed well and resulted in a fuel cost of $ 70/g ²³³U (compared to $ 80/g for molten salt) and had a support ratio of 9, which is not as high as the fission-suppressed molten-salt case of 20 but is still a large number. The general class of fission suppressed blankets of which molten salt is only one example was judged to be well worth further study.The electric power capacity of ²³³U-fueled, light-water fission reactors that can be supported by the hybrid of the same nuclear power is 11 000 MWe for the gas-cooled case and 28 000 MWe for the molten salt case at an add-on cost of electricity of 24% for He and 14% for molten salt to account for the hybrid part of the system.     

Assessment of Fuel Coolant Interactions (FCIs) in the FBR Core Disruptive Accident (CDA)

Application of general behavior principles (GBPs) and consideration of relevant contact modes suggest that only incoherent small-scale fuel coolant interactions (FCIs) with negligible damage potential appear possible with the molten oxide fuel-liquid sodium system as the fuel disperses away from the core into a coolable non-critical array.

In contrast to the SPERT-1, BORAX-1 and SL-1 nuclear transients that ultimately led to energetic vapor or steam explosions, the presence of molten fuel and liquid sodium in the FBR core always requires the presence of solid cladding which separates the fuel and coolant and, hence prevents energetic FCIs prior to coolant escape.

Furthermore, unlike the CORECT-II experiments which examined dynamic re-entry of liquid sodium on molten fuel pools that resulted in unstable interfaces leading to significant sodium entrapment and relatively energetic FCIs, the prevailing contact mode in the FBR core disruptive accident (CDA) scenario is displacement of the lighter and less viscous liquid sodium by the heavier and more viscous molten fuel resulting in stable interfaces with no significant sodium entrapment and FCIs. Dynamic re-entry of liquid sodium into the core is not possible with the two-component steel vapor-liquid sodium system, since the interface contact temperature upon steel vapor condensation is well in excess of the sodium boiling temperature. A pressure reduction in the steel vapor region due to condensation is immediately compensated for by an equivalent pressure increase due to sodium evaporation.

Finally, considering that the molten oxide fuel-liquid sodium interface contact temperature is well below the sodium homogeneous nucleation temperature which in turn is well below the fuel melting temperature, not only eliminates the potential for large-scale vapor explosions as molten fuel streams are injected into liquid sodium pools, but also implies that small scale superheat explosions are possible which are consistent with the usually observed incoherent sharp pressurization events (amplitudes up to the order of 10 MPa and duration of the order of 1 ms). These general behavior characteristics are also consistent with complete fuel fragmentation with fragment sizes ranging from 100 to 1,000 μm, and the absence of significant or damaging FCIs.     

Droplet size estimation of two-phase flashing jets

Loss-of-coolant accident analyses for CANDU reactors include consideration of postulated scenarios in which high-enthalpy coolant discharges into the containment building as a two-phase jet. This jet may contain dissolved fission products. The fraction of jet fluid airborne as aerosol-sized droplets limits the postulated release of fission products to the outside atmosphere, and so is of interest. A model has been developed to predict the droplet size distribution of such a jet. It incorporates the aerodynamic and thermal fragmentation of the jet and is based on a Monte Carlo technique. The results show that the average droplet size increases from 6 μm to 14 μm as the discharge pressure and temperature decrease from 10 MPa and 550 K to 2.5 MPa and 475 K.