Fragmentation of a single molten metal droplet penetrating into sodium pool. IV. Thermal and hydrodynamic effects on fragmentation in copper

To characterize the relationship between thermal and hydrodynamic effects on fragmentation of molten metallic fuels, with the interaction of the sodium coolant under a wide range of thermal and hydrodynamic conditions, in this paper, we focus on the fragmentation characteristics of a single molten copper droplet (1 and 5 g) with an ambient Weber number (We _a) from 102 to 614 and superheating conditions from 15 to 574°C, which penetrates into a sodium pool at an initial temperature from 298 to 355°C. In our experiments, fine fragmentations of the single molten copper droplets with a high We _a were clearly observed even under a supercooled condition that is well below the copper melting point of 1083°C. The dimensionless mass median diameters (D _m /D ₀) of molten droplets with a high We _a are less than the molten droplets with a low We _a under the same thermal condition. When We _a was approximately >200, the hydrodynamic effect on fragmentation became dominant over the thermal effect under a relatively low superheating condition. For a higher We _a range, the comparisons indicated that the fragment sizes of the molten copper droplets had similar distributions to those of copper and metallic fuel jets and stainless steel droplets even with different thermophysical properties and a 1000-fold mass difference, which implied the possibility that the fragment size characteristics of the molten metal jets could be evaluated by the interaction of a single droplet with the sodium coolant without consideration of dropping modes and mass.     

Boiling fragmentation of molten stainless steel and copper in sodium

Approximate measurements were made on fuel fragmentation of stainless steel/sodium and copper/sodium systems: the surface area of stainless steel increased by a factor of 260 to 3.1 and that of copper by a factor of 300 to 2.7 m²/kg. The number of particles obtained was about 10⁸ per kg fuel. The conditions were: stainless steel 1600°C, copper 1927°C, sodium 400°C at 1 bar ambient pressure (argon cover gas); no detectable pressures accompanied the interaction.A violent sodium boiling model is used for the explanation of the results. A specified number of sodium vapor bubbles grow and collapse with high frequency on the contact surface. The collapse effectively increases the fuel (=heating) surface, and an appropriate energy transfer coefficient is assumed. Contact temperatures, nucleation, bubble statistics, mechanical energy transfer, surface increase and heat transfer are coherently treated and describe the fragmentation transient. The copper surface area is calculated to increase by a factor of about 750 to 6.6 m²/kg within very short times of 1 ms or even less, the stainless steel surface by 200 to 2.4 m²/kg.     

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.     

Breakup and fragmentation behavior of molten material jet in multi-channel of BWR lower plenum

To estimate the current status of reactor pressure vessel of Fukushima Daiichi nuclear power plant, it is important to clarify the breakup and the fragmentation behavior of molten material jet in boiling water reactor (BWR) lower plenum by a numerical simulation. To clarify the effects of complicated structures on jet breakup and fragmentation behavior, we conducted visualized experiments simulating the severe accident in the BWR by using the multi-channel experimental apparatus. In this study, the jet falling behavior, the jet breakup length, the fragmentation behavior and internal/external velocity profiles of the jet are observed by the backlight method and the particle image velocimetry. It is clarified that the complicated structures prolong the jet breakup length or make the fragments fall together to the lower plenum similar to the bulk state. In addition, it is clarified that strong shearing stress occurs at the crest of interfacial waves at the side of the jet. Finally, the fragment diameters measured in the present study well agree with the theory based on the shering stress by changing the coefficient term. Thus, it is suggested that the fragmentation mechanism is controlled by shearing stress and the fragment diameter can be estimated by adjusting the characteristic value.     

Distance for fragmentation of a simulated molten-core material discharged into a sodium pool

A series of experiments has been carried out to obtain experimental knowledge on the distance for fragmentation of a molten core material discharged into the sodium plenum during postulated core disruptive accidents of sodium-cooled fast reactors. In the current experiments, 0.9 kg of molten aluminum (initial temperature: around 1473 K) was discharged into a sodium pool (diameter: 0.11 m, depth: 1 m, initial temperature: 673 K) through a nozzle (inner diameter: 20 mm). Visual observation of the fragmentation behavior was performed using an X-ray imaging system. The following experimental results were obtained. (1) Liquid column of molten aluminum was intensively fragmented almost simultaneously with a rapid expansion of sodium vapor in the vicinity of the column. (2) Due to the intensive fragmentation, penetration of the liquid column was limited to approximately 100 mm or so from the sodium level. (3) The molten aluminum was rapidly cooled after the intensive fragmentation. Based on these results, the distance for fragmentation of the liquid column was estimated to be 100 mm in the experiments. Through the current experiment, useful knowledge was obtained for the future development of an evaluation method of the distance for fragmentation of the molten core material.     

Simulation of molten metal freezing behavior on to a structure

In the severe accident analysis of liquid metal reactors (LMRs), understanding the freezing behavior of molten metal onto the core structure during the core disruptive accidents (CDAs) is of importance for the design of next-generation reactor. CDA can occur only under hypothetical conditions where a serious power-to-cooling mismatch is postulated. Material distribution and relocation of molten metal are the key study areas during CDA. In order to model the freezing behavior of molten metal of the postulated disrupted core in a CDA of an LMR and provide data for the verification of the safety analysis code, SIMMER-III, a series of fundamental experiments was performed to simulate the freezing behavior of molten metal during penetrating onto a metal structure. The numerical simulation was performed by SIMMER-III with a mixed freezing model, which represents both bulk freezing and crust formation. The comparison between SIMMER-III simulation and its corresponding experiment indicates that SIMMER-III can reproduce the freezing behavior observed on different structure materials and under various cooling conditions. SIMMER-III also shows encouraging agreement with experimental results of melt penetration on structures and particle formation.     

Phase segregation model and molten pool thermal-hydraulics during molten core-concrete interaction

A new model for melt thermal-hydraulics during molten core concrete interaction (MCCI) is presented. This model assumes that phase segregations occur in the melt, leading to a crust formation composed of refractory materials (UO₂ZrO₂). The interface temperature between this crust and the liquid melt is linked to the solid fraction and is calculated on the basis of a thermal equilibrium assumption. The solid fraction is also controlled by conduction heat transfer through the solid crust. It is shown that the temperatures measured in the ACE experiments are recalculated within a maximum deviation of 10%, (when referenced to the solidus temperature) without any adjustment. Other important consequences for this new approach are outlined: for physical properties, physico-chemical interactions, fission products behavior, mixing with sacrificial materials, and crust stabilities.     

钠冷快堆中熔融池模型的建立与验证

快堆在超设计基准事故下运行时,会导致钠沸腾和干涸,如果不能及时停堆,接着就会产生燃料元件的熔化坍塌,在组件盒下部形成熔融池.为了对熔融池给出合理的安全分析,采用机理建模的方法,建立了完整的熔融池模型,并在法国的SCARABEE系列实验中的BF1三种功率的实验上进行了验证,和实验吻合较好,通过和所验证过的GEYSER及BF2等实验模型进行比较,得出了有关熔融池机理的相关结论.通过排热和温升等相关数据的比较,对熔融池向外的排热形式给出了合理分析,并得出了相关结论.     

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.     

Heat and fission product transport in molten core material pool with crust

Heat transfer and fluid flow in a molten pool are influenced by internal volumetric heat generated from the radioactive decay of fission product species retained in the reactor vessel during a severe accident. The pool superheat is determined based on the overall energy balance that equates the heat production rate to the heat loss rate. Decay heat of fission products in the pool is estimated by product of the mass concentration and energy conversion factor of each fission product. Twenty-nine elements are chosen and classified by their chemical properties to calculate heat generation rate in the pool. The mass concentration of a fission product is obtained from released fraction and the tabular output of the ORIGEN 2 code. The initial core and pool inventories at each time can also be estimated using ORIGEN 2. The released fraction of each fission product is calculated based on the bubble dynamics and mass transport. Numerical analysis is performed for heat and fission product transport in a molten core material pool during the Three Mile Island Unit 2 (TMI-2) accident. The pool is assumed to be a partially filled hemisphere, whose change in geometry is neglected during the numerical calculation. Calculated results indicate that the peak temperature in the molten pool is significantly lowered, since a substantial amount of the volatile fission products is released from the molten pool during progression of the accident. The results may directly be applied to the existing severe accident analysis codes to more mechanistically determine the thermal load to the reactor vessel lower head during the in-vessel retention.     

Dynamics of liquid sodium pool spreading under sodium fire conditions

The spreading of burning liquid sodium has been investigated using a depth-averaged shallow water equation for isothermal and non-isothermal (burning) conditions. In the latter case, the spreading is one-way coupled with the flame through a separate energy equation for the pool, with appropriate source terms for radiative and conductive heat transfer from the flame, and a sink term (for the continuity equation) to account for loss due to burning. Pool fires on soil and concrete surface have been considered with appropriate friction and heat transfer terms in the momentum and energy equations, respectively. Using this model, numerical simulations have been carried out for a wide range of leak rates, and for a range of burning rates of liquid sodium. Results obtained from the non-isothermal model show that the non-isothermal effects of liquid sodium spreading can safely be neglected for the case or spreading of burning liquid sodium on a typical ground surface such as concrete or soil. Based on these conclusions, dimensionless correlations are proposed for the prediction of spreading parameters such as, equilibrium pool radius, pool formation time, and for mass inventory under pool fire conditions for liquid sodium. These parameters which are obtained from the spreading code can be specified, as input parameters for the existing sodium fire safety codes.     

Experimental study on fragmentation behaviors of molten LBE and water contact interface

Based on the design of CLEAR(China LEAd-based Reactor), it is important to study the molten LBE(LeadBismuth Eutectic)/water interaction following an incidental steam generator tube rupture(SGTR) accident.Experiments were carried out to investigate the fragmentation behavior of the molten LBE/water contacting interface, with a high-speed video camera to record the fragmentation behavior of 300–600?C LBE at 20?C and 80?C of water temperature. Violent explosion phenomenon occurred at water temperature of 20?C, while no explosion occurred at 80?C. Shapes of the LBE debris became round at 80?C of water temperature, whereas the debris was of the needle-like shape at 20?C. For all the molten LBE and water temperatures in the present study,the debris sized at 2.8–5.0 mm had the largest mass fraction. The results indicate that the dominant physical mechanism of the molten LBE fragmentation was the Kelvin-Helmholtz instability between LBE/water direct contact interface.     

Influence of corium oxidation on fission product release from molten pool

Qualitative and quantitative determination of the release of low-volatile fission products and core materials from molten oxidic corium was investigated in the EVAN project under the auspices of ISTC. The experiments carried out in a cold crucible with induction heating and RASPLAV test facility are described. The results are discussed in terms of reactor application; in particular, pool configuration, melt oxidation kinetics, critical influence of melt surface temperature and oxidation index on the fission product release rate, aerosol particle composition and size distribution. The relevance of measured high release of Sr from the molten pool for the reactor application is highlighted. Comparisons of the experimental data with those from the COLIMA CA-U3 test and the VERCORS tests, as well as with predictions from IVTANTHERMO and GEMINI/NUCLEA codes are made. Recommendations for further investigations are proposed following the major observations and discussions.     

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.     

Analysis of molten pool physico-chemical interactions and interpretation of the Phebus FP tests observations

The new 2D model for non-equilibrium U–Zr–O melt oxidation is developed on the base of the previously developed 1D model and extended to consideration of the general case of simultaneous UO₂ dissolution and melt oxidation accompanied with growth of the peripheral ceramic layer (crust) and bulk ceramic precipitates. The model is validated against isothermal crucible tests where precipitation of ceramic phase during molten Zr interactions with ceramic crucible walls along with oxide growth on non-oxidised surface of the melt were observed. In order to analyse melt oxidation under transient temperature conditions of the Phebus FP tests, the new physico-chemical model was tightly coupled with the heat exchange model and applied to interpretation of the post-test microstructure observations of the molten pool in the FP bundles.     

规则球床堆熔盐流动压降与对流换热CFD模拟

球床堆复杂的几何结构导致直接建模进行热工水力模拟非常困难,一般使用多孔介质模型简化处理,但多孔介质已有的压降和对流换热公式在熔盐冷却球床中的有效性仍待验证。本文基于固态燃料熔盐堆建立了6 cm直径小球的规则球床模型,给定球床进口熔盐流量和球壳发热功率,模拟了球床内的稳态流动与换热,计算了对应的压降和对流换热系数,并分别得到了球床压降、对流换热Nu随球床内流动Re变化的曲线。对比发现:模拟压降结果与已有公式差异较大,而模拟对流换热Nu结果与已有公式的差异相对较小。结合模拟结果和已有的公式,拟合得到了修正的压降和对流换热Nu公式。将修正公式应用于3 cm直径规则球床中,结果表明多孔介质修正模型与直接模拟结果一致。     

Study on flow characteristics in gas-molten metal mixture pool

As part of basic research on the flow characteristics of a two-phase mixture pool under severe accident of fast breeder reactor (FBR), visualization and measurement of nitrogen gas-molten lead/bismuth two-phase flow in a rectangular pool were performed by using the neutron radiography technique. Measurements of drag coefficient of a single bubble and bubble shape regime showed that the relationship between the shape, size and the rising velocity of a single isolated nitrogen bubble in the molten lead/bismuth was not much different from that for an ordinary one. Appropriate correlation for drift velocity and drag coefficient between phases were recommended based on the drift flux correlation of measured pool void fraction. One- and two-dimensional analyses were performed by using a next generation computational code for safety analysis of severe accident of FBRs, SIMMER-III with various drag coefficient models. It was revealed that Kataoka–Ishii’s equation was suitable basically for estimation of drift velocity, namely, drag force between phases.     

On the explosivity of a molten drop submitted to a small pressure perturbation

Under some circumstances that we aim to determine, a hot molten fuel drop flowing into a volatile liquid coolant and submitted to a small pressure wave, can be destabilized and explode in a few milliseconds. We propose a new approach to address this problem: in contrast with previous studies, we do not try to model the complete phenomenon but concentrate on its initiation. This way, we can differentiate favourable and non-favourable conditions with applications to PWR/BWR safety. We do the hypothesis that the occurrence of contacts between the two fluids is the criterion of explosion and phenomena occurring up to the contacting event are modelled, including the vapour film oscillations and the amplification of Rayleigh-Taylor instabilities at its interface. The latter feature receives a particular attention with a transient modelling adapted for variable acceleration cases. The fragmentation process itself is not studied in details but we give arguments supporting the fact that contacts between both liquids should induce a strong destabilization of the drops and initiate fragmentation. In this way, we can characterize the explosivity, i.e. the ability for the drop to explode, as a function of the various physical properties (e.g. pressure, temperatures). The model so deduced is qualified by comparison with the explosivity maps provided by Nelson and Duda [Nelson, L.S., Duda, P.M., 1985. Steam explosion experiments with single drops of iron oxide: Part II: parametric studies, NUREG CR-2718, April 1985]. Results obtained with this model confirm the experimental trends regarding the role of ambient pressure and liquid temperature. The influence of other parameters as the drop and the trigger characteristics are also investigated. We conclude this paper with some consideration on the implications for nuclear safety.     

Solid particle effects on heat transfer in a multi-layered molten pool with gas injection

In the very unlikely event of a severe reactor accident involving core melt and pressure vessel failure, it is important to identify the circumstances that would allow the molten core material to cool down and resolidify, bringing core debris to a stable coolable state. To achieve this, it has been proposed to flood the cavity with water from above forming a layered structure where upward heat loss from the molten pool to the water will cause the core material to quench and solidify. In this situation the molten pool would become a three-phase mixture: e.g., a solid and liquid slurry formed by the molten pool as it cools to a temperature below the temperature of liquidus, agitated by the gases formed in the concrete ablation process. The present work quantifies the partition of the heat losses upward and downward in this multi-layered configuration, considering the influence of the viscosity and the solid fraction in the pool, from test data obtained from intermediate scale experiments at the University of Wisconsin-Madison. These experimental results show heat transfer behavior for multi-layered pools for a range of viscosities and solid fractions. These results are compared to previous experimental studies and well known correlations and models.