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。     

Collapsing criteria for vapor film around solid spheres as a fundamental stage leading to vapor explosion

Following a partial fuel-melting accident, a Fuel-Coolant Interaction (FCI) can result with the fragmentation of the melt into tiny droplets. A vapor film is then formed between the melt fragments and the coolant, while preventing a contact between them. Triggering, propagation and expansion typically follow the premixing stage.In the triggering stage, vapor film collapse around one or several of the fragments occurs. This collapse can be the result of fragments cooling, a sort of mechanical force, or by any other means. When the vapor film collapses and the coolant re-establishes contact with the dry surface of the hot melt, it may lead to a very rapid and rather violent boiling. In the propagation stage the shock wave front leads to stripping of the films surrounding adjacent droplets which enhance the fragmentation and the process escalates. During this process a large quantity of liquid vaporizes and its expansion can result in destructive mechanical damage to the surrounding structures. This multiphase thermal detonation in which high pressure shock wave is formed is regarded as “vapor explosion”. The film boiling and its possible collapse is a fundamental stage leading to vapor explosion. If the interaction of the melt and the coolant does not result in a film boiling, no explosion occurs.Many studies have been devoted to determine the minimum temperature and heat flux that is required to maintain a film boiling. The present experimental study examines the minimum temperature that is required to maintain a film boiling around metal spheres immersed into a liquid (subcooled distilled water) reservoir. In order to simulate fuel fragments that are small in dimension and has mirror-like surface, small spheres coated with anti-oxidation layer were used. The heat flux from the spheres was calculated from the sphere's temperature profiles and the sphere's properties. The vapor film collapse was associated with a sharp rise of the heat flux during the cooling process—from values typical for film boiling to much higher values typical for nucleate boiling. Correlations for the minimum temperature and the minimum heat flux necessary to maintain film boiling were established in terms of the subcooling level, the size of the spheres and their material.The minimum temperature to maintain film boiling was used as the principle criteria for the occurrence of vapor explosion. Other criteria, for the intensity of the vapor film collapse was derived from the maximum heat flux following the vapor film collapse, and the audible sound (which is generated by the shock wave). It is assumed that a high intensity of the vapor film collapse will result in a more efficient propagation stage and enhancement of the vapor explosion.     

Time-Optimal Power-Change Control for Coupled-Core Reactors

The numerical method used in this study is Moving Particle Semi-implicit (MPS) method which is based on moving particles and their interactions. Grids are not necessary. Large deformation of fluids can be calculated without grid tangling. A surface tension calculation model is developed to analyze droplet breakup. This model is verified by the simulation of vibration of an ethanol droplet. Two-dimensional numerical analyses of droplet breakup in liquid-liquid and gas-liquid systems are carried out. The correlation between the Weber number and the breakup mode observed in the calculations agrees with that in the experiments. Breakup behavior of a droplet surrounded by a vapor film is analyzed. Flow in the vapor film is considered, though boiling of water and solidification of the melt droplets are ignored. It is found that the breakup of a droplet is suppressed by the vapor film. The critical Weber number in the vapor film is obtained as 50. Molten core coolability is considered by using this result. The median diameter of stable droplets of the molten core is expected as 5 mm in a typical condition, which is consistent with FARO experiment. This result shows that in Advanced Boiling Water Reactor (ABWR) the debris bed up to 40% of the core can be cooled down in the lower head of the reactor pressure vessel.     

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.     

Self-Triggering Mechanism of Vapor Explosions for a Molten Tin and Water System

The self-triggering mechanism of vapor explosions was investigated analytically and experimentally using molten tin and water. First, we modeled a simple droplet system consisting of a hot liquid droplet in a pool of cold liquid. Then, to model the self-triggering mechanism, we assumed that an instability (i.e. perturbed oscillation) in the vapor/cold-liquid interface produces a collapse of the vapor film, which in turn would produce a vapor explosion. To investigate the stability of perturbed oscillations in a vapor film, we did a linear stability analysis of a vapor film surrounding a hot liquid. We found that there was a region of film stability in the cold-liquid temperature where spontaneous vapor explosions did not occur.

To validate our model, we experimentally determined the thermal interaction zone (TIZ) in which spontaneous vapor explosions occur. The occurrence conditions for spontaneous vapor explosions were investigated for molten tin, as the hot liquid, dropped into a water pool, as the cold liquid. We varied the tin temperature and the water temperature, and then monitored the occurrence and location of spontaneous vapor explosions. We found that the upper limit for the water temperature of the TIZ can be explained by our model.     

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.     

Numerical analysis of fragmentation mechanisms in vapor explosions

Fragmentation of molten metal is the key process in vapor explosions. However, this process is so rapid that the mechanisms have not yet been clarified in experimental studies. In addition, numerical simulation is difficult because we have to analyze water, steam and molten metal simultaneously with boiling and fragmentation. The authors have been developing a new numerical method, the moving particle semi-implicit (MPS) method, based on moving particles and their interactions. Grids are not necessary. Incompressible flows with fragmentation on free surfaces have been calculated successfully using the MPS method. In the present study, numerical simulation of the fragmentation processes using the MPS method is carried out to investigate the mechanisms. A numerical model to calculate boiling from water to steam is developed. In this model, new particles are generated on water–steam interfaces. A two-step pressure calculation algorithm is also developed. Pressure fields are separately calculated in both heavy and light fluids to maintain numerical stability with the water and steam system. The new model and algorithm are added to the MPS code. Water jet impingement on a molten tin pool is calculated using the MPS code as a simulation of collapse of a vapor film around a melt drop. Penetration of the water jet, which is assumed in Kim–Corradini’s model, is not observed. If the jet fluid density is hypothetically larger, the penetration appears. Next, impingement of two water jets is calculated. A filament of the molten metal is observed between the two water jets as assumed in Ciccarelli–Frost’s model. If the water density is hypothetically larger, the filament does not appear. The critical value of the density ratio of the jet fluid over the pool fluid is ρ_jet/ρ_pool=0.7 in this study. The density ratios of tin–water and UO₂–water are in the region of filament generation, Ciccarelli–Frost’s model. The effect of boiling is also investigated. Growth of the filament is not accelerated when the normal boiling is considered. This is because normal boiling requires more time than that of the jet impingement, although the filament growth is governed by an instant of the jet impingement. Next, rapid boiling based on spontaneous nucleation is considered. The filament growth is markedly accelerated. This result is consistent with the experimental fact that the spontaneous nucleation temperature is a necessary condition of vapor explosions.     

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.     

Transient film boiling under transient conditions related to vapor explosion (effects of transient flow and fragmentation under a shock pressure)

Two fundamental phenomena are significant when a shock pressure interacts with the large scale coarse mixing state. One is an intensive flow and the other is the surface area enhancement due to the disintegration of the hot drops. The effects of these phenomena on the transient heat transfer and behavior of vapor film under a shock pressure are investigated. Transient heat transfer of film boiling from an electrically heated platinum ribbon 2.5 mm wide and 0.15 mm thick was measured immediately after passage of a shock pressure from 0.1 to 0.7 MPa. The heater was set horizontally in a vertical shock tube which was filled with vapor liquid bubbly mixture and kept initially in the film boiling state. That is, the heater corresponds to a typical hot drop and the bubbles around it correspond to the coarse mixture around the drop. The liquid was Freon-113 with an initial void fraction in the range from 0 to 3%. When the shock wave arrives at the heater, intensive transient flow occurs due to collapse of bubbles around the heater. First, the effects of the initial void fraction, the intensity of the shock and the heated wall temperature on the transient heat fluxes and collapse of the vapor film were investigated experimentally and analytically under the shock pressure. Compared with a heated wall in the liquid alone, the transient heat flux at the heated wall increases and the collapse of the vapor film becomes easier in the bubbly mixture due to the transient flow. Effects of surface enhancement during the fragmentation process on the heat transfer rate and transient behavior of vapor film are investigated analytically by application of the newly proposed surface stretch model. It is made clear when the surface area is increasing, the vapor film is apt to collapse and the transient heat transfer is enhanced by the surface stretch.     

A Thermal Fragmentation Model Induced by Surface Solidification

A fragmentation phenomenon of a melt droplet induced by surface solidification has been studied for many years, but the fragmentation rate model, based on such a thermal mechanism, is not available for numerical simulation tools. In this study, in order to develop a fragmentation rate correlation of a melt droplet, induced by surface solidification, a thermal fragmentation mechanism is proposed, based on the Taylor instability. The theoretical fragmentation model is developed and a simplified non-dimensional correlation is proposed for convenient application to simulation tools. The developed fragmentation rate correlation is verified by simulating the MIXA experiment.     

熔融金属液滴热细粒化过程研究

熔融液滴的细粒化是决定燃料与冷却剂相互作用破坏后果的关键过程,它决定最终的热能与动能的转化比,是预测事故后果的重要因素之一。然而目前对该过程中基于本身内能的热细粒化机理尚不清楚。本工作通过单个熔融金属液滴与水相互作用的实验,借助高速摄像系统对熔融液滴的热细粒化现象进行拍摄,观察发现熔融金属液滴与水的相互作用经历了若干次加速膨胀细粒化过程,测量到熔融液滴的细粒化时间为0.8ms,两次细粒化的时间间隔为0.8ms,细粒化加速膨胀时间仅为0.4ms。根据实验观察和分析,提出了一种由熔融液滴与水接触面不稳定沸腾效应引起的热细粒化机理。     

Molten fuel-coolant interaction phenomena with application to carbide fuel safety

This paper reviews the major phases occurring during an energetic molten fuel/coolant interaction (MFCI), the categories of interaction and modes of contact between molten fuel and liquid coolant, the film boiling destabilization and collapse mechanisms, and the important fragmentation mechanisms of the melt. Two major models that describe the processes involved in an MFCI event are discussed: the spontaneous nucleation model and the pressure detonation model. Finally, the MFCI experiments involving carbide fuel and liquid sodium are reviewed and the potential for an energetic interaction between molten carbide fuel and liquid sodium is discussed. Recommendations are given for future work on MFCI phenomena relative to the carbide fuel/sodium system.     

Improved solidification influence modelling for Eulerian fuel-coolant interaction codes

Steam explosion experiments revealed important differences in the efficiency between simulant alumina and oxidic corium melts. The experimentally observed differences are importantly attributed to the differences in the melt droplets solidification and void production, which are limiting phenomena in the steam explosion process and have to be adequately modelled in fuel-coolant interaction codes. This article focuses on the modelling of the solidification effect. An improved solidification influence modelling approach for Eulerian fuel-coolant interaction codes was developed and is presented herein.The solidification influence modelling in fuel-coolant interaction codes is strongly related to the modelling of the temperature profile and the mechanical effect of the crust on the fragmentation process. Therefore the first objective was to introduce an improved temperature profile modelling and a fragmentation criterion for partly solidified droplets. The fragmentation criterion was based on the established modified Weber number, which considers the crust stiffness as a stabilizing force acting to retain the crust under presence of the hydrodynamic forces. The modified Weber number was validated on experimental data. The application of the developed improved solidification influence modelling enables an improved determination of the melt droplet mass, which can be efficiently involved in the fine fragmentation during the steam explosion process. Additionally, also the void production modelling is improved, because it is strongly related to the temperature profile modelling in the frame of the solidification influence modelling. Therefore the second objective was to enable an improved solidification influence modelling in codes with an Eulerian formulation of the droplet field. Two additional transported model parameters based on the most important droplets features regarding the fuel-coolant interaction behaviour, were derived. First, the crust stiffness was considered as an important property, because it enables the correct prediction of the amount of droplets participating in the fine fragmentation process during the explosion phase. Second, the heat flux from the droplet interior to the surface was considered as an important feature, because it enables to improve the surface temperature determination and reflects the history of the droplet's cooling. The last objective was to implement the improved solidification influence modelling into the Eulerian code MC3D. The first demonstrative simulations with the implemented modelling are promising and are showing improvements in the simulation capability.     

Unit Sphere Concept for Macroscopic Triggering of Large-scale Vapor Explosions

The unit sphere concept was developed to predict the triggering stage of vapor explosions for coarse mixtures composed of hot liquid droplets, cold liquid and its vapor. With an assumption that hot liquid droplets are arranged with a uniform spatial interval to construct a hexagonal cell structure, a unit sphere with thirteen droplets is formed in the coarse mixture. A droplet and adjacent twelve droplets were placed at the center and on the surface of the unit sphere, respectively. Two indices for triggering were introduced in the unit sphere concept. The first index is the ratio of mechanical energy generated at the center droplet to one required for the mechanical collapse of vapor film on an adjacent droplet. Another shows the probability that the mechanical energy at the center droplet impacts onto the minimum number of molten adjacent droplets. The present concept predicted that the triggering could occur at smaller water subcooling for a coarse mixture with alumina droplets and water than corium droplet case, and that vapor explosions were suppressed when the ambient pressure was elevated up to approximately 0.5 MPa in both cases. The evaluation of KROTOS experiments indicated that the latter triggering index was smaller for corium droplets than alumina case due to the increase in the fraction of solidified droplets in the coarse mixture, implying less triggerability for corium droplets. Those findings showed a consistency with the results of vapor explosion experiments using corium and alumina. It was qualitatively confirmed in the experiments where a molten tin jet penetrated into a water pool that the latter index is applicable to the evaluation of the triggerability.     

Experimental and analytical studies of melt jet-coolant interactions: a synthesis

Instability and fragmentation of a core melt jet in water have been actively studied during the past 10 years. Several models, and a few computer codes, have been developed. However, there are, still, large uncertainties, both, in interpreting experimental results and in predicting reactor-scale processes. Steam explosion and debris coolability, as reactor safety issues, are related to the jet fragmentation process. A better understanding of the physics of jet instability and fragmentation is crucial for assessments of fuel-coolant interactions (FCIs). This paper presents research, conducted at the Division of Nuclear Power Safety, Royal Institute of Technology (RIT/NPS), Stockholm, concerning molten jet-coolant interactions, as a precursor for premixing. First, observations were obtained from scoping experiments with simulant fluids. Second, the linear perturbation method was extended and applied to analyze the interfacial-instability characteristics. Third, two innovative approaches to computational fluid dynamics (CFD) modeling of jet fragmentation were developed and employed for analysis. The focus of the studies was placed on (a) identifying potential factors, which may affect the jet instability, (b) determining the scaling laws, and (c) predicting the jet behavior for severe accident conditions. In particular, the effects of melt physical properties, and the thermal hydraulics of the mixing zone, on jet fragmentation were investigated. Finally, with the insights gained from a synthesis of the experimental results and analysis results, a new phenomenological concept, named ‘macrointeractions concept of jet fragmentation’ is proposed.     

Numerical Study on Influence of Blowdown Parameter on Coolant Blowdown Characteristic in LOCA

The coolant blowdown process is one of the important processes of the loss of coolant accident (LOCA). It is of great significance to study the thermal hydraulic characteristics of coolant blowdown process for understanding LOCA and predicting the migration process of radioactive source term after accident. The numerical simulation model of coolant blowdown was established by FLUENT software and verified. The model was used to study the effects of blowdown parameters such as diameter of nozzle, blowdown distance and blowdown pressure on flow field temperature, droplet velocity and vapor velocity. The results show that the increase of diameter of nozzle increases the blowdown parameters. As the blowdown distance increases, the flow field temperature and the droplet velocity increase first and then decrease, while the vapor velocity first rises and then stabilizes. The greater the blowdown pressure is, the farther the blowdown parameter is from the blowdown outlet. The maximum values of droplet velocity and vapor velocity increase gradually with the blowdown pressure, while the maximum value of the flow field temperature does not change.     

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.     

LOCA下喷放参数对冷却剂喷放特性影响数值研究

冷却剂喷放过程是失水事故（LOCA）的重要过程之一,研究冷却剂喷放过程的热工水力特性对认识LOCA以及预测事故后放射性源项迁移过程有着重要意义。本文利用FLUNET软件建立冷却剂喷放数值计算模型,并对其进行验证。利用模型研究喷口直径、喷放距离和喷放压力等喷放参数对计算域内流场温度、液滴速度和蒸汽流速等特性的影响。研究结果表明：喷口直径的提高使得喷放参数均有提高;随喷放距离的增大,流场温度和液滴速度先上升后下降,而蒸汽流速先上升后趋于平稳;喷放压力越大,喷放参数的最大值离喷放出口越远,液滴速度和蒸汽流速的最大值随喷放压力的增大逐渐上升,而流场温度最大值没有变化。     

Simulation of drop deposition process in annular mist flow using three-dimensional particle method

The three-dimensional moving particle semi-implicit (MPS) method is employed to simulate the deposition process of single droplet on the liquid film. The model accounts for the presence of inertial, gravitation, viscous and surface tension and is validated by comparison with experimental results. The parameters of liquid droplets and film are calculated by a one-dimensional mixture model in which correlations and methods on void fraction, entrainment fraction and droplet velocity and size distribution are employed. The simulation results are analyzed to study the effect of splash on the deposition and re-entrainment processes in annular-mist flow. It is found that splash plays an important role in the deposition and re-entrainment processes in high quality conditions of BWR.