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。     

Numerical Analysis of Jet Breakup Behavior Using Particle Method

A continuous jet changes to droplets where jet breakup occurs. In this study, two-dimensional numerical analysis of jet breakup is performed using the MPS method (Moving Particle Semi-implicit Method) which is a particle method for incompressible flows. The continuous fluid surrounding the jet is neglected. Dependencies of the jet breakup length on the Weber number and the Froude number agree with the experiment. The size distribution of droplets is in agreement with the Nukiyama-Tanasawa distribution that has been widely used as an experimental correlation. Effects of the Weber number and the Froude number on the size distribution are also obtained.     

事故容错燃料包壳表面液滴碰撞行为及Leidenfrost现象实验研究

为了研究事故容错燃料包壳表面的液滴Leidenfrost现象,本研究采用高速相机对液滴与事故容错燃料包壳SiC和FeCrAl的碰撞行为进行可视化观测,并与常规包壳材料Zr-4对比。结果表明,液滴碰撞方式有沉积、带二次液滴散射的反弹、带二次液滴散射的碎化、反弹和碎化5种;沉积属于核态沸腾换热,反弹和碎化属于膜态沸腾,带二次液滴散射的反弹和带二次液滴散射的碎化属于过渡沸腾换热;液滴的临界热流密度（CHF）温度与韦伯数（We）无关,而Leidenfrost温度随着We和固体表面蓄热系数的增大而增大;在膜态沸腾阶段,液滴的铺展行为与温度无关,随着We的增大,液滴铺展的更快,且能达到更高的铺展因子。      

Development of Simplified Wave-type Vane in BWR Steam Dryer and Assessment of Vane Droplet Removal Characteristics

Air-water experiments were performed for the BWR steam dryer in order to elucidate droplet removal characteristics of the vane. Based on the results, a simplified vane was developed and its droplet removal characteristics were confirmed by air-water experiments using a whole dryer model.

Phase-Doppler anemometer was used to measure droplet diameter distributions. In the experiments of the current vane with four-wave stages and 120° bend angle, almost all of the droplets were found to be trapped in the first and second vane stages. For the air velocity of 3.1 m/s, 90% of the inlet droplets were trapped there and 4% were trapped in the third and fourth stages, resulting in 6% being carried over. Sauter mean diameters at the exit were 6 and 5μm while at the inlet they were 71 and 64μm for the respective air velocities of 1 and 3 m/s. Based on the Weber number evaluation, the possible mechanism for the fine droplet generation was considered to be the breakup of droplets due to impingement on the liquid film formed in the vane surface.

From the above results, the simplified vane with two-wave stages was developed. In order to remove fine droplets, the bend angle of the vane was reduced to 90°, in which a larger inertia force is exerted on finer droplets generated by breakup. Experiments for the whole dryer model showed that the developed vane could achieve the same droplet removal characteristics as the current vane without increasing the pressure drop of the dryer. A design having ten dryer bank rows and 1.2 m height, which is 0.8 m shorter than the current dryer, is possible for the dryer using the new simplified vane.     

Dynamics of droplet breakup through a grid spacer in a rod bundle

The dynamics of droplet breakup associated with the flow of a dispersed two-phase mixture through a rod bundle grid spacer during a reflood transient in a pressurized water reactor is studied theoretically. By considering the conservation of liquid mass and the kinetic as well as the surface energies of the droplets, an expression is derived for the ratio of the Sauter mean diameters of the droplets downstream and upstream of the grid. It is found that the Sauter mean diameter could decrease appreciably as a result of the shattering of the droplets when flowing through the grid spacer, thus increasing the interfacial heat transfer surface area. The decrease in the droplet size is dependent upon the Weber number of the incoming droplets, the blockage ratio of the grid spacer, and the fraction of the kinetic energy of the incoming droplets required to convert to the surface energy of the newly generated droplets during the breakup process. Comparisons of the theoretical results are made with the experimental data obtained at the rod bundle heat transfer test facility as well as with other relevant data in the literature and found to be good.     

单钩波形板分离器内二次携带机理分析

通过理论分析与三维数值模拟研究了实际运行工况下单钩波形板分离器内二次携带机理。采用Realizable k-ε湍流模型对波形板内气相流场进行数值模拟,利用离散相模型结合涡交互模型对水滴运动进行计算,根据壁面水膜运动方程求解水膜的速度与厚度分布;依据理论分析,对可能形成二次水滴的4种方式进行判定。结果表明：波形板内发生气体动力造成的水滴破碎与水滴撞击水膜产生飞溅的可能性较低,但较冷态工况的可能性高;水膜主要集中在波形板的前两级,随入口蒸汽速度或湿度的增加,水膜增厚并向下游移动;将水膜剥落和水膜分离的判别式进行统一,并证实波形板二次携带主要由水膜的剥落和分离造成,且相较水膜剥落,钩峰处的水膜分离更易发生。     

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.     

Vapor film collapse triggered by external pressure pulse and the fragmentation of melt droplet in FCIs

The fragmentation process of high-temperature molten drop is a key factor to determine the ratio heat transferred to power in FCIs,which estimates the possible damage degree during the hypothetical severe accident in the nuclear reactors.In this paper,the fragmentation process of melt droplet in FCIs is investigated by theoretic analysis.The fragmentation mechanism is studied when an external pressure pulse applied to a melt droplet,which is surrounded by vapor film.The vapor film collapse which induces fragmentation of melt droplet is analyzed and modeled.And then the generated pressure is calculated.The vapor film collapse model is introduced to fragmentation correlation,and the predicted fragment size is calculated and compared with experimental data.The result shows that the developed model can predict the diameter of fragments and can be used to calculate the fragmentation process appreciatively.     

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.     

丝网分离器水滴撞击水膜的机理研究

运用VOF多相流模型,对丝网分离器内水滴撞击网丝表面沉积水膜的过程进行数值模拟,研究和预测大水滴在较高汽速条件下撞壁产生二次携带的机理。深入研究水滴因素,如水滴大小、初始速度和水膜厚度对丝网的二次携带现象的影响,为丝网分离器设计提供参考。数值结果分析表明,水滴的大小和撞击速度是影响撞击飞溅发生的主要原因,飞溅生成的二次小水滴是造水装置丝网分离器二次携带的重要组成。丝网分离器内水滴撞击网丝水膜能否发生二次携带取决于阈值K_cr＝Oh•Re^a,当K大于K_cr时必然产生二次携带。     

Numerical Simulation of Liquid Drop Deposition in Annular-Mist Flow Regime of Boiling Water Reactor

The deposition process of a single droplet on the liquid film is numerically simulated by the Moving Particle Semi-implicit (MPS) method to analyze the possibility and effect of splash occurring in Boiling Water Reactor (BWR) condition. A simple one-dimensional mixture model is used to calculate the necessary parameters for the simulation of deposition. The rationality of the model is confirmed by comparison with the experimental results. A film buffer model is developed to arrange the simulation results. A correlation of the critical impact Weber number for splash is obtained. It is found that splash and subsequent re-entrainment process is significant and cannot be ignored in the high quality condition in BWR.     

Flow structure of steam–water mixed spray

In this study, the flow structure of a steam–water mixed spray is studied both numerically and experimentally. The velocity and pressure profiles of single-phase flow are calculated using numerical methods. On the basis of the calculated flow fields, the droplet behavior is predicted by a one-way interaction model. This numerical analysis reveals that the droplets are accelerated even after they are sprayed from the nozzle. Experimentally, the mixed spray is observed using an ultra-high-speed video camera, and the velocity field is measured by using the oarticle image velocimetry (PIV) technique. Along with this PIV velocity field measurement, the velocities and diameters of droplets are measured by phase Doppler anemometry. Furthermore, the mixing process of steam and water and the atomization process of a liquid film are observed using a transparent nozzle. High-speed photography observations reveal that the flow inside the nozzle is annular flow and that most of the liquid film is atomized at the nozzle throat and nozzle outlet. Finally, the optimum mixing method for steam and water is determined.     

Two-dimensional simulation of drop deformation and breakup at around the critical Weber number

The breakup of two-dimensional liquid drops is numerically investigated at around the critical Weber number. The Moving Particle Semi-implicit (MPS) method is used to solve the unsteady Navier–Stokes equations for both the drops and the ambient fluid. The two dominant forces affecting drop breakup, pressure drag and surface tension force, are verified using the two benchmarks: pressure distribution on the surface of a cylinder in a uniform flow and oscillation of a square drop under surface tension force. The results show that the breakup process occurs in two stages. During the first stage, the drops become stretched and thinned normal to the flow direction of the ambient fluid. During the second stage, detached points appear on the surface of the drops, which are ascribed to the unstable growth of surface waves. The post-breakup topology of the drops is dependent on the value of the Weber number: the larger the Weber number is, the more detached points on the surface of the drops emerge. Another feature commonly shared in the two stages is that some fine fragmentations are stripped from the equatorial edges of the drops. The critical Weber number is predicted to be 13 for uranium dioxide drops in water, at which breakup regime is consistent with the so-called vibration regime.     

A numerical study of impact force caused by liquid droplet impingement onto a rigid wall

Liquid droplet impingement (LDI) erosion could be regarded to be one of the major causes of unexpected troubles occasionally occurred in the inner bent pipe surface. Evaluating the LDI erosion is an important topic of the thermal hydraulics and structural integrity in aging and life extension for nuclear power plants. One of the causes of LDI erosion is the impact pressure by the impingement of droplets in the involved steam. We investigated a simple droplet impingement to a rigid wall using volume of fluid (VOF) model, which is a two-phase Eulerian-Eulerian approach. The impact of a single water droplet with a high velocity towards a solid surface is examined numerically. The high Reynolds number value implies inertia dominated the phenomena and supports an inviscid approach to the problem. The high Weber number is justifying that an assumption to neglect the surface tension effect is adopted. We show that the compressibility of the liquid medium plays a dominant role in the evolution of the phenomenon. Both generation and propagation of shock waves are directly computed by solving the fluid dynamics continuity and momentum equations. In the simulation we employed a front tracking solution procedure, which is particularly suitable for two-phase free surface computation. The numerical results show that critical maximum pressure is not highest at the center of droplet contact on the surface at the first instantaneous moment but highest behind the contact angle later before jet eruption. It agrees generally well (within 20%) with the mathematical analysis. Finally, a droplet impact angle function is proposed for the global LDI erosion prediction.     

A numerical study on turbulence attenuation model for liquid droplet impingement erosion

The bent pipe wall thinning has been often found at the elbow of the drain line and the high-pressure secondary feed-water bent pipe in the nuclear reactors. The liquid droplet impingement (LDI) erosion could be regarded to be one of the major causes and is a significant issue of the thermal hydraulics and structural integrity in aging and life extension for nuclear power plants safety. In this paper two-phase numerical simulations are conducted for standard elbow geometry, typically the pipe diameter is 170 mm. The turbulence attenuation in vapor-droplets flow is analysed by a damping function on the energy spectrum basis of single phase flow. Considering the vapor turbulent kinetic energy attenuation due to the involved droplets, a computational fluid dynamic (CFD) tool has been adopted by using two-way vapor-droplet coupled system. This computational fluid model is built up by incompressible Reynolds Averaged Navier–Stoke equations using standard k–ε model and the SIMPLE algorithm, and the numerical droplet model adopts the Lagrangian approach, a general LDI erosion prediction procedure for bent pipe geometry has been performed to supplement the CFD code. The liquid droplets diameter, velocity, volume concentration are evaluated for the effects of carrier turbulence attenuation. The result shows that carrier turbulence kinetic energy attenuation is proved to be an important effect for LDI erosion rate when investigating the bent pipe wall thinning phenomena.     

Droplet deposition measurement with high-speed camera and novel high-speed liquid film sensor with high spatial resolution

A sensor based on the electrical conductance method is presented for the measurement of dynamic liquid films in two-phase flow. The so called liquid film sensor consists of a matrix with 64 × 16 measuring points, a spatial resolution of 3.12 mm and a time resolution of 10 kHz. Experiments in a horizontal co-current air-water film flow were conducted to test the capability of the sensor to detect droplet deposition from the gas core onto the liquid film. The experimental setup is equipped with the liquid film sensor and a high speed camera (HSC) recording the droplet deposition with a sampling rate of 10 kHz simultaneously. In some experiments the recognition of droplet deposition on the sensor is enhanced by marking the droplets with higher electrical conductivity. The comparison between the HSC and the sensor shows, that the sensor captures the droplet deposition above a certain droplet diameter. The impacts of droplet deposition can be filtered from the wavy structures respectively conductivity changes of the liquid film using a filter algorithm based on autoregression. The results will be used to locally measure droplet deposition e.g. in the proximity of spacers in a subchannel geometry.     

液滴撞击干燥倾斜壁面铺展实验研究

通过高速摄影技术及像素分析方法对液滴撞击干燥倾斜壁面进行实验研究，分析了不同倾斜角及韦伯数（We）对液滴飞溅及铺展的影响，结果表明，倾斜角的增加有利于抑制飞溅的产生；We一定时，液滴的前铺展因子随着倾斜角的增加而增加，后铺展因子随着倾斜角的增加而减小；液滴的前后初始铺展速度均大于液滴的撞击速度，且随着倾斜角的增加而减小。      

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.     

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.