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.     

Experimental observation of the droplet size change across a wet grid spacer in a 6 × 6 rod bundle

During the reflood phase of a postulated loss of coolant accident in a nuclear reactor, entrainment of liquid droplets can occur at a quench front of reflooding water. It is widely recognized that the behavior of the entrained droplets crucially affects the reflood heat transfer phenomena by decreasing the superheated steam temperature and interacting with a rod bundle and spacer grids. For this reason, various experimental and numerical studies have been performed to examine droplet behavior such as the droplet size, velocity and droplet fraction inside a rod array. In this study, an experiment on the droplet behavior inside a heated rod bundle has been performed. The experiment was focused on the change of droplet size induced by a spacer grid in a rod bundle geometry, which results in the change of the interfacial heat transfer between droplets and superheated steam. A 6 × 6 rod bundle test facility in Korea Atomic Energy Research Institute was used for the experiment. Steam was supplied by an external boiler into the bottom of the test channel, and a droplet injection nozzle was equipped instead of simulating a quench front of reflooding water. The major measuring parameters of the experiment were the droplet size and velocity, which were measured by a high-speed camera and a digital image processing technique. A series of experiments were conducted with various flow conditions of a steam injection velocity, heater temperature, droplet size, and droplet flow rate. The experiments provided the data on the change of the Sauter mean diameter of droplets after collision with a wet grid spacer depending on flow conditions.     

Visualized measurement of extremely high-speed droplets in Venturi scrubber

Venturi scrubbers for filtered venting have been installed in nuclear power plants worldwide. Venturi scrubbers can eliminate fission products from a polluted gas by interaction through gas–liquid interfaces. Therefore, droplet diameter is important from the viewpoint of decontamination. When Venturi scrubbers are used in severe accidents, the gas flow velocity might be extremely high. In these studies, the authors did not measure droplet diameter under extremely high gas velocity conditions. In the scenarios, experimental data pertaining to droplet diameter, under the extremely high gas flow velocity, are required. Therefore, this objective is to evaluate the diameter of extremely high-speed droplets. A visualization experiment was conducted using a Venturi scrubber. The droplet diameter distribution and the Sauter mean diameter (SMD) were determined. By comparing between the experimental value of SMDs and the one evaluated using Nukiyama–Tanasawa equation, it was confirmed that the Nukiyama–Tanasawa equation can be used to evaluate SMD with good accuracy in the gas velocity range of 82–250 m/s, except the highest gas velocity conditions. Furthermore, the droplet generation mechanism in the Venturi scrubber was considered to clarify the main reason why the Nukiyama–Tanasawa equation can be used to evaluate SMD droplet diameter.     

高温液滴流辐射换热及蒸发特性

本文针对可应用于空间堆的矩形液滴辐射器（LDR）,研究其液滴流的辐射换热及蒸发特性。在传统的高温液滴流辐射换热模型的基础上,添加了液滴流蒸发模型,并将辐射换热模型与蒸发模型进行耦合,在该模型的基础上开发了高温液滴流辐射换热-蒸发特性分析程序LDFAC。将该程序的液滴层温度分布计算结果进行校核,其相对误差不超过1.9%。使用该程序对装载DC705硅油下不同光学厚度及长度的液滴层辐射换热蒸发特性进行了分析。结果表明：在液滴层的光学厚度较大的情况下,液滴层内部的温度分布非常不均匀,液滴层中心的温度没有显著降低,而液滴层接近外表面部分的温度下降较为明显;温度对LDR的系统寿命有着较大影响,温度每降低10 K,系统寿命可提高约450%,同时,液滴层光学厚度越大,系统寿命也越长。     

COSINE多相场子通道分析程序的开发与评估

COSINE多相场子通道分析程序基于两流体三相子通道守恒方程,在气液两相的基础上,单独考虑了液滴相的行为,并通过考虑通道间的交混,提高了对压水堆压力容器内的热工水力学现象分析能力及大破口事故的计算能力。本研究介绍了程序的基本模型及求解方法,选取代表性算例及实验工况进行建模计算,验证多相场子通道程序的计算能力。计算结果表明：程序可以对多通道热工水力现象进行模拟计算,计算结果与理论分析相符,程序可以精确模拟堆芯交混及再淹没工况,计算结果与实验数据具有良好的一致性,COSINE多相场子通道程序具备对压力容器内热工水力工况的计算能力。     

液滴撞击湿壁面实验研究

采用高速摄像仪以11 000 帧/s的拍摄速度对3种不同尺寸的液滴以不同速度分别撞击湿壁面（水平及不同倾斜角度）的过程进行了观测。研究了铺展、产生冠状不飞溅、飞溅3种实验现象。定性分析了初始液滴直径、液滴撞击速度、湿壁面倾斜角度对飞溅现象的作用。定量统计出液滴撞击湿壁面产生飞溅现象的各项临界参数,给出飞溅判据的经验关系式并进行误差分析。结果表明：随液滴撞击速度的增大,撞击湿壁面后会依次出现铺展、产生冠状不飞溅、产生二次液滴飞溅等现象。液滴直径的增加与湿壁面倾斜角度的降低均对飞溅的产生有促进作用。并通过拟合实验数据得到用于判别液滴撞击湿壁面是否发生产生二次液滴飞溅现象的无量纲参数K与无量纲液膜层厚度H^*关系K=3210-122 284.48H^*+2.234 26×10⁶H^*2（0.008 56*<0.033 18）。     

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。     

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.     

液滴破碎方程的三种数值解法及分析比较

介绍了求解群体平衡模型液滴破碎方程的三种数值方法：固定点法（fixed pivot technique,FPT）,Attarakih 2004法和单元平均法（cell averaged technique,CAT）。针对固定点法在第一区间数密度突变（值过低）的问题作了适当的修正,得到的结果与整体分布曲线及另两种方法的计算值很好地吻合。三种方法得到的常微分方程组均采用定步长的四阶龙格-库塔法求解,由C语言编写计算程序。计算结果表明,固定点法和Attarakih 2004法在区间宽度相同的情况下计算结果几乎完全吻合,单元平均法比上述两种方法有更高的精度和计算效率。     

FIDAS: Detailed subchannel analysis code based on the three-fluid and three-field model

The Film Dryout Analysis Code in Subchannels, FIDAS, has been developed with the main objective of predicting dryout and post-dryout heat transfer in a channel and in rod bundles. In FIDAS, two-phase flow consisting of continuous liquid film, continuous vapor and entrained droplets is modeled by a three-fluid, three-field representation of 12 field equations, i.e. three continuity, three energy and six momentum equations. FIDAS can predict dryout without any empirical CHF correlations by introducing annular flow modeling and the ‘film dryout criterion’. Experiments on film flow characteristics, subchannel flow and enthalpy distributions, dryout and post-dryout heat transfer in tubes and rod bundles were analyzed to demonstrate the performance of FIDAS. The predictions of FIDAS are in close agreement with the experiments.     

波形板汽水分离器内分离效率的影响因素分析

基于壁面液膜模型,进行无钩波形板汽水分离器内液膜生成情况的三维数值模拟,模拟中采用Realizable k-ε模型和壁面液膜模型对波形板内的气相和液相进行数值模拟计算,根据模拟结果分析波形板内的分离效率。研究结果表明：在不改变波形板的结构和不考虑二次携带的前提下,随进口速度或液滴直径的增加,壁面形成液膜面积和高度增加,分离效率也随之提高。当进口速度和液滴直径一定时,液膜高度和面积随蒸汽湿度的增加呈先增加后减小的趋势,当湿度达到10%时,液膜高度和面积达到最大,分离效率最佳。     

气泡破裂及其夹带特性行为测量综述

自由液面处气泡破裂造成的液滴夹带现象广泛存在于水冷反应堆中,在事故工况下液池中滞留的气溶胶可通过夹带的方式进入气相中,对释放量的准确计算是源项评估的重要基础。气溶胶最终的释放特性由气泡寿命、液膜厚度及产生的液滴尺寸等参数决定。由于气泡破裂是一复杂且随机的过程,因此液相表面气泡破裂关键参数的测量没有普遍适用的方法,且各方法的测量结果并不互相适用,这就给气溶胶释放特性的研究带来困难。为对该现象进行研究,本文总结了上述物理参数的多种测量方法及部分经验公式,比较了不同测量方法的适用范围,最后展望适用于此领域的测量方法及后续的研究方向。     

Assessment for explosion strength of liquid lithium droplet coolant interaction

Liquid lithium served as plasma-facing material for limiters and divertor target plates are useful for the improvement of plasma performances. However, the liquid lithium water interaction is a main concern for the safety of fusion reactors. The assessment of explosion strength is significant to the risk analysis of application of liquid lithium. An experiment of liquid lithium droplet coolant interaction has been conducted. The experimental result indicates that the mass and initial temperature of liquid lithium droplet has a significant impact on the explosion strength. The peak pressure rises with the increase of the mass and the temperature of liquid lithium. Based on the theory of shock wave overpressure and experimental data, an overpressure formula for liquid lithium droplet coolant interaction is fitted by the least-square method. The optimum values of undetermined coefficients are obtained and the model to assess explosion strength of liquid lithium droplet coolant interaction is established. The model is verified by experimental data and proved to be applicable. It reflects the influence of the mass and initial temperature of lithium on the explosion strength and also provides a novel method for the evaluation of explosion strength of liquid lithium droplet coolant interaction.     

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.     

Review of Measurement Method for Bubble Rupture and Entrainment Behavior

The phenomenon of droplet entrainment caused by bubble rupture at the free liquid surface exists widely in water-cooled reactors. Under accident conditions, the aerosol detained in the liquid pool can be transferred into the air by entrainment. Accurate calculation of the release amount is an important basis for the evaluation of the source term. The final release characteristics are directly determined by parameters such as bubble lifetime, liquid film thickness, and droplet size etc. Owing to complex and random process of bubble rupture, there is no universally applicable method for measuring the crucial parameters of bubble rupture on the liquid surface, and the results are not applicable to each other. This brings great difficulties to the evaluation of the release characteristics of the final source term. In order to investigate this phenomenon, the measurement methods of the above physical parameters and some empirical formulas were summarized. The applicable scope of different methods was compared. Finally, various measurement schemes and subsequent research directions for bubble rupture behavior were summarized and prospected.     

节块展开法求解对流扩散方程的稳定性和数值耗散特性分析

本文研究了节块展开法求解对流扩散方程的稳定性和数值耗散特性。通过离散方程精确解和数值实验方法分析不同阶节块展开法的稳定性和数值耗散特性,并将其与有限体积法中的中心差分和一阶迎风格式进行对比。结果表明:偶数阶节块展开法的稳定是有条件的,即Peclet数(Pe)小于限值,且Pe限值会随展开阶数的增大而增大,其稳定性范围和精度均优于中心差分格式;奇数阶节块展开法是无条件稳定的,但随Pe的增大,数值耗散增大、计算误差增大,且当Pe大于一定值后,产生的数值耗散大于一阶迎风格式。     

Modifications to COBRA-TF to model dispersed flow film boiling with two flow,four field Eulerian–Eulerian approach – Part 2

In the first part of the paper, the modifications performed to improve the dispersed flow film boiling model in COBRA-TF have been described. The improvements were achieved by adding a small droplet field to the code’s solution scheme. The conservation equations, the source terms for the equations and the models developed were summarized. In this paper, the effects of spacer grids on the dispersed flow heat transfer and COBRA-TF modifications for the spacer grid models are presented. The results of the code predictions are presented by comparing the experimental data from Rod Bundle Heat Transfer experiments with the results of code simulations performed with original and modified code. Measurements and calculations for the spacer grid temperature have been compared. The results of the analysis performed with the modified code indicate the improvement in code predictions for the spacer grid temperature.     

Comparison of natural convection flows under VHTR type conditions modeled by both the conservation and incompressible forms of the Navier-Stokes equations

This paper illustrates a comparative study to analyze the physical differences between numerical simulations obtained with both the conservation and incompressible forms of the Navier-Stokes equations for natural convection flows in simple geometries. The purpose of this study is to quantify how the incompressible flow assumption (which is based upon constant density advection, divergence-free flow, and the Boussinesq gravitational body force approximation) differs from the conservation form (which only assumes that the fluid is a continuum) when solving flows driven by gravity acting upon density variations resulting from local temperature gradients. Driving this study is the common use of the incompressible flow assumption in fluid flow simulations for nuclear power applications in natural convection flows subjected to a high heat flux (large temperature differences). A series of simulations were conducted on two-dimensional, differentially heated rectangular geometries and modeled with both hydrodynamic formulations. From these simulations, the selected characterization parameters of maximum Nusselt number, average Nusselt number, and normalized pressure reduction were calculated. Comparisons of these parameters were made with available benchmark solutions for air with the ideal gas assumption at both low and high heat fluxes. Additionally, we generated specific force quantities and velocity and temperature distributions to provide a basis for further analysis. The simulations and analysis were then extended to include helium at the Very High Temperature gas-cooled Reactor (VHTR) normal operating conditions. Our results show that the consequences of incorporating the incompressible flow assumption in high heat flux situations may lead to unrepresentative results. The results question the use of the incompressible flow assumption for simulating fluid flow in an operating nuclear reactor, where large temperature variations are present.     

One-dimensional three-field model of condensation in horizontal countercurrent flow with supercritical liquid velocity

A one-dimensional three-field model was developed to predict the flow of liquid and vapor that results from countercurrent flow of water injected into the hot leg of a PWR and the oncoming steam flowing from the upper plenum. The model solves the conservation equations for mass, momentum, and energy in a continuous-vapor field, a continuous-liquid field, and a dispersed-liquid (entrained-droplet) field. Single-effect experiments performed in the upper plenum test facility (UPTF) of the former SIEMENS KWU (now AREVA) at Mannheim, Germany, were used to validate the countercurrent flow limitation (CCFL) model in case of emergency core cooling water injection into the hot legs. Subcooled water and saturated steam flowed countercurrent in a horizontal pipe with an inside diameter of 0.75 m. The flow of injected water was varied from 150 kg/s to 400 kg/s, and the flow of steam varied from 13 kg/s to 178 kg/s. The subcooling of the liquid ranged from 0 K to 104 K. The velocity of the water at the injection point was supercritical (greater than the celerity of a gravity wave) for all the experiments. The three-field model was successfully used to predict the experimental data, and the results from the model provide insight into the mechanisms that influence the flows of liquid and vapor during countercurrent flow in a hot leg. When the injected water was saturated and the flow of steam was small, all or most of the injected water flowed to the upper plenum. Because the velocity of the liquid remained supercritical, entrainment of droplets was suppressed. When the injected water was saturated and the flow of steam was large, the interfacial shear stress on the continuous liquid caused the velocity in the liquid to become subcritical, resulting in a hydraulic jump. Entrainment ensued, and the flow of liquid to the end of the hot leg was greatly reduced.The influence of condensation on the transition from supercritical to subcritical flow as observed in the experimental data is also predicted with the three-field model. When the injected water was subcooled, condensation on the flow of continuous liquid caused a reduction in the flow of vapor and, consequently, a reduction in the interfacial shear stress. Therefore, the flow of liquid remained supercritical to the end of the hot leg at the upper plenum. The entire flow of injected water flowed to the end of the hot leg at higher flows of steam when the injected water was subcooled than when it was saturated. When the flow of vapor was large enough to cause a hydraulic jump in the subcooled liquid, the rate of entrained droplets was greatly increased. The interfacial surface area of the droplets was several orders of magnitude greater than for the continuous-liquid field, and condensation rate on the droplet field was also several orders of magnitude greater. When the flow of vapor from the upper plenum was at its greatest, most of the flow in the continuous liquid was entrained before reaching the upper plenum. The large flow of subcooled droplets caused three-quarters of the steam to condense.     

Experimental and numerical studies of pressure drop in PbLi flows in a circular duct under non-uniform transverse magnetic field

Experiments and three-dimensional (3D) numerical simulations are performed to investigate the magnetohydrodynamic (MHD) characteristics of liquid metal (LM) flows of molten lead-lithium (PbLi) eutectic alloy in an electrically conducting circular duct subjected to a transverse non-uniform (fringing) magnetic field. An indirect measurement approach for differential pressure in high temperature LM PbLi is first developed, and then detailed data on pressure drop in this PbLi MHD flow are measured. The obtained experimental results for the pressure distribution are in good agreement with numerical simulations. Using the numerical simulation results, the 3D effects caused by fringing magnetic field on the LM flow are illustrated via distributions for the axial pressure gradients and transverse pressure differences. It has been verified that a simple approach for estimation of pressure drop in LM MHD flow in a fringing magnetic field proposed by Miyazaki et al. [22] i.e., a simple integral of pressure gradient along the fringing field zone using a quasi-fully-developed flow assumption, is also applicable to the conditions of the present experiment providing the magnetic interaction parameter is large enough. Furthermore, for two different sections of the LM flow at the entry to and at the exit from the magnet, it is found that the pressure distributions in the duct cross sections in these two regions are different.