Thermal-hydraulic analysis of a fluoride-salt-cooled pebble-bed reactor with CFD methodology

The Fluoride Salt Cooled High Temperature Reactor (FHR) is an innovative concept reactor that inherits the technical foundation and advantages of the six optional generation-IV reactors and pressurized water reactors, which is mainly in process in both China and the United States. In this paper, the porous and realistic modeling approaches are adopted to analyze the thermal hydraulic characteristics of a FHR core and a unit segment of pebbles in the core respectively. The distributions of temperature and pressure of the fluoride salt, as well as the reflector temperature profile, are obtained using the porous model. The detailed local flow and heat transfer are investigated by the realistic modeling method for the locations which may have the maximum coolant temperature based on the results of the porous model. The profiles of temperature, velocity, pressure and Nusselt number (Nu) of the coolant on the surface of the pebble are also obtained and analyzed. Numerical results showed that the flow field between the fuel pebbles is complex including secondary flow and back-flow phenomenon, which are hard to measure by experiments. This work can provide useful information for the experimental and mechanism research of FHRs.     

强内热源球床通道单相对流换热特性实验研究

球床水冷反应堆的堆芯为球形燃料元件堆积成的多孔通道,具有显著的强化换热作用。球床通道内的孔隙因具有多变性、随机性的特点,换热情况非常复杂,相关研究较少。为了研究含内热源球床通道内的换热特性,本文用直径为8 mm碳钢球堆积形成球床,以蒸馏水为工质,采用电磁感应加热方式对球床进行整体加热,研究球床通道内部的换热特性。通过对实验数据进行分析,得到了球床通道内部的功率分布和换热系数随热流密度、工质Re的变化规律,根据实验数据拟合得到了球床通道内平均换热系数的无量纲准则关联式,拟合结果与实验结果的相对偏差在12%以内,符合良好。     

DEM-CFD simulation of modular PB-FHR core with two-grid method

For designing and optimizing the reactor core of modular pebble-bed fluoride salt-cooled high-temperature reactor (PB-FHR),it is of importance to simulate the coupled fluid and particle flow due to strong coolantpebble interactions.Computational fluid dynamics and discrete element method (DEM) coupling approach can be used to track particles individually while it requires a fluid cell being greater than the pebble diameter.However,the large size of pebbles makes the fluid grid too coarse to capture the complicated flow pattern.To solve this problem,a two-grid approach is proposed to calculate interphase momentum transfer between pebbles and coolant without the constraint on the shape and size of fluid meshes.The solid velocity,fluid velocity,fluid pressure and void fraction are mapped between hexahedral coarse particle grid and fine fluid grid.Then the total interphase force can be calculated independently to speed up computation.To evaluate suitability of this two-grid approach,the pressure drop and minimum fluidization velocity of a fluidized bed were predicted,and movements of the pebbles in complex flow field were studied experimentally and numerically.The spouting fluid through a central inlet pipe of a scaled visible PB-FHR core facility was set up to provide the complex flow field.Water was chosen as liquid to simulate the molten salt coolant,and polypropylene balls were used to simulate the pebble fuels.Results show that the pebble flow pattern captured from experiment agrees well with the simulation from two-grid approach,hence the applicability of the two-grid approach for the later PB-FHR core design.     

球床内流动与传热特性等效模型的优化研究

提出研究球形燃料元件水冷堆热工-水力问题的等效模型方法。运用计算流体力学软件对窄间隙带环肋片细棒束结构进行三维建模、网格划分和流动传热模拟计算,得到表观流速在0.076~0.334 m/s范围内的压降和换热系数,并与已有的球床实验数据进行比较。根据比较结果对等效模型几何参数进行优化,得到最优等效模型。研究结果表明:最优等效模型与球床的流动与传热特性一致,从数值方法上证明采用等效模型方法对球形燃料元件水冷堆热工-水力问题进行研究是可行的。     

熔盐冷却球床实验堆堆内热源分布计算与分析

熔盐冷却球床堆采用球形燃料元件,冷却剂采用高温熔盐,其堆内热源分布与压水堆有着明显的区别,而与同样使用球形燃料元件的高温气冷堆相比,燃料球产生的中子和γ会在冷却剂中沉积更多的能量,因此准确计算堆内释热率分布对于这种新型反应堆的热工水力设计、瞬态分析、结构力学设计等都有重要意义。本文使用蒙特卡罗计算程序MCNP对中国科学院设计的10 MW固态燃料钍基熔盐实验堆（TMSR-SF1）堆内的释热率分布进行了详细计算研究,通过使用光子产生偏倚卡（pikmt）,经过3次MCNP输运计算得到了TMSR-SF1寿期初（BOL）及寿期末（EOL）堆内各部件的总释热率、体积释热率分布和最大体积释热率。计算结果显示,燃料球释热率占堆内总释热率的94%以上,熔盐和反射层释热率占总释热率的1%以上,其他堆内部件释热率的比例都小于1%。寿期末燃料球、控制棒与石墨球的释热率均有所减少,而反射层等其他构件的释热率有所增加。     

Numerical treatment of pebble contact in the flow and heat transfer analysis of a pebble bed reactor core

This paper studies the numerical treatment of the inter-pebble regions in the modeling of a packed bed geometry for the computational fluid dynamics (CFD) analysis of a pebble bed reactor (PBR) core, where the pebbles are physically in contact with each other. In some studies, the inter-pebble regions have been approximated with gaps, in consideration of the problems on mesh quality or economy of the CFD calculation. To examine such a methodology, a sensitivity analysis for the gap size was conducted with two spherical pebbles, where the inter-pebble region was modeled by means of two kinds of inter-pebble gap and two kinds of direct contact. The cases of direct contact showed numerous differences in the results of the flow regime around the pebbles as well as in the wake, compared to the cases of the inter-pebble gap. No large differences were found between the two cases of direct contact. Based on the result of the sensitivity analysis, the two cases of inter-pebble modeling, i.e., the 1-mm gap and area-contact, were applied to the PBR simulation. It was concluded that the flow regimes and their relevant flow-induced local heat transfer were significantly dependent on the modeling of the inter-pebble region.     

Investigating the advantages and disadvantages of realistic approach and porous approach for closely packed pebbles in CFD simulation

A pebble bed geometry is usually adopted for high-temperature gas-cooled reactors (HTGRs), which exhibits inherently safe performance, high conversion efficiency, and low power density design. It is important to understand the thermal-hydraulic characteristics of HTGR core for optimum design and safe operation. Therefore, this study investigates the thermal-hydraulic behaviors in a segment of pebbles predicted by the Reynolds-averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) model using porous and realistic approaches for the complicated geometry. The advantages of each approach's methodology for the closely packed pebble geometry can be revealed by comparing the calculated results. In an engineering application, a CFD simulation with the porous approach for the pebble geometry can quickly and reasonably capture the averaged behaviors of the thermal-hydraulic parameters as the gas flows through the core, including the pressure drop and temperature increase. However, it is necessary to utilize the realistic approach for this complicated geometry to obtain the detailed and localized characteristics within the fluid and solid fuel regions. The present simulation results can provide useful information to help CFD researchers to determine an appropriate approach to be used when investigating the thermal-hydraulic characteristics within the reactor core of a closely packed pebble bed.     

加/减速流动下棒束通道内速度分布和湍流特性研究

事故工况及海洋条件下反应堆处于非稳态工况,堆芯燃料组件内热工水力行为复杂多变,对反应堆安全提出了更高挑战,因此有必要对非稳态下燃料组件内流动换热特性开展研究。基于粒子图像测速（PIV）技术,结合远心镜头和脉冲控制器,实现对燃料组件内复杂流场的高时空分辨率、长时间的连续测量,获得了流量波动下燃料组件内时空演变的流场结构,分析了棒束通道内速度分布、湍流强度、雷诺应力等瞬时流场信息的空间演变特性。以定常流动下流场分布特性为基准,对比分析了加速度对燃料组件内空间流场分布的贡献特点。实验结果表明：加速流动提高了棒束通道内流层之间的速度梯度,抑制了横向速度和湍流强度;减速流动减弱了棒束通道内流层之间的速度梯度,提高了横向速度和湍流强度。实验结果有助于揭示燃料组件在非稳态条件下的瞬态特性,并为燃料组件的设计和优化奠定基础。     

Development of an innovative detection system for pebble bed kinematic studies

Pebble bed reactors enable the circulation of pebble fuel elements when the reactors are in operation.This unique design helps to optimize the burnup and power distribution, reduces the excessive reactivity of the reactor,and provides a mean to identify and segregate damaged fuel elements during operation. The movement of the pebbles in the core, or the kinematics of the pebble bed,significantly affect the above features and is not fully understood. We designed and built a detection system that can measure 3-axis acceleration, 3-axis angular velocity,3-axis rotation angles, and vibration and temperature of multiple pebbles anywhere in the pebble bed. This system uses pebble-shaped detectors that can flow with other pebbles and does not disturb the pebble movement. We used new technologies to enable instant response, precise measurement, and simultaneous collection of data from a large number of detectors. Our tests show that the detection system has a negligible zero drift and the accuracy is better than the designed value. The residence time of the pebbles in a moving pebble bed was also measured using the system.     

Visualization experiment of complex flow field in a sphere-packed pipe by detailed PIV measurement

A sphere-packed pipe has been proposed as a heat transfer promoter for the first wall cooling in a Flibe blanket. In this study, the flow field in a sphere-packed pipe was well investigated by means of two-dimensional PIV method by matching refractive index of a channel material and working fluid. Three-dimensional flow structure was clarified by integrating the obtained data. The feature of the flow was tortuous high-velocity region formed near pebbles and large velocity fluctuation in the vicinity of the channel wall. And, to apply this flow structure to the actual first wall cooling, a new cooling system using finger-stacked structure was proposed and discussed.     

球床式高温气冷堆MOX燃料循环优化

与压水堆相比,球床式高温气冷堆能在堆芯结构不做明显改变的情况下采用全堆芯装载混合氧化物（MOX）燃料元件。基于250 MW球床模块式高温气冷堆堆芯结构,设计了4种球床式高温气冷堆下MOX燃料循环方式,包括铀钚混合的燃料球和独立的钚球与铀球混合装载的等效方式,采用高温气冷堆设计程序VSOP进行分析,比较了初装堆的有效增殖因数、燃料元件在堆芯内滞留时间、卸料燃耗、温度系数等主要物理特性。结果表明：采用纯铀和纯钚两种分离燃料球且铀燃料球循环时间更长的方案,平均卸料燃耗较高,总体性能较其他循环方式优越。     

Optimization of a radially cooled pebble bed reactor

By altering the coolant flow direction in a pebble bed reactor from axial to radial, the pressure drop can be reduced tremendously. In this case the coolant flows from the outer reflector through the pebble bed and finally to flow paths in the inner reflector. As a consequence, the fuel temperatures are elevated due to the reduced heat transfer of the coolant. However, the power profile and pebble size in a radially cooled pebble bed reactor can be optimized to achieve lower fuel temperatures than current axially cooled designs, while the low pressure drop can be maintained.The radial power profile in the core can be altered by adopting multi-pass fuel management using several radial fuel zones in the core. The optimal power profile yielding a flat temperature profile is derived analytically and is approximated by radial fuel zoning. In this case, the pebbles pass through the outer region of the core first and each consecutive pass is located in a fuel zone closer to the inner reflector. Thereby, the resulting radial distribution of the fissile material in the core is influenced and the temperature profile is close to optimal.The fuel temperature in the pebbles can be further reduced by reducing the standard pebble diameter from 6 cm to a value as low as 1 cm. An analytical investigation is used to demonstrate the effects on the fuel temperature and pressure drop for both radial and axial cooling.Finally, two-dimensional numerical calculations were performed, using codes for neutronics, thermal-hydraulics and fuel depletion analysis, in order to validate the results for the optimized design that were obtained from the analytical investigations. It was found that for a radially cooled design with an optimized power profile and reduced pebble diameter (below 3.5 cm) both a reduction in the pressure drop ( bar), which increases the reactor efficiency with several percent, and a reduction in the maximum fuel temperature (C) can be achieved compared to present axially cooled designs.     

Individual pebble temperature peaking factor due to local pebble arrangement in a pebble bed reactor core

Scientists at the German AVR pebble bed nuclear reactor discovered that the surface temperature of some of the pebbles in the AVR core were at least 200 K higher than previously predicted by reactor core analysis calculations. The goal of this research paper is to determine whether a similar unexpected fuel temperature increase of 200 K can be attributed solely or mostly to elevated power production resulting from exceptional configurations of pebbles. If it were caused by excessive pebble-to-pebble local power peaking, there could be implications for the need for core physics monitoring which is not now being considered for pebble bed reactors. The PBMR-400 core design was used as the basis for evaluating pebble bed reactor safety. Through exhaustive Monte Carlo modeling of a PBMR-400 pebble environment, no simple pebble-to-pebble burn-up conditions were found to cause a sufficiently high local power peaking to lead to a 200 K temperature increase. Simple thermal hydraulics analysis was performed which showed that a significant core coolant flow anomalies such as higher than expected core bypass flows, local pebble flow variation or even local flow blockage would be needed to account for such an increase in fuel temperature. The identified worst case scenarios are presented and discussed in detail. The conclusion of this work is that the stochastic nature of the pebble bed cannot lead to highly elevated fuel temperatures but rather local or core-wide coolant flow reductions are the likely cause.     

Characteristic Features of Heat Transfer and Gas Dynamics in Fuel Assemblies with Spherical Fuel Elements and Radial Dispensing of the Coolant

Certain basic results from the study of the special features of the gas dynamics and heat transfer in fuel assemblies with spherical fuel elements placed in a ring-shaped gap between two perforated cases are presented. The gaseous coolant flows in a radial direction from periphery to center. The special features of the packing of spherical fuel elements in such gaps are studied. The formation of a gas-dynamic structure of the coolant flows inside fuel-element packings and in the dispensing collectors as well as heat transfer and the working capacity of fuel assemblies was investigated. 17 figures, 3 tables, 6 references.     

A discrete element method study on the evolution of thermomechanics of a pebble bed experiencing pebble failure

The discrete element method (DEM) is used to study the thermal effects of pebble failure in an ensemble of lithium ceramic spheres. Some pebbles crushing in a large system is unavoidable and this study provides correlations between the extent of pebble failure and the reduction in effective thermal conductivity of the bed. In the model, we homogeneously induced failure and applied nuclear heating until dynamic and thermal steady-state. Conduction between pebbles and from pebbles to the boundary is the only mode of heat transfer presently modeled. The effective thermal conductivity was found to decrease rapidly as a function of the percent of failed pebbles in the bed. It was found that the dominant contributor to the reduction was the drop in inter-particle forces as pebbles fail; implying the extent of failure induced may not occur in real pebble beds. The results are meant to assist designers in the fusion energy community who are planning to use packed beds of ceramic pebbles. The evolution away from experimentally measured thermomechanical properties as pebbles fail is necessary for proper operation of fusion reactors.     

CFD methodology and validation for single-phase flow in PWR fuel assemblies

This paper presents the CFD modeling methodology and validation for steady-state, normal operation in a PWR fuel assembly. This work is part of a program that is developing a CFD methodology for modeling and predicting single-phase and two-phase flow conditions downstream of structural grids that have mixing devices. The purpose of the mixing devices (mixing vanes in this case) is to increase turbulence and improve heat transfer characteristics of the fuel assembly. The detailed CFD modeling methodology for single-phase flow conditions in PWR fuel assemblies was developed using the STAR-CD CFD code. This methodology includes the details of the computational mesh, the turbulence model used, and the boundary conditions applied to the model. The methodology was developed by benchmarking CFD results versus small-scale experiments. The experiments use PIV to measure the lateral flow field downstream of the grid, and thermal testing to determine the heat transfer characteristics of the rods downstream of the grid. The CFD results and experimental data presented in the paper provide validation of the single-phase flow modeling methodology. Two-phase flow CFD models are being developed to investigate two-phase conditions in PWR fuel assemblies, and these can be presented at a future CFD Workshop.     

Numerical investigation of a heat transfer within the prismatic fuel assembly of a very high temperature reactor

The complex geometry of the hexagonal fuel blocks of the prismatic fuel assembly in a very high temperature reactor (VHTR) hinders accurate evaluations of the temperature profile within the fuel assembly without elaborate numerical calculations. Therefore, simplified models such as a unit cell model have been widely applied for the analyses and designs of prismatic VHTRs since they have been considered as effective approaches reducing the computational efforts. In a prismatic VHTR, however, the simplified models cannot consider a heat transfer within a fuel assembly as well as a coolant flow through a bypass gap between the fuel assemblies, which may significantly affect the maximum fuel temperature. In this paper, a three-dimensional computational fluid dynamics (CFD) analysis has been carried out on a typical fuel assembly of a prismatic VHTR. Thermal behaviours and heat transfer within the fuel assembly are intensively investigated using the CFD solutions. In addition, the accuracy of the unit cell approach is assessed against the CFD solutions. Two example situations are illustrated to demonstrate the deficiency of the unit cell model caused by neglecting the effects of the bypass gap flow and the radial power distribution within the fuel assembly.     

流量分配比对环形燃料芯块传热特性影响数值模拟研究

环形燃料具有两条冷却通道,外通道与内通道的冷却水流量分配比（φ）的变化可能会对芯块传热特性产生影响。本文建立了环形燃料单棒流固耦合CFD计算模型,在4种不同的流量分配比工况下,通过计算3个反映芯块传热特性的评价指标,研究了流量分配比变化对环形燃料芯块传热特性的影响。由分析计算结果可知,流量分配比变化不会对有间隙结构的环形燃料的芯块传热特性产生显著影响。