计算流体动力学在燃料组件热工水力性能分析和格架研制中的应用

国外使用商用计算流体动力学(CFD)软件分析燃料组件中流体的三维流场和温度场,并将验证的方法用于燃料组件格架设计,获得了成功。中国核动力研究设计院空泡物理和自然循环重点实验室用CFX程序对带格架棒束内流场进行了计算,解决了小尺寸复杂结构几何体的模拟,边界条件的选取和CFX计算能力的评价,然后完成了单相,空气一水两相流场和流动特性的计算分析及试验对比验证。已完成的研究表明,尽管CFX程序目前在计算两相流动和传热方面还存在不足,但通过比较单相流场的湍流,旋涡和棒束附近流体温度分布基本可以评价格架对流体的交混性能;格架上的弹簧和刚突对于流动有相当的作用,对其进行模拟是必要的。研究还建议在使用CFD方法进行燃料组件格架热工水力分析前要先进行基准练习以保证分析结果的正确性。     

The SABRE code for fuel rod cluster thermohydraulics

This paper describes the capabilities of the SABRE code for the calculation of single phase and two phase fluid flow and temperature in fuel pin bundles, discusses the methods used in the modelling and solution of the problem, and presents some results including comparison with experiments.The SABRE code permits calculation of steady-state or transient, single or two phase, flows and the geometrical options include general representation of grids, wire wraps, multiple blockages, bowed pins, etc. Transient flows may be calculated using either semi-implicit or fully implicit time solution methods and the temperature distributions within the fuel pins are determined as well as the velocity and temperature of the coolant. Two phase flows are calculated using a homogeneous boiling model, with the possibility of a specified slip between the two phases. General inlet boundary conditions are available (including pressure, velocity, total mass flow) and these may vary linearly with time; the outlet boundary condition is taken as constant pressure. The treatment of grids allows for irreversible head losses at entry and exit. The wire wrap model introduces a grid resistance tensor with its principal axes along and perpendicular to the wire, resulting in a very satisfactory modelling of inducement of swirl.The derivation and solution of the difference equations is discussed. Emphasis is given to the derivation of the spatial differences in triangular subchannel geometry, and the use of central, upwind or vector upwind schemes. The method of solution of the difference equations is described for both steady state and transient problems. Together with these topics we consider the problems involved in turbulence modelling and how it is implemented in SABRE. This includes supporting work with a fine scale curvilinear coordinate programme to provide turbulence source data. The problem of modelling boiling flows is discussed, with particular reference to the numerical problems caused by the rapid density change on boiling.The final part of the paper presents applications of the code to the analysis of blockage situations, the study of flow and power transients and analysis of natural circulation within clusters to demonstrate the scope of the code and compare with available experimental results. The comparisons include the calculation of a flow pressure drop characteristic of a boiling channel showing the Ledinegg instability, examples of overpower and flow rundown transients which lead to coolant boiling, and calculation of natural circulation within a rod cluster.     

Crossflow characteristics of HTGR fuel blocks

Leakage crossflow characteristics in an HTGR core have been studied experimentally and numerically. Two-block crossflow experiments were carried out and the crossflow rate and the pressure difference were measured for various interface gap configurations. A numerical model has been proposed to predict crossflow rates, and the numerical results using the finite element method agreed well with experimental ones. In addition, empirical crossflow equations, which apply to various fuel blocks, were derived for the analysis of the flow distribution in an HTGR core.     

Modeling and validation of a mechanistic tool (MEFISTO) for the prediction of critical power in BWR fuel assemblies

Westinghouse is currently developing the MEFISTO code with the main goal to achieve fast, robust, practical and reliable prediction of steady-state dryout Critical Power in Boiling Water Reactor (BWR) fuel bundle based on a mechanistic approach. A computationally efficient simulation scheme was used to achieve this goal, where the code resolves all relevant field (drop, steam and multi-film) mass balance equations, within the annular flow region, at the sub-channel level while relying on a fast and robust two-phase (liquid/steam) sub-channel solution to provide the cross-flow information. The MEFISTO code can hence provide highly detailed solution of the multi-film flow in BWR fuel bundle while enhancing flexibility and reducing the computer time by an order of magnitude as compared to a standard three-field sub-channel analysis approach.Models for the numerical computation of the one-dimensional field flowrate distributions in an open channel (e.g. a sub-channel), including the numerical treatment of field cross-flows, part-length rods, spacers grids and post-dryout conditions are presented in this paper. The MEFISTO code is then applied to dryout prediction in BWR fuel bundle using VIPRE-W as a fast and robust two-phase sub-channel driver code. The dryout power is numerically predicted by iterating on the bundle power so that the minimum film flowrate in the bundle reaches the dryout criteria. Predicted dryout powers (including trends with flow, pressure, inlet subcooling and power distribution) and predicted dryout locations (both axial and radial) are compared to experimental results, using the entire Westinghouse SVEA-96 Optima3 dryout database, and are shown to yield excellent results.     

数值堆热工流体程序CVR-PACA验证及典型应用

谱元方法是一种高精度的数值计算方法,采用该方法开发了数值堆高精度热工水力并行CFD计算程序CVR-PACA。应用CVR-PACA对单棒光棒通道湍流流场、3×3光棒棒束湍流流场、Matis-H压水堆棒束通道基准题、19棒带绕丝组件通道湍流流场进行了仿真计算。通过与实验测量值对比,研究定量验证了大涡模拟(LES)模型及非稳态雷诺时均(URANS)模型对各类棒束通道流场预测的准确性。算例在建模过程中采用网格分裂技术实现了复杂几何的纯六面体网格划分,用于支撑谱元方法计算。研究较为全面地积累了高精度谱元方法模拟流场流动及换热的建模经验,获取了各类棒束通道内丰富的流动和换热细节,获得的建模经验能更加精准有力地指导相关设计的优化改进。     

Application of FELTRAN to NEACRP TN12 shipping cask benchmark

The finite element technique has received attention as a method of solving the Boltzmann equation in one, two and three spatial dimensions. In particular much work has been published concerning the geometrical flexibility, speed and accuracy of the method.

British Nuclear Fuels plc and Imperial College have collaborated in developing the finite element code FELTRAN to near production code status. FELTRAN solves the even parity form of the Boltzmann equation using a functional approach. The solution is found in one or two spatial dimensions using various orders of finite elements to specify the problem geometry. The angular dependence of the even parity flux is expressed using spherical harmonics. FELTRAN has been interfaced to ANISN formatted nuclear data libraries such as CASK and BUGLE. Anisotropic scattering may be specified to any order. Methods have been incorporated within the code to analyse systems with voids. FELTRAN is currently undergoing further development as part of a BNFL sponsored MSc research programme at the University of Salford.

The purpose of this paper is to consider the application of FELTRAN to a practical shield design problem. The OECD have adopted a benchmark experiment to measure the neutron and gamma ray radiation dose rates around a spent fuel transport flask. As part of an international collaboration the physical details of the flask design and contents have been provided to the nuclear industry. The objective is to perform an international comparison of the methods used in the analysis of cask shielding. BNFL is one of the companies involved, using the well established codes RANKERN and MCBEND. The FELTRAN calculations are performed using the same source and geometry data and equivalent angular flux expansions as for these two codes. FELTRAN is then compared with experimental and calculated results.     

A New Mixed Method with Finite Difference and Finite Element Method for Neutron Diffusion Calculation

A new method for obtaining three-dimensional neutron flux distribution in a reactor has been developed by taking into account the fact that the X-Y planar geometry is generally complex but the geometry along Z-axis is simple. In this method, the finite element method is applied to the X-Y plane calculation and the finite difference method to the Z-axis. For solving a three-dimensional neutron diffusion equation, these two methods are iterated successively until a consistency of the leakage coefficients is attained between the two. The present method is embodied as a computer program FEDM for FACOM M200 computer. With this program, a three-dimensional diffusion calculation was performed for comparing some numerical results with those by a conventional standard computer code ADC. The comparison has shown that they agree well with each other. Computing time required for this problem by the FEDM was shorter than that by the ADC for obtaining same accuracy on the eigenvalue. To indicate usefulness of this method, a demonstration calculation for a reactor with a complex geometry was performed, which was a difficult case to calculate with a conventional finite difference code.     

Numerical investigation of supercritical water-cooled nuclear reactor in horizontal rod bundles

The commercial CFD code STAR-CD v4.02 is used as a numerical simulation tool for flows in the supercritical water-cooled nuclear reactor (SCWR). The basic heat transfer element in the reactor core can be considered as round rods and rod bundles. Reactors with vertical or horizontal flow in the core can be found. In vertically oriented core, symmetric characters of flow and heat transfer can be found and two-dimensional analyses are often performed. However, in horizontally oriented core the flow and heat transfer are fully three-dimensional due to the buoyancy effect. In this paper, horizontal rods and rod bundles at SCWR conditions are studied. Special STAR-CD subroutines were developed by the authors to correctly represent the dramatic change in physical properties of the supercritical water with temperature. In the rod bundle simulations, it is found that the geometry and orientation of the rod bundle have strong effects on the wall temperature distributions and heat transfers. In one orientation the square bundle has a higher wall temperature difference than other bundles. However, when the bundles are rotated by 90° the highest wall temperature difference is found in the hexagon bundle. Similar analysis could be useful in design and safety studies to obtain optimum fuel rod arrangement in a SCWR.     

Analysis of low-heat-flux sodium boiling test in a 37-pin bundle by the two-fluid model computer code SABENA

This paper summarizes the development of a new detailed multi-dimensional multi-field computer code SABENA and its application to an out-of-pile low-heat-flux sodium boiling test in a 37-pin bundle. The semi-implicit numerical method employed in the two-fluid six-equation two-phase flow model has proved in solving a wide spectrum of sodium boiling transients in a rod bundle under low pressure conditions. The code is capable of predicting the spatial incoherency of the boiling, dryout on fuel cladding surfaces and fuel pin heat transfer. Essential to the successful application of such a mechanistic model computer code are validational efforts aimed at the LMFBR accident phenomenology analyses. Through the simulation of the natural circulation boiling conditions, this study provides a consistent analytical interpretation of the experimental data. The important influences of such parameters as the inlet flow restriction and bundle geometry have been examined through interpretations of two-phase flow analysis including considerations of the flow instability induced dryout mechanism.     

Fender: A finite element code for the solution of the diffusion equation in shield design applications

Diffusion theory remains an important method of calculation for shield design. Using adjusted coefficients the method provides an inexpensive solution of adequate accuracy for survey and optimization studies in two- and three-dimensional geometries. Solved in the adjoint mode, the method provides an estimate of the importance function which may be used for the acceleration of generalized-geometry Monte Carlo calculations.A number of computer codes exist to solve the diffusion equation by a finite difference approximation in one-, two- and three-dimensions. The mesh systems used in such codes usually impose restrictions on the accuracy of representation of shields with complicated geometries.The computer code FENDER solves the diffusion equation for neutron or gamma transport using the finite element technique. At present the code is written for a two-dimensional problem in which the geometry is specified as an array of triangular or rectangular elements. This permits a good representation to be made of shields containing curved surfaces. The variation of the calculated particle fluxes within an element is assumed to be quadratic.FENDER may take details of the element structure from an external mesh generating package but also contains a semi-automatic mesh generating routine for use as a stand-alone code. Multigroup diffusion parameters may be either input directly or generated from material compositions. The code is capable of handling problems with at least 1000 elements which is roughly equivalent in size and attenuation to 10,000 finite difference meshes. A variety of boundary conditions may be specified.The paper includes an example of application to demonstrate the potential usefulness of the method and the code. The case chosen is the calculation of neutron fluxes in a stylized fast reactor.     

基于双区域模型的钠冷快堆组件子通道分析程序的开发与验证

子通道分析程序是钠冷快堆堆芯热工水力设计和安全分析的重要工具。本文为计算和分析钠冷快堆组件在径向均匀与倾斜功率分布工况下的热工水力特性,利用双区域绕丝交混模型开发了一款适用于钠冷快堆组件分析的子通道程序SPLICA,并与FFM2A 19棒束实验数据与WARD 61棒束实验数据进行了对比验证。由于本文开发的子通道分析程序SPLICA使用了详细的绕丝交混模型,与经过二次开发后的COBRA程序的计算结果相比,对于FFM2A实验SPLICA程序计算得到的结果与实验结果符合得更好。这两个实验数据的验证结果证明了本文开发的子通道分析程序的准确性以及对高流量工况和低流量工况均具有良好的适用性。本程序能为钠冷快堆组件热工水力分析提供有效的设计和研究手段。     

管束结构的流致振动特性研究

为研究管束结构的流致振动问题,利用有限体积法离散大涡模拟的流体控制方程及有限元方法离散结构动力学方程,结合动网格技术,建立了正方形顺排排列弹性管束流固耦合系统的三维数值模型,并研究了不同弹性管束模型的流体力及振动响应特性。结果表明,管束结构的排列方式对流体力及动力学响应有很大的影响,5管模型能基本反映弹性管束的振动特性,而单管模型预测的临界速度较大,却可定性反映节径比为1.5正方形管束的流致振动特性。     

FLICA-4: a three-dimensional two-phase flow computer code with advanced numerical methods for nuclear applications

This paper is devoted to new numerical methods developed for three-dimensional two-phase flow calculations. These methods are finite volume numerical methods. They are based on an extension of Roe’s approximate Riemann solver to define convective fluxes versus mean cell quantities [Godunov, S.K., 1959, Math. Sb. 47, 217; Roe, P.L., 1981, Approximate Riemanns solvers parameter vectors and difference scheme. J. Comp. Phys. 43, 357–372; Toumi, I., 1992, A weak formulation of Roe’s approximate Riemann solver. J. Comp. Phys. 102, 360–373]. To go forward in time, a linearized conservative implicit integrating step is used [Yee, H.C., 1987. NASA TM-89464], together with a Newton iterative method. We also present here some improvements performed to obtain a fully implicit solution method that provides fast running steady state calculations. This kind of numerical method, which is used widely for fluid dynamic calculations, has proved to be very efficient for the numerical solution to two-phase flow problems. This numerical method has been implemented for the three-dimensional thermal-hydraulic code FLICA-4 that is mainly dedicated to core thermal-hydraulic transient and steady-state analysis [Toumi, I., Caruge, D., 1998. An implicit second order method for 3D two phase flow calculations. Nucl. Sci. Eng. 130, 213–225; Raymond, P., Toumi, I., 1992. Numerical method for three-dimensional steady-state two-phase flow calculation, NURETH-5, Salt Lake City]. Hereafter, elements of physical validation against hydraulic and two-phase flow rod bundle experiments are presented. We will also find some results obtained for the EPR reactor running in a steady-state at 60% of nominal power with three pumps out of four, and a thermal-hydraulic core analysis for a 1300 MW PWR at low flow Steam-Line-Break conditions.     

钠冷快堆燃料组件热工水力特性数值模拟与分析

利用CFD程序CFX,分别对7、19、37、61根棒组成的三角形排列螺旋绕丝定位的钠冷快堆燃料组件棒束通道进行了热工水力特性的分析研究,并将结果与子通道程序SuperEnergy进行了对比验证。重点考察了棒束通道轴向流动分布、横向流交混效应及子通道轴向温升,分析了定位绕丝的影响。结果表明,绕丝对棒束通道的横向流交混效应、轴向流动分布及子通道温升有着重要影响,且随棒束的增多,通道内的流动趋向复杂化,轴向流动不均匀性有升高趋势。     

核电蒸汽发生器接管嘴外表面裂纹应力强度因子计算

核电蒸汽发生器（SG）接管嘴处由于其结构的特殊性,易在制造及服役过程中产生缺陷。为评价该处缺陷的安全性,需要工程可用的应力强度因子解。本文以核电SG接管嘴外表面裂纹为研究对象,采用有限元方法（FEM）及RSE-M规范计算获得了不同方向及尺寸裂纹在内压、弯矩和温度载荷下的等效应力强度因子值,并分析了不同载荷作用下等效应力强度因子在裂纹前沿的分布规律。将计算结果与RSE-M规范的直管应力强度因子解进行比较,发现RSE-M规范的直管应力强度因子计算方法可保守地应用于SG接管嘴处裂纹,并且随着裂纹深度的增加保守度增大。为实现SG接管嘴处缺陷安全的准确评价,基于有限元计算和RSE-M影响系数法给出了适用于SG接管嘴外表面裂纹的应力强度因子计算方法,该方法可以为SG的设计与维护提供指导。      

Development of the finite element method of body fit nodalization for mixed convection analysis in rod bundles

In the reactor rod bundle analysis, mixed convection phenomena are very important after the reactor shutdown. In this paper, the finite element method based on the body fit nodalization are developed to analyze the mixed convection phenomena in a complex geometry. The velocity distribution and the temperature distribution in the reactor rod bundles are obtained using the above two methods. To validate the developed methods, a comparison of the present results with the analytic solutions for a concentric tube is taken. The results show that the mixed convection in a complex geometry can be treated very well with these two methods, and that the finite element method with the body fit nodalization is more efficient than the finite difference method with the body-fitted coordinate system.     

有限元SN中子输运模拟的区域分解并行

确定论中子输运方法具有计算速度快、可获取物理量的精细场分布、可高效多物理耦合等优点,随着有限元方法在中子输运模拟中的应用,复杂几何结构、大尺度下的屏蔽问题和临界问题都能得到高保真建模和分析。离散纵标（S_N）法是求解中子输运方程的有效数值方法,基于OpenMP并行机制对各独立离散方向进行并行求解,可提高S_N输运模拟的计算速度,但并行规模较有限。对几何空间进行区域分解并采用MPI并行机制,可实现大规模并行扩展,进而实现对大型问题的高精度快速求解。本文采用并行自适应非结构网格应用框架JAUMIN进行区域分解和进程间通信,通过并行S_N扫描实现了自主有限元输运程序ENTER的高效并行,完成正确性检验后在天河Ⅱ号超级计算机上使用1 440个CPU核完成了1.43×10⁷网格单元、2.81×10⁹自由度规模问题的测试,计算时间约7.4 h。表明该程序具备了有效模拟大型复杂结构中子输运问题的能力,具有一定工程应用价值。     

CPR1000蒸汽发生器二次侧三维稳态热工水力分析

采用三维稳态分析软件GENEPI,对CPR1000蒸汽发生器二次侧管束区进行了热工水力计算,利用多孔介质及局部阻力系数来表征传热管及各几何部件的复杂结构和压降影响,得到了二次侧管束区流场、温度场等的分布情况。计算结果表明:管束区最大干度为0.3;将典型传热管的动能数据提供给流致振动软件进行计算分析,结果显示在本工况下,传热管的流致振动在可接受范围内;对管板附近的流场及温度场进行分析,预测了此模型及工况下的泥渣沉积区域,为排污管的设计提供了输入数据。计算结果验证了CPR1000蒸汽发生器二次侧管束区设计的合理性。     

Impact of gas in sodium flow on the temperature variation in an LMFBR rod bundle

The impact of gas in sodium flow on the temperature variation in an LMFBR rod bundle was studied in two types of experiments: (1) The gas fraction of the subchannels as well as the gas bubble spectra across the outlet of an unheated 61-rod bundle with wire spacers were measured in water/air flow. The distributions of the gas fractions at the inlet of the bundle were performed under uniform and non-uniform conditions. The results show that the distribution of the averaged gas fractions between the individual subchannels at the outlet of the bundle was almost the same as the distribution at the inlet. The measured bubble spectra show a dependency existing between the bubble frequencies, the bubble lengths, and the gas fraction in a subchannel. (2) A model for computing the transient temperature distributions within a heated rod was supported by experiments performed in a sodium/argon flow. For slug flow conditions a comparison indicates that the measured variations of wall temperatures can be well interpreted as being functions of the bubble contact time, rod power, and gas fraction in the flow.