Temporal adaptive algorithm for TRAC-BF1/NEM/COBRA-TF coupled calculations in BWR safety analysis

A temporal adaptive algorithm was developed to perform the synchronization and optimization of the performance of TRAC-BF1/NEM/COBRA-TF three-dimensional neutron/thermal-hydraulics sub-channel analysis coupled code system. The multi-level coupling scheme for time synchronization of the TRAC-BF1/NEM and COBRA-TF under PVM is developed considering the different time-step selection algorithms of TRAC-BF1, NEM and COBRA-TF codes. The developed methodology allows one to synchronize the codes in time without doing significant code modifications to the time-step selection logic of the involved codes. The advantage of this approach is that COBRA-TF can capture the nature of a given transient, without losing any time-dependent data. Results for steady state and transient calculations that show how the implemented temporal adaptive algorithm works are presented. In addition selected results are presented to illustrate dynamic behavior and the type of thermal-hydraulic boundary conditions provided by the system code.     

Features and performance of a coupled three-dimensional thermal-hydraulic/kinetics TRAC-PF1/NEM pressurized water reactor (PWR) analysis code

This paper summarizes the current status of the Pennsylvania State University (PSU) version of the coupled three-dimensional (3-D) thermal-hydraulic/kinetics TRAC-PF1/NEM code for pressurized water reactor (PWR) transient and accident analysis and describes applications to reactivity insertion accident (RIA) simulations as well as recent developments. The TRAC-PF1/NEM methodology utilizes closely coupled 3-D thermal-hydraulics and 3-D core neutronics transient models to simulate the vessel and a 1-D simulation of the primary system. An efficient and flexible cross-section generation procedure was developed and implemented into TRAC-PF1/NEM. These features make the coupled code capable of modeling PWR reactivity transients, including boron dilution transients, in a reasonable amount of computer time. Three-dimensional studies on hot zero power (HZP) rod ejection and main steam line break (MSLB) transients in a PWR, as well as a large break loss-of-coolant-accident (LBLOCA) and boron dilution transients, were accomplished using TRAC-PF1/NEM. The results obtained demonstrate that this code is appropriate for analysis of the space-dependent neutronics and thermal-hydraulic coupled phenomena related to most current safety issues.     

Numerical diffusion and the tracking of solute fields in system codes: Part III. Application to a boron dilution transient analysis in the AP600

A study of a pump restart scenario in the AP600 with an unborated coolant plug in two of the four cold legs is presented. It has been performed with TRAC-PF1/MOD2 coupled with a 3-dimensional core neutronics model based on the nodal expansion method (NEM), and high order boron tracking algorithms. These are based on ULTIMATE-QUICKEST for 1-dimensional components and a flux corrected method developed by Smolarckievicz in the 3-dimensional vessel in order to reduce the numerical diffusion inherent to the upwind method used by most system codes to solve the transport equations. No turbulent diffusion model was included in the calculation to produce more conservative results. The results show that reduction of the numerical diffusion yields predictions with a significantly reduced margin in the size of the unborated plugs allowed to form in the primary side piping. In addition, two pump restart strategies have been suggested by the results, which could substantially decrease the size of an unborated plug injected into the core, in case it was suspected to have formed in a primary loop.     

NODHEX: A 2-D diffusion code based on the nodal expansion method in hexagonal geometry and its validation

A 2-D neutron diffusion theory computer code NODHEX for hexagonal geometry has been developed. The nodal algorithm is based on the nodal expansion method proposed by Lawrence. The nodal equation formulation is accomplished by using a second-order polynomial approximation for the flux. The equations include additional terms of discontinuity which occur in the expression of transverse leakage for the hexagonal geometry, unlike the nodal equations (using a second-order polynomial approximation) formulated by Lawrence. The code has been validated by comparing its predictions for the SNR-300 and VVER-1000 benchmarks with the results of other standard computer codes like DIF3D and SNAP. The inclusion of the additional terms of discontinuity is found to improve the predictions relative to Lawrence's predictions, though the same second-order polynomial approximation was used for solving the nodal equations.     

Consistent generation of point feedback reactivity parameters for stability and thermalhydraulic codes

This paper shows a consistent methodology to obtain the point kinetics feedback reactivity parameters to be used by stability codes, like LAPUR-5, or transient codes, like TRAC-BF1. This methodology has been implemented in the code PAPU that generates the point kinetic parameters and feedback reactivity coefficients for the LAPUR and TRAC-BF1 codes. The results of the nodal reactivities obtained with the PAPU methodology have been compared with the results of other codes for different types of perturbations. Also, the reactivity tables generated by PAPU have been used in the LAPUR-5 code obtaining good results when the DR computed by LAPUR with these reactivity tables have been compared with the experimental DR obtained from signal analysis of Cofrentes NPP.     

Improved nodal expansion method for solving neutron diffusion equation in cylindrical geometry

The challenges encountered in the development of nodal expansion method (NEM) in cylindrical geometry and the method to circumvent these difficulties are introduced and discussed in this paper. Due to the fact that the azimuthal term contains a factor 1/r², the traditional transverse integration fails to produce a 1D transverse integrated equation in θ-direction; a simple but effective approach is employed to obtain the θ-directional transverse integration equation. When the traditional polynomials are used to solve the 1D transverse integral equation in r-direction, some additional approximations, which may undermine the precision of the method, are required in the derivation of the moment equations; in order to preserve the accuracy of calculations, the special polynomial approximation is used to solve the 1D transverse integrated equations in r-direction. Moreover, the Row-Column iterative scheme, which is considered to be the more efficient and convenient schemes in cylindrical geometry, is used to solve the partial currents equations. An improved NEM for solving the multidimensional diffusion equation in cylindrical geometry is implemented and tested. And its accuracy and efficiency are demonstrated through several benchmark problems.     

COSINE软件包堆芯物理分析程序CORE开发与初步测试验证

堆芯物理分析程序CORE是1个少群、一维、二维、三维稳态节块法程序,用于压水堆堆芯设计和分析。COSINE软件包是大型压水堆国家重大专项软件自主化课题中的一部分,CORE是COSINE软件包的1个子程序系统,CORE第1版采用节块展开法（NEM）进行二维、三维扩散计算,采用差分法进行一维扩散计算,截面处理采用插值表的方式,燃耗计算采用带预估修正的宏观燃耗计算方法,精细功率重构采用调制方法。目前CORE的核心模块已完成,并进行了初步测试验证,结果表明其扩散求解模块基本满足功能和精度要求。     

Developing and modeling of the “Laguna Verde” BWR CRDA benchmark

Reactivity initiated accidents (RIA) and design basis transients are one of the most important aspects related to nuclear power reactor safety. These events are re-evaluated whenever core alterations (modifications) are made as part of the nuclear safety analysis performed to a new design. These modifications usually include, but are not limited to, power upgrades, longer cycles, new fuel assembly and control rod designs, etc. The results obtained are compared with pre-established bounding analysis values to see if the new core design fulfills the requirements of safety constraints imposed on the design. The control rod drop accident (CRDA) is the design basis transient for the reactivity events of BWR technology. The CRDA is a very localized event depending on the control rod insertion position and the fuel assemblies surrounding the control rod falling from the core. A numerical benchmark was developed based on the CRDA RIA design basis accident to further asses the performance of coupled 3D neutron kinetics/thermal-hydraulics codes. The CRDA in a BWR is a mostly neutronic driven event. This benchmark is based on a real operating nuclear power plant — unit 1 of the Laguna Verde (LV1) nuclear power plant (NPP). The definition of the benchmark is presented briefly together with the benchmark specifications. Some of the cross-sections were modified in order to make the maximum control rod worth greater than one dollar. The transient is initiated at steady-state by dropping the control rod with maximum worth at full speed. The “Laguna Verde” (LV1) BWR CRDA transient benchmark is calculated using two coupled codes: TRAC-BF1/NEM and TRAC-BF1/ENTRÉE. Neutron kinetics and thermal hydraulics models were developed for both codes. Comparison of the obtained results is presented along with some discussion of the sensitivity of results to some modeling assumptions.     

TRAC-PF1程序简介及其移植

ＴＲＡＣ－ＰＦ１程序是压水堆系统安全分析的最佳估算程序［１］。它采用两流体模型处理两相流动，是目前核反应堆系统分析软件中模型比较完善、简化较少的少数软件之一。为了充分利用国外这一先进的系统软件和国内现有的计算设备，将从美国引进的ＩＢＭ版ＴＲＡＣ－ＰＦ１程序经修改移植到了ＣＤＣＮＯＳ／ＶＥ系统及ＳＵＮ工作站上，对不同机器在ＦＯＲＴＲＡＮ语言及汇编语言上的差别进行了修改。对随程序带来的所有标准例题进行了校核计算，结果表明移植是成功的。     

用于轻水堆扩散计算的格林函数节块展开法

提出一种用于轻水堆多维扩散计算的新方法─—格林函数节块展开法（ＧＮＥＭ），它是对节块展开法（ＮＥＭ）和节快格林函数方法（ＮＧＦＭ）的改进。参照ＮＥＭ把节块内偏中于通量用高阶多项式展开，利用格林函数求出节块表面偏中子通量与中子流的耦合关系，并用净中子流作为中间变量以简化计算。根据提出的理论编制了二维计算程序ＧＮＥＭ，对ＬＷＲ基准问题的数值计算表明，ＧＮＥＭ的计算精度与ＮＧＦＭ相当，而计算速度较ＮＧＦＭ和ＮＥＭ分别提高了１倍与１／３倍。应用ＧＮＥＭ取代ＰＳＵＩ－ＬＥＯＰＡＲＤ／ＡＤＭＡＲＣ中的扩散程序，对三里岛核电站（ＴＭＩ－１）的第１、第６循环进行了燃耗计算，其计算速度提高了３倍多，且具有更高的精度。     

Simulation of the VVER-1000 pump start-up experiment of the OECD V1000CT benchmark with CATHARE and TRAC-PF1

In the framework of joint effort between the Nuclear Energy Agency (NEA) of OECD, the United States Department of Energy (US DOE), and the Commissariat a l'Energie Atomique (CEA), France a coupled three-dimensional (3D) thermal-hydraulics/neutron kinetics benchmark for VVER-1000 was defined. The benchmark consists of calculation of a pump start-up experiment labelled V1000CT-1 (Phase 1), as well as a vessel mixing experiment and main steam line break (MSLB) transient labelled V1000CT-2 (Phase 2), respectively. The reference nuclear plant is Kozloduy-6 in Bulgaria. The overall objective is to assess computer codes used in the analysis of VVER-1000 reactivity transients. A specific objective is to assess the vessel mixing models used in system codes. Plant data are available for code validation consisting of one experiment of pump start-up (V1000CT-1) and one experiment of steam generator isolation (V1000CT-2). The validated codes can be used to calculate asymmetric MSLB transients involving similar mixing patterns. This paper summarizes a comparison of CATHARE and TRAC-PF1 system code results for V1000CT-1, Exercise 1, which is a full plant point kinetics simulation of a reactor coolant system (RCS) pump start-up experiment. The reference plant data include integral and sector average parameters. The comparison is made from the point of view of vessel mixing and full system simulation. CATHARE used a six-sector multiple 1D vessel thermal-hydraulic model with cross flows and TRAC used a six-sector, 18-channel coarse-mesh 3D vessel model. Good agreement in terms of integral parameters and inter-loop mixing is observed.     

Development and Verification of an Efficient Spatial Neutron Kinetics Method for Reactivity-Initiated Event Analyses

A space/time nodal diffusion code based on the nodal expansion method (NEM), EPISODE, was developed in order to evaluate transient neutron behavior in light water reactor cores. The present code employs the improved quasi-static (IQS) method for spatial neutron kinetics, and neutron flux distribution is numerically obtained by solving the neutron diffusion equation with the nonlinear iteration scheme to achieve fast computation. A predictor-corrector (PC) method developed in the present study enabled to apply a coarse time mesh to the transient spatial neutron calculation than that applicable in the conventional IQS model, which improved computational efficiency further. Its computational advantage was demonstrated by applying to the numerical benchmark problems that simulate reactivity-initiated events, showing reduction of computational times up to a factor of three than the conventional IQS. The thermohydraulics model was also incorporated in EPISODE, and the capability of realistic reactivity event analyses was verified using the SPERT-III/E-Core experimental data.     

离散节块输运方法在二维柱坐标系中的应用

讨论粗网离散节块法在二维柱坐标系内中子输运方程数值求解中的应用.给出方法的数学模型,在节块内中子通量采用二次近似,表面泄漏采用常数近似.根据所提出的理论模型,编制了考虑各向异性散射的二维节块输运程序DNSN/2D,并对一系列检验和基准问题作了计算.计算结果表明,与传统S_N方法相比,它具有很高的计算效率,在很粗的节块分割下具有非常高的精度.     

Progress in nodal methods for the solution of the neutron diffusion and transport equations

Recent progress in the development of coarse-mesh nodal methods for the numerical solution of the neutron diffusion and transport equations is reviewed. In contrast with earlier nodal simulators, more recent nodal diffusion methods are characterized by the systematic derivation of spatial coupling relationships that are entirely consistent with the multigroup diffusion equation. These relationships most often are derived by developing approximations to the one-dimensional equations obtained by integrating the multidimensional diffusion equation over directions transverse to each coordinate axis. Both polynomial and analytic approaches to the solution of the transverse-integrated equations are discussed, and the Cartesian-geometry polynomial approach is derived in a manner which motivates the extension of this formulation to the solution of the diffusion equation in hexagonal geometry. Iterative procedures developed for the solution of the nodal equations are discussed briefly, and numerical comparisons for representative three-dimensional benchmark problems are given.

The application of similar ideas to the neutron transport equation has led to the development of coarse-mesh transport schemes that combine nodal spatial approximations with angular representations based on either the standard discrete-ordinate approximation or double P_n expansions of the angular dependence of the fluxes on the surfaces of the nodes. The former methods yield improved difference approximations to the multidimensional discrete-ordinates equations, while the latter approach leads to equations similar to those obtained in interface-current nodal-diffusion formulations. The relative efficiencies of these two approaches are discussed, and directions for future work are indicated.     

中子输运方程的三角形节块SN方法研究

利用面积坐标思想,将任意三角形变换为正三角形,使用横向积分方法对正三角形节块进行处理.节块内横向积分通量、中子源的空间分布使用新的正交二次多项式近似;横向泄漏项的空间分布使用二阶多项式近似;中子通量和横向泄漏的角度通过离散纵坐标(SN)求积组离散.采用节块平衡有限差分方法建立稳定有效的迭代方案;编制了二维三角形节块SN输运计算程序(DNTR),对一系列基准题进行了验证.结果表明,本方法在同等计算精度下比细网差分程序(DOT4.2)快5～7倍,在同等计算精度和相同节块尺寸下比矩形离散节块输运方法(DNTM)快1～3倍,但DNTR程序可应用于非结构几何区域问题,具有DNTM等其它结构化节块SN程序无可比拟的优势.     

基于先进节块法的六边形三维中子物理程序的开发与验证

六边形燃料组件在液态金属冷却快堆尤其是钠冷快堆中被广泛应用,针对这类堆型的设计与安全分析需要对堆芯中子通量与中子流进行三维全堆芯耦合计算。经过多年发展,目前已有多种解析节块法、积分节块法、节块展开法等先进节块法能在笛卡尔坐标系下较为精确求解多维中子扩散方程。本文通过径向半解析节块法耦合轴向高阶节块展开法的综合节块方法开发了反应堆三维中子物理计算软件SA HNHEX,并对VVER 440二维、三维基准题进行建模与仿真计算。计算结果与参考值符合较好,初步验证了使用该方法进行反应堆堆芯中子扩散计算的正确性。     

Analysis of the OECD/NEA ROSA Project experiment simulating a PWR small break LOCA with high-power natural circulation

OECD/NEA ROSA Project experiment with the large scale test facility (LSTF) in JAEA was conducted simulating a PWR 1% cold leg small break LOCA with an assumption of high-power natural circulation due to failure of scram and total failure of high pressure injection system. The core power curve for the LSTF experiment was obtained by PWR LOCA analysis using JAEA-developed coupled three-dimensional kinetics and thermal-hydraulics code SKETCH-INS/TRAC-PF1 with detailed core model. A post-test analysis was performed against the obtained data by using JAEA-modified RELAP5/MOD3.2.1.2 code to validate the code predictability. The JAEA-modified RELAP5/MOD3.2.1.2 code was used by incorporating a break model that employs maximum bounding flow theory with a discharge coefficient of 0.61 for two-phase break flow. In the experiment, flow in hot legs became supercritical during two-phase natural circulation, causing the hot leg liquid level to be quite low. Liquid accumulation in steam generator U-tube upflow-side took place during reflux condensation mode due to high vapor velocity. The RELAP5 code predicted reasonably well the overall thermal-hydraulic phenomena observed in the experiment. The code, however, overpredicted the break flow rate especially during two-phase flow discharge period probably because of the failure in the correct simulation of the cold leg liquid level due to late decrease in the primary loop flow rate.     

注量展开节块法求解三维六角形几何中子扩散方程

提出了一种在三维六角形几何节块内数值求解中子扩散方程的节块法该方法把节块内各群中子注量分布用解析基函数近似展开为了改善节块耦合关系．提出了,一种新的节块边界条件：面平均偏流零次矩和一次矩同时保持连续。此外．将响应矩阵技术应用于迭代求解过程,使得该方法具有较高的计算效率基于本文提出的模型,发展了三维六角形组件中子扩散计算程序FEMHEX。通过对二维、三维VVER基准问题校验计算表明,该方法能高效．准确的给出有效增殖系数以及节块功率分布。     

用于求解细网SP3中子输运方程的两节块方法的精度与效率分析

采用两节块方法求解细网3阶简化球谐函数（SP3）中子输运方程,该方法只对零阶角通量密度的拉普拉斯算子进行节块法处理,对应的零阶通量密度采用2阶展开,横向泄漏采用零阶近似;以此方法开发了适用于细网全堆输运计算的CORCA-PIN程序,该程序同时集成了细网有限差分方法。验证算例采用KAIST 3A基准问题及扩展三维问题。数值结果表明,采用栅元1×1划分的两节块法具有可接受的计算精度,而计算时间只有相同精度的细网有限差分方法的11%。因此,本文提出的两节块方法适用于细网SP3中子输运方程计算。      

Axial SPN and Radial MOC Coupled Whole Core Transport Calculation

The Simplified P_N (SP_N) method is applied to the axial solution of the two-dimensional (2-D) method of characteristics (MOC) solution based whole core transport calculation. A sub-plane scheme and the nodal expansion method (NEM) are employed for the solution of the one-dimensional (1-D) SP_N equations involving a radial transverse leakage. The SP_N solver replaces the axial diffusion solver of the DeCART direct whole core transport code to provide more accurate, transport theory based axial solutions. In the sub-plane scheme, the radial equivalent homogenization parameters generated by the local MOC for a thick plane are assigned to the multiple finer planes in the subsequent global three-dimensional (3-D) coarse mesh finite difference (CMFD) calculation in which the NEM is employed for the axial solution. The sub-plane scheme induces a much less nodal error while having little impact on the axial leakage representation of the radial MOC calculation. The performance of the sub-plane scheme and SP_N nodal transport solver is examined by solving a set of demonstrative problems and the C5G7MOX 3-D extension benchmark problems. It is shown in the demonstrative problems that the nodal error reaching upto 1,400 pcm in a rodded case is reduced to 10pcm by introducing 10 sub-planes per MOC plane and the transport error is reduced from about 150pcm to 10pcm by using SP₃. Also it is observed, in the C5G7MOX rodded configuration B problem, that the eigenvalues and pin power errors of 180 pcm and 2.2% of the 10 sub-planes diffusion case are reduced to 40 pcm and 1.4%, respectively, for SP₃ with only about a 15% increase in the computing time. It is shown that the SP₅ case gives very similar results to the SP₃ case.