Reactivity calculation in the frequency domain for BWR stability codes

This paper deals with the problem of computing the feedback reactivity in the frequency domain codes as the LAPUR code. First, we explain how to calculate the feedback reactivity in the frequency domain using slab-geometry (1D) kinetics, also we show how to perform the coupling of the 1D kinetics with the thermal–hydraulic part of the LAPUR code in order to obtain the density to reactivity feedback coefficients, the power to reactivity feedback coefficients and the inlet temperature to reactivity feedback coefficients for the different channels.     

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.     

Comparative RELAP5-3D analysis in support of the NPP DBA analysis in Ukraine

In the Ukrainian in-depth safety assessment (ISA) projects the computer code RELAP5/Mod3.2 with point kinetics approximation is being used in the deterministic safety analysis of VVERs. It is generally accepted that the use of this approximation, with the proper modeling assumptions, results in conservative results. However, only coupled three-dimensional codes are capable to estimate the real localized feedback effects for such VVER specific transients as control rod ejection or main steam line break. Some results of the comparative RELAP5-3D analysis for the scenarios, that present strong local reactivity effects, are discussed in this paper. The goal of this RELAP5-3D analysis is to examine the differences in results obtained by the three-dimensional approach and the methodology that was used in Ukrainian ISA projects.     

Nodal kinetics model upgrade in the Penn State coupled TRAC/NEM codes

The Pennsylvania State University currently maintains and does development and verification work for its own versions of the coupled three-dimensional kinetics/thermal-hydraulics codes TRAC-PF1/NEM and TRAC-BF1/NEM. The subject of this paper is nodal model enhancements in the above mentioned codes. Because of the numerous validation studies that have been performed on almost every aspect of these codes, this upgrade is done without a major code rewrite. The upgrade consists of four steps. The first two steps are designed to improve the accuracy of the kinetics model, based on the nodal expansion method. The polynomial expansion solution of 1D transverse integrated diffusion equation is replaced with a solution, which uses a semi-analytic expansion. Further the standard parabolic polynomial representation of the transverse leakage in the above 1D equations is replaced with an improved approximation. The last two steps of the upgrade address the code efficiency by improving the solution of the time-dependent NEM equations and implementing a multi-grid solver. These four improvements are implemented into the standalone NEM kinetics code. Verification of this code was accomplished based on the original verification studies. The results show that the new methods improve the accuracy and efficiency of the code. The verification of the upgraded NEM model in the TRAC-PF1/NEM and TRAC-BF1/NEM coupled codes is underway.     

Kuosheng BWR/6 stability analysis with LAPUR5 code

Unstable power/flow oscillation of a nuclear power reactor core is one of the main reasons that cause minor core damage. Stability analysis to determine system’s decay ratio needs to be performed at each core reload design to prevent core instability events from happening. Making use of LAPUR5 and SIMULATE-3 codes, we have established a methodology to conduct such analysis. Comparisons made with vendor’s STAIF results indicated close agreements, within acceptable ±0.2 in decay ratios, for Kuosheng NPP Unit2 Cycle 17 reloads design. Sensitivity studies have shown that density reactivity coefficient, delayed-neutron fractions (β) and decay constants (λ), total core flow, and core power axial shape are the most important parameters that might affect the accuracy of decay ratios. We have also found that core conditions at EOC result in larger decay ratios than those at BOC.     

The Monte Carlo codes MCNP and MCU for RBMK criticality calculations

The modern Monte Carlo codes MCNP and MCU have been established as important tools to determine the neutronic behavior of reactor cores. For a comparison of their capabilities, detailed representations of seven critical experiments performed at the Russian Research Center ‘Kurchatov Institute’ were developed, identical in geometry and material composition for each code. Despite the different philosophy of code development, especially in the process of generating cross-section tables, the calculated isotopic reaction rates and the flux distributions are in excellent agreement. Effective multiplication factor and void reactivity effect agree well with experiment. Additional uniform lattice calculations confirm the equivalent potential of MCNP and MCU, but exhibit significant differences to results achieved with transport codes like WIMS-D4.     

The method of characteristics applied to solving slowing down equation to estimate the self-shielded resonance cross sections with an explicit geometrical effect

The conventional resonance treatment in the transport lattice codes requires resonance integral tables in which resonance integrals are tabulated as a function of the background cross sections to be a measure of dilution. Typically self-shielded resonance cross sections in the resonance integral table are generated by performing slowing down calculations with point-wise cross sections defined on an ultra fine energy grid for one-dimensional cylindrical pin cells. Collision probability, interface current method and discrete ordinate method have been used for the one-dimensional cylindrical slowing down calculations. These resonance integral tables are to be used in estimating the self-shielded resonance cross sections for the rectangular or hexagonal pin cells, which results in a reactivity difference due to the geometrical effect on the effective resonance cross sections. In order to improve this problem, the method of characteristics has been applied to the slowing down calculations for two-dimensional square pin cells. The geometrical effect on the reactivity has been quantitatively analyzed by using the Monte Carlo code MCNP and the transport lattice code KARMA. The method of characteristics has been implemented into the MERIT code developed at KAERI for slowing down calculations. The computation results show that the reactivity differences and the discrepancies of the effective resonance cross sections due to the geometrical inconsistency could be significantly improved by using the method of characteristics.     

Safety analysis of reactivity insertion accidents in a heavy water nuclear research reactor core using coupled 3D neutron kinetics thermal-hydraulic system code technique

Nuclear power plant Safety analysis using coupled 3D neutron kinetics/thermal-hydraulic codes technique is increasingly used nowadays. Actually, the use of this technique allows getting less conservatism and more realistic simulations of the physical phenomena. The challenge today is oriented toward the application of this technique to the operating conditions of nuclear research reactors. In the current study, a three-Dimensional Neutron Kinetics and best estimate Thermal-Hydraulic model based upon the coupled PARCS/RELAP5 codes has been developed and applied for a heavy water research reactor. The objective is to perform safety analysis related to design accidents of this reactor types. In the current study two positive reactivity insertion transients are considered, SCRAM protected and self-limiting power excursion cases. The results of the steady state calculations were compared with results obtained from conventional diffusion codes, while transient calculations were assessed using the point kinetic model of the RELAP5 code. Through this study, the applicability and the suitability of using the coupled code technique with respect to the classical models are emphasized and discussed.     

核动力装置自然循环及其过渡过程计算模型的建立

为准确分析含反应性反馈的核动力装置自然循环及其过渡过程中重要参数的响应特性,以核动力装置瞬态最佳估算程序RELAP5/MOD3为基础,采用两群三维时空中子动力学模型替代RELAP5/MOD3的点堆模型,并建立三维空间内中子物理与热工水力的耦合模型,编制相应的计算程序。利用所研制的程序对实际核动力装置的自然循环及其过渡过程进行分析计算,并与试验结果进行比较。结果表明:本文建立的时空中子动力学计算模型克服了点堆方程不能准确计算反应性反馈的缺点,计算精度高,研制的程序可作为核动力装置强迫循环与自然循环及其过渡过程的计算分析工具。     

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.     

Determination of major kinetic parameters of the Syrian MNSR for different fuel loading using Monte Carlo technique

A comprehensive 3-D model of the Syrian MNSR reactor has been developed using the MCNP-4C code aiming at accurate predicting of key core physics parameters. For the currently utilized HEU fuel (89.87% UAl4-Al) and two possible alternative LEU fuels (UO2 12%, and UO2 20%) the main core kinetics parameters like prompt neutron generation time, effective delayed neutron fraction, clean cold core excess reactivity and reactivity feedback coefficients of moderator temperature have been calculated. In this regard the role of particle weight loss on capture, fission and escape in determining the temperature effect of reactivity has been evaluated. The calculated results for the HEU fuel agree well with experimental values. The evaluated kinetics parameters are being used in accomplishing necessarily safety analyses related to the conversion of MNSR reactor to low enriched uranium.     

PWS: an efficient code system for solving space-independent nuclear reactor dynamics

The reactor kinetics equations are reduced to a differential equation in matrix form convenient for explicit power series solution involving no approximations beyond the usual space-independent assumption. The coefficients of the series have been obtained from a straightforward recurrence relation. Numerical evaluation is performed by PWS (power series solution) code, written in Visual FORTRAN for a personal computer. The results are applied to the step reactivity insertion, ramp input, zigzag input, and oscillatory reactivity changes. When the reactivity is given, including the case in which the feedback reactivity is a function of neutron density, the developed method can provide a straightforward procedure for computing reactor dynamics problems. The solution of this method was compared to some other analytical and numerical solutions of the point reactor kinetics equations; the results proved that the approach is both efficient and accurate to several significant figures.     

Analyses of pressure perturbation events in boiling water reactor

In order to design more stable and safer core configurations, experimental and theoretical studies about BWR (Boiling Water Reactor) instability have been performed to characterize the phenomenon and to predict the conditions for its occurrence. The instabilities can be caused by interdependencies between thermal-hydraulic and reactivity feedback parameters such as the void-coefficient, for example, during a pressure perturbation event. In this work, the RELAP5-MOD3.3 thermal-hydraulic system code and the PARCS-2.4 3D neutron kinetic code were coupled to simulate BWR transients. The pressure perturbation is considered in order to study in detail this type of transient. Two different algorithms developed at the University of Pisa were used to calculate the Decay Ratio (DR) and the natural frequency (NF) from the power oscillation signals obtained from the transient calculations. The validation of a code model set up for the Peach Bottom-2 BWR plant is performed against Low-Flow Stability Tests (LFST). The four series of Stability Tests were performed at Peach Bottom Unit 2 in 1977 at the end of cycle 2 in order to measure the reactor core stability margins at the limiting conditions used in design and safety analysis.     

热管冷却双模式空间堆堆芯瞬态安全特性分析

为研究热管冷却双模式空间堆(HP-BSNR)概念设计的可行性和推进模式下堆芯瞬态安全特性,本文基于堆芯结构和稳态程序计算的初始参数分布,建立了堆芯数学物理模型,并开发了适用于HP-BSNR的瞬态安全分析程序TTHA_HPBSNR,计算了HP-BSNR在推进模式下反应性引入和堆芯失流等不同瞬态事故工况下的安全特性,同时分析了反应堆关键参数对HP-BSNR堆芯瞬态安全特性的影响。结果表明,由于堆芯固有负反馈机制的作用,发生反应性引入事故时,堆芯功率最终达到一新的稳定值,且燃料最高温度并未超出安全限值。而发生失流事故时,反应堆能实现自动停堆,且负反馈系数的大小决定了自动停堆的响应时间。相较于反应性引入事故,失流事故对HP-BSNR的安全运行威胁更大。     

Self-Limiting Power Excursion Characteristics of Light Water Reactor, (VI)

The theoretical analysis code named REACT, devised for covering pulsed operation of the HTR, is based on a two-point kinetic model, one point representing the average of the core, while the other is optional (e.g. hottest spot). The behavior of reactor power and other parameters are calculated by the average point, and the temperature of the hottest spot by the other point at same time.

Improvements were brought to the code based on experimental data, and good agreement was found between calculation and experimental results obtained for pulsed operation. The feedback reactivity due to the Doppler effect was comprehensively evaluated by recalculation of experimental data; the void behavior was also investigated.     

快堆系统分析程序FASYS堆芯分析模块验证

中国原子能科学研究院自主开发了快堆系统分析程序FASYS,已用于中国实验快堆的调试试验分析,目前正用于中国示范快堆的事故分析。FASYS程序包含堆芯分析模块、一二回路模块、事故余热排出系统模块等,其中堆芯分析模块包括点堆、衰变热、反应性反馈、堆芯通道热工水力模型等。本文采用解析解、DINROS程序、SAS4A/SASSYS-1程序验证FASYS程序的点堆模型;采用SAS4A/SASSYS-1程序验证FASYS程序的衰变热、反应性反馈和堆芯通道热工水力模型,各模型的验证结果均符合良好。对FASYS程序堆芯分析模块各模型的计算偏差和整体计算偏差进行评估,为中国示范快堆的事故分析提供参考。     

COSINE软件包中子动力学程序KIND的点堆动力学模块设计

围绕实现点堆动力学程序工程化设计的问题，简介了COSINE软件包的点堆动力学计算模块。关于点堆算法的选取，本文对比了显式方法和去刚性算法计算各种典型瞬态问题的结果。结果表明，上述两种算法能充分满足设计可靠性的要求。关于反应性模型的设计，本文简介了全面覆盖各种反应性引入形式和反馈形式的设计思想。此外，还简介了本模块内置的热工模型。本文点堆动力学模块的设计具有良好的可靠性和灵活性。     

Thermal–hydraulics system codes uncertainty assessment: A review of the methodologies

By revising the ECCS licensing rules in 1989, the USNRC has allowed the use of “best estimate” thermal–hydraulics computer codes (such as RELAP5, TRAC, and TRACE), with the requirement that uncertainty analysis accompany the results. Several methodologies have been developed for the quantification of the uncertainties of such codes. These methodologies are either input-driven or output-driven. They disagree in definition for the uncertainty range, qualification and quantification steps, types of uncertainty sources considered, methods of assignment of uncertainty distribution or range to various parameters, approach to propagation of uncertainty, and the way the dynamic characteristics of TH codes are handled. The IMTHUA methodology, developed by the author, is a hybrid approach where an input-driven “white box” method is augmented with output correction based on experimental results relevant to code output. This paper offers a comparative assessment of uncertainty analysis methodologies for thermal–hydraulics transient calculations. The methods will be compared based on their approaches for treatment of input, propagation, and code models and correlations, as well as output. Comprehensiveness, approach to data treatment, and interpretation of results are among the criteria for comparison. Several examples are provided to clarify the differences.     

Modeling of void, fast power and graphite temperature reactivity coefficients measurements for the validation of RELAP5-3D RBMK-1500 reactor model

This paper deals with the modeling of RBMK-1500 specific transients taking place at Ignalina NPP: measurements of void and fast power reactivity coefficients, as well as change of graphite cooling conditions transient. The simulation of these transients was performed using RELAP5-3D code model of RBMK-1500 reactor. At the Ignalina NPP void and fast power reactivity coefficients are measured on a regular basis and based on the obtained experimental results the actual values of these reactivity coefficients are determined. Graphite temperature reactivity coefficient at the plant is determined by changing graphite cooling conditions in the reactor cavity. This type of transient is unique and important from the point of view of model validation for the gap between fuel channel and the graphite bricks. The measurement results, obtained during this transient, enabled to determine the thermal conductivity coefficient for this gap and to validate the graphite temperature reactivity feedback model. The performed validation of RELAP5-3D model of Ignalina NPP RBMK-1500 reactor allowed to improve the model, which in the future would be used for the safety substantiation calculations of RBMK-1500 reactors.