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.     

基于反应性温度系数的金属型脉冲堆波形计算

金属型脉冲堆的反应性反馈效应主要由热膨胀引起,本文在反应性温度系数的基础上建立了波形计算方法,该方法由蒙特卡罗中子输运程序、热力学计算程序和点堆方程3部分组成。首先由三维中子输运程序和热力学计算程序计算出热功率和反应性的耦合关系,然后将耦合关系代入点堆方程,即可求解出波形。采用该方法计算了Lady Godiva的波形,计算结果与LANL的实验结果一致。     

Regional instability evaluation of Ringhals unit 1 based on extended frequency domain model

The frequency domain model has been extended for the regional instability evaluation while retaining its practicality and improving the reliability of major influential numerical models. The unified friction and local pressure loss model of the original LAPUR was modified considering the different dynamic characteristic of two pressure loss mechanisms. The detailed ex-core recirculation loop model was implemented and the neutron point kinetics model was also modified to reflect the inter-mode void reactivity interaction. The neutron flux modal analysis code, ACCORD-N, was developed based on the nonlinear iterative nodal method. Efficient schemes were proposed to give the higher mode initial flux guess. The modified code system was verified based on the Ringhals unit 1 stability test data. Extensive studies were performed to identify influential factors in the regional instability. A dependence of the decay ratio was investigated with regard to the sub-criticality of the first azimuthal mode, Nyquist plots and several power shape indices. It seemed reasonable to conclude that the regional instability was strongly influenced by the thermal hydraulic mechanism. Including the simulation results of other reactors, the distance weighted axial power momentum, named the AS-value, gave a good account of both core-wide and regional instability modes.     

快堆三维瞬态反应性反馈计算研究

在处理快堆时空动力学计算的反应性反馈问题时，提出了一种反应性直接反馈的数学模型。结合快堆的反应性反馈机制，在快堆中子学软件NAS的基础上，给出一种在时空动力学计算中截面反馈与反应性直接反馈相结合的反馈模式。同时，将快堆并群系统加入到程序中，实现了在线并群。对中国实验快堆(CEFR)等温温升过程进行模拟，通过计算结果与CEFR温度反应性系数实验测量结果的对比，证明了本模型和程序的正确性。     

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.     

核反馈实时模拟程序

为了在堆外实验中实现核反馈实时模拟,用C 语言开发了核反馈模拟程序.该程序由3个主要模块组成:反应性反馈模拟、功率控制系统模拟及反应堆模拟.采用的主要物理模型有:点堆模型、一维均匀流体模型、瞬态导热模型等;堆功率控制系统模拟方案为平均温度控制方案;其他辅助计算包括物性参数、几何参数的计算.用Retran-02计算分析数据对模拟程序进行了测试,结果表明,模拟程序的数学模拟正确,运算速度快,计算准确.     

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.     

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.     

Assessment of RELAP5 point kinetic model against reactivity insertion transient in the IAEA 10 MW MTR research reactor

The current study emphasizes an aspect related to the assessment of a model embedded in a computer code. The study concerns more particularly the point neutron kinetics model of the RELAP5/Mod3 code which is worldwide used. The model is assessed against positive reactivity insertion transient taking into account calculations involving thermal-hydraulic feedback as well as transients with no feedback effects. It was concluded that the RELAP5 point kinetics model provides unphysical power evolution trends due most probably to a bug during the programming process.     

Modified Quasi-Steady-State Method to Evaluate the Mean Power Profiles of Nuclear Excursions in Fissile Solution

A modified quasi-steady-state method has been developed in order to evaluate the mean power during a nuclear excursion in fissile solution. The conventional method used the critical equation based on the one-group theory in order to calculate the reactivity. However, the one-group approximation reduces the calculation accuracy, and the geometrical buckling used in the critical equation is not applicable to complex geometries. Thus, we have modified the method to use the reactivity feedback coefficients, which are widely used in the calculation of one-point reactor kinetics. Although the modified method requires an external calculation to obtain the feedback coefficients, it is applicable to complex geometries and provides more accurate results than does the one-group approximation when the proper coefficients are given.

Moreover, a new method to calculate the boiling power has been developed. In this method, the power corresponding to the void fraction that compensated for the inserted reactivity along with the temperature feedback was calculated using the relationship, which was derived using the French SILENE experimental data.

Experimental analyses have been conducted to validate the new method for the French CRAC and Japanese TRACY experiments. The analytical results showed close agreement with the experimental results.     

Monte Carlo simulation of core physics parameters of the Nigeria Research Reactor-1 (NIRR-1)

The Monte Carlo N-Particle (MCNP) code, version 4C (MCNP4C) and a set of neutron cross-section data were used to develop an accurate three-dimensional computational model of the Nigeria Research Reactor-1 (NIRR-1). The geometry of the reactor core was modeled as closely as possible including the details of all the fuel elements, reactivity regulators, the control rod, all irradiation channels, and Be reflectors. The following reactor core physics parameters were calculated for the present highly enriched uranium (HEU) core: clean cold core excess reactivity (ρ_ex), control rod (CR) and shim worth, shut down margin (SDM), neutron flux distributions in the irradiation channels, reactivity feedback coefficients and the kinetics parameters. The HEU input model was validated by experimental data from the final safety analyses report (SAR). The model predicted various key neutronics parameters fairly accurately and the calculated thermal neutron fluxes in the irradiation channels agree with the values obtained by foil activation method. Results indicate that the established Monte Carlo model is an accurate representation of the NIRR-1 HEU core and will be used to perform feasibility for conversion to low enriched uranium (LEU).     

Transient and stability analysis of a BWR core with thorium–uranium fuel

The kinetic response of a boiling water reactor (BWR) equilibrium core using thorium as a nuclear material, in an integrated blanket–seed assembly, is presented in this work. Additionally an in-house code was developed to evaluate this core under steady state and transient conditions including a stability analysis. The code has two modules: (a) the time domain module for transient analysis and (b) the frequency domain module for stability analysis. The thermal–hydraulic process is modeled by a set of five equations, considering no homogeneous flow with drift-flux approximation and non-equilibrium thermodynamic. The neutronic process is calculated with a point kinetics model. Typical BWR reactivity effects are considered: void fraction, fuel temperature, moderator temperature and control rod density. Collapsed parameters were included in the code to represent the core using an average fuel channel. For the stability analysis, in the frequency domain, the transfer function is determined by applying Laplace-transforming to the calculated pressure drop perturbations in each of the considered regions where a constant total pressure drop was considered. The transfer function was used to study the system response in the frequency domain when an inlet flow perturbation is applied. The results show that the neutronic behavior of the core with thorium uranium fuel is similar to a UO₂ core, even during transient conditions. The stability and transient analysis show that the thorium–uranium fuel can be operated safely in current BWRs.     

RIA基准题验证堆芯三维物理-热工耦合程序

以COBRA-Ⅳ和NLSANMT程序为基础,开发了堆芯三维物理-热工耦合程序C4/NK。针对两个典型的反应性引入事故（RIA）,即NEACRP弹棒基准题和提棒基准题,分别进行了验证计算。与参考值和其他程序的计算结果相比,C4/NK耦合程序具有较好的精度,能正确模拟瞬态过程中的物理-热工反馈现象。     

Reactivity feedback coefficients of a low enriched uranium fuelled material test research reactor at end-of-life

The reactivity feedback coefficients at end-of-life of a material test reactor fuelled with low enriched uranium fuel were calculated. The reactor used for the study was the IAEA’s 10 MW benchmark reactor. Simulations were carried out to calculate the different reactivity feedback coefficients including Doppler feedback coefficient, reactivity coefficient for change of water temperature and reactivity coefficient for change of water density. Nuclear reactor analysis codes including WIMS-D4 and CITATION were employed to carry out these calculations. It was observed that the magnitude of all the reactivity feedback coefficients increased at end of life of the reactor by almost 2–5%.     

Generalization of the analytical exponential model to solve the point kinetics equations of Be- and D2O-moderated reactors

A new mathematical formula of the period–reactivity relation for beryllium and heavy-water-moderated reactors has been presented. This formula is represented in a polynomial form with a degree I+J+1 for I-group of delayed neutrons and J-group of photoneutrons. A sample form for the coefficients of such a polynomial is presented which have a linear dependence on the step reactivity insertion. The analytical exponential model (AEM) is developed and generalized. The generalization of the analytical exponential model (GAEM) is analyzed and applied to solve point kinetics equations of the U²³⁵-fuelled, Be- and D₂O-moderated reactors. The generalized method provides a fast and accurate computational technique for the point reactor kinetics equations of photoneutrons and delayed neutrons with step, ramp, sinusoidal and temperature feedback reactivity. Results of this method are presented for different types of reactivity and compared with other referenced methods.     

Calculation of temperature coefficients of reactivity for EBR-II kinetic analyses

Component and regional temperature coefficients of reactivity for four loading configurations of the Experimental Breeder Reactor-II (EBR-II) are compared. The coefficients are calculated by summations of microcoefficients obtained by fine axial delineations of every subassembly. A special-sum method for obtaining effective coefficients for use in kinetics code channels representing subassembly groupings is described. Evaluations of rod-bank suspension coefficients and of grid-plate radial-expansion coefficients are also presented.     

Measurement and analysis of feedback reactivity in the Monju restart core

The purpose of this study is to develop a feedback reactivity measurement technique in the Japanese prototype fast breeder reactor Monju and to validate calculation methodology to forecast the nuclear feedback phenomena. A feedback reactivity measurement technique has been developed based on a reactivity model featuring components that depend on the reactivity coefficients, denoted as reactor power (K_R) and reactor vessel inlet temperature (K_in). This technique can precisely measure the two reactivity components simultaneously and was applied to the feedback reactivity experiment conducted in the Monju system start-up test in May 2010. A thorough evaluation considering all possible biases and uncertainties demonstrated that the reactivity coefficients can be evaluated with a measurement uncertainty smaller than 3%. The evaluated reactivity coefficients were simulated considering the temperature distribution in the core. The calculated and measured values of K_R agreed within 1%, and the value of K_in was consistent with that reported in a previous isothermal temperature coefficient experiment. The measured and calculated fuel subassembly outlet temperatures also agreed well within 0.2°C, which supports the validity of the temperature calculation.     

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.     

Burn-up effect on inherent safety parameters and reactivity insertion transient analysis of Pakistan Research Reactor-1

Burn-up dependent feedback coefficients of reactivity for the reference operating core of Pakistan Research Reactor-1 (PARR-1), have been calculated employing standard computers codes WIMSD/4 and CITATION. Fast reactivity insertion transient (1.5 $/0.5 s) is simulated at each burn step using computer code RELAP5/MOD3.4 and PARET. Calculation reveals that fuel temperature coefficient of reactivity is 1.77 %Δk/k/ΔT less negative while moderator temperature and void coefficients of reactivity are 7.74 %Δk/k/ΔT and 2.04 %Δk/k/ΔT more negative at end of cycle (EOC), respectively. Fast reactivity insertion transient analysis shows that due to larger value of prompt generation time (Λ), reactor response to transient is slow at EOC. Therefore peak power, maximum fuel centreline and clad temperature decrease as the fuel is burned. This is the sign of enhanced inherent safety with the burn-up of reference operating core of PARR-1. Removal of in-pile experiment accident has also been modelled in RELAP5/MOD3.4 and results in this study are compared with PARET.     

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。