Simulation of start-up measurements with the KIKO3D code and its application for determining the scram rod worth uncertainty in the VVER-440 reactor

The reasons for large discrepancies between the computed and measured values of the efficiency of control rods observed during start-up experiments on the Russian pressurized water type VVER reactors are discussed. The numerical simulation of the measurements including the prediction of the ex-core detector signals was used to resolve the discrepancies. The time and space dependent neutron flux in the core during these measurements have been calculated by the KIKO3D nodal kinetic code. For calculating the ionization chamber signals the Green function technique has been applied. The Green functions of ionization chambers have been evaluated via solving the neutron transport equation in the reflector regions with the MCNP Monte Carlo code. The detector signals have been calculated and compared with measured ones using the inverse point kinetics transformation. Large number of asymmetric rod drop measurements (with one rod stuck) and some differential rod worth measurements from the Zero Power Physics Tests were provided by the Paks NPP for validation. The experiments cover different fuels (without and with enrichment zoning) and loading patterns. The intermediate range ionization chambers have been used during the scram measurements. The newly developed method provides fairly sufficient match of measured and calculated results. The time behavior of the detector readings observed in the measurements are described by the code in a consistent manner.As a further application the uncertainty of scram rod worth of the KARATE-440 code system was determined by static calculations and subsequent simulation of rod drop with the KIKO3D code. The calculated results were compared to measurements carried out by the Paks NPP. The uncertainty of scram rod worth is established by statistical analysis.     

先进反应性测量系统的研发与应用

相比于传统的反应堆控制棒价值测量方法,快速的动态棒价值测量方法要求反应性测量设备具有更高的精度和性能,以准确获取和处理堆外探测器的电流信号,并需通过额外的堆芯中子学计算对试验过程中的空间效应进行修正。为此本研究开发了一套包含先进物理试验测量仪（APTC）和动态棒价值测量软件包（LIGHT）的先进反应性测量系统（SMART）,并对SMART开展了一系列验证试验。结果表明,SMART具备完整的物理启动试验功能,其精度和性能能够满足包括动态棒价值测量在内的物理启动试验的要求;在300 MW压水堆核电厂中的成功应用也充分验证了SMART的工程应用能力。      

An assessment of a VVER-1000 core during Turbo-Generator load reduction test using RELAP5/MOD3.2 and WIMSD-5B/PARCSv2.7

Reactor dynamic tests, which are categorized as one of the power start-up test groups, are the most complex tests during commissioning of the new nuclear power plants. This paper presents the results of Turbo-Generator load reduction test as one of the reactor dynamic tests for VVER-1000/V446 unit at Bushehr Nuclear Power Plant (BNPP). In this test modeling because of the need for control rod bank worth and core reactivity coefficients, the core geometry has been modeled first by using WIMSD-5B/PARCSv2.7 codes for neutronic calculations. For performing the thermal-hydraulic analysis, the RELAP5/MOD3.2 computer code has been used. The control rod bank worth and core reactivity coefficients obtained from WIMSD-5B/PARCSv2.7 are compared with BNPP FSAR that confirm the ability and reliability of the method. Also comparison of the thermal-hydraulic core parameters obtained from RELAP5/MOD3.2 against actual plant data, indicate that this code can properly predict behavior of VVER-1000 reactor for this dynamic start-up test.     

Diagnostics of core barrel vibrations by in-core and ex-core neutron noise

Diagnostics of core-barrel vibrations has traditionally been made by use of ex-vessel neutron detector signals. We suggest that in addition to the ex-core noise, also the in-core noise, induced by core barrel vibrations, be also used. This would enhance the possibilities of diagnostics where the number of the ex-core detectors is not sufficient or their positions are disadvantageous for effective diagnostics, especially for shell-mode vibrations.

To this order, the theory of in-core noise induced by a fluctuating core boundary has been elaborated and applied to the diagnostics of beam and shell mode vibrations. The formulas were tested on some measurements taken in the Ringhals PWRs. The results confirm the validity of the model itself, and the possibilities for enhanced diagnostics were demonstrated. A more effective use of these novel possibilities requires more in-core detectors and/or better detector positioning.     

Power peak factor for protection systems – Experimental data for developing a correlation

This paper aims to construct a data set that can be used to train neural networks to furnish the power density peak factor during reactor operation. The inputs considered were those available in the reactor protection systems, namely, the axial and quadrant power differences obtained from measured ex-core detector signals, and the position of control rods. The response of ex-core detector signals was measured in experiments performed in the IPEN/MB-01 zero-power reactor. Several reactor states with different power density distribution were obtained by positioning the control rods in different configurations. The power distribution and its peak factor were calculated for each of these reactor states. The obtained results show that the power peak factor correlates well with the control rod position and the quadrant power difference, and with a lesser degree with the axial power differences. The data presented an inherent organisation and could be classified into different classes of power peak factor behaviour as a function of position of control rods, axial power difference and quadrant power difference. The analysis of the data set indicates that the power peak factor can be determined through a neural network having as input the position of control rods. Regarding only signals of ex-core detectors, the data indicate that a neural network may estimate better the power peak factor if the input vector comprises both the axial and the quadrant power differences.     

Benchmark Analysis of TRIGA Mark II Reactivity Experiment Using a Continuous Energy Monte Carlo Code MCNP

The benchmark analysis of reactivity experiments in the TRIGA-II core at the Musashi Institute of Technology Research Reactor (Musashi reactor, 100 kW) was performed by a three-dimensional continuous-energy Monte Carlo code MCNP4A. The reactivity worth and integral reactivity curves of the control rods as well as the reactivity worth distributions of fuel and graphite elements were used in the validation process of the physical model and neutron cross section data from the ENDF/B-V evaluation. The calculated values of integral reactivity curves of the control rods were in agreement with the experimental data obtained by the period method. The integral worth measured by the rod drop method was also consistent with the calculation. The calculated values of the fuel and the graphite element worth distributions were consistent with the measured ones within the statistical error estimates. These results showed that the exact core configuration including the control rod positions to reproduce the fission source distribution in the experiment must be introduced into the calculation core for obtaining the precise solution. It can be concluded that our simulation model of the TRIGA-II core is precise enough to reproduce the control rod worth, fuel and graphite elements reactivity worth distributions.     

Development of a control rod depletion methodology for the Westinghouse NEXUS system

The NEXUS project is an effort to merge and modernize the methods employed in Westinghouse PWR and BWR steady-state reactor physics codes. The NEXUS system relies on a once-through nodal cross-section generation methodology with an innovative and efficient technique for pin power recovery. The pin power methodology overcomes a well-known limitation of existing methodologies, namely the incapacity to properly account for heterogeneity changes due to the depletion environment. The so-called control rod history problem where control rods are repeatedly inserted and withdrawn during core depletion is a good example of such a case. In addition to the control rod history impact on pin power distributions, the insertion of control rods during extended periods leads to significant control rod depletion that affects the reactivity worth of the control rods which in turn can have a significant impact on pin powers. The importance of accurately predicting pin powers, combined with the need to adequately estimate the reactivity worth and nuclear end of life of control rods in BWRs and in generation III+ PWRs, has motivated the development of a novel control rod depletion model. This methodology and its numerical qualification, initially for PWR application only, is the topic of this paper. The focus is on describing the salient features of the model and on illustrating its performance by means of numerical experiments. It is shown that together with the NEXUS pin power recovery model, the control rod depletion methodology accurately predicts the reactivity feedback from repeated control rod insertions in a PWR core.     

用硼中毒法进行脉冲堆控制棒效率和总后备反应性测量

本文介绍了在脉冲堆零功率物理实验中,利用硼中毒法测量反应性的原理和方法,给出了脉冲堆堆芯的硼微分价值、控制棒效率和总后备反应性的实验结果。还利用硼中毒法和脉冲中子源法配合进行脉冲堆控制棒之间反应性干涉效应的实验研究,取得了初步结果。     

DF-VI快中子临界装置2号堆芯临界实验

DF-VI快中子临界装置在改造完成、堆芯发生了变化以后,进行了重新启动和一系列的实验测量。测量内容有：根据29次临界实验的数据对2号堆芯平均临界元件数和临界质量进行了计算;应用周期法和棒补偿法对控制棒价值进行了刻度;用逆动态反应性计对安全棒和安全块的价值进行了测量;对单根边缘元件价值和径向元件价值分布进行子测量。通过以上实验测量,确定了DF-VI快中子临界装置2号堆芯的主要安全运行参数。     

Significant spatial dependence observed in inverse kinetics analysis for a loosely coupled-core system of the Kyoto University Critical Assembly

A loosely coupled-core system was constructed in the Kyoto University Critical Assembly to study the spatial effect observed in inverse kinetics analysis of control rod reactivity worth. In a rod drop experiment, the conventional inverse kinetic method resulted in a space- and time-dependent rod worth, which depended significantly on detector position and varied remarkably with the elapse of time. In another rod worth measurement, where a control rod was continuously inserted, the similar spatial dependence could be also observed. In this study, a modal expansion approach was proposed to reduce the above spatial dependence of the measured rod worth. Applying the present approach to inverse kinetics analysis, the troublesome dependence could be solved to obtain space-independent rod worth. This approach requires only the eigenfunctions of fundamental and higher modes for an unperturbed system but makes both static and transient calculations for various perturbed systems unnecessary.     

Analysis of the MOX critical experiments BASALA by pin-by-pin core analysis method using three-dimensional direct response matrix

An analysis of the MOX critical experiments BASALA was performed to verify the pin-by-pin core analysis method using a three-dimensional direct response matrix. The BASALA experiments simulate full MOX BWR cores, and they were carried out in the EOLE critical facility of the French Atomic Energy Commission (CEA) by the Nuclear Power Engineering Corporation (NUPEC) in collaboration with CEA. The BASALA experimental cores are very heterogeneous because their size is much smaller than that of commercial power plants. The main features of the pin-by-pin core analysis method using the three-dimensional direct response matrix are that the response matrix can reflect the intra-assembly heterogeneous effect, the diffusion approximation is not involved, and the fuel rod fission rate can be directly evaluated. The maximum difference of the critical k-effective values among all nine cores analyzed was about 0.4% Δk. The root mean square differences between the calculated and measured radial fuel rod fission rate distributions in the test assembly of all cores were within 1.8% and nearly comparable to measurement error. The calculated results of the reactivity worth agreed with the measured results within 9%. These good agreements mean that the pin-by-pin core analysis method using the three-dimensional direct response matrix accurately reflects the effects of the intra- and inter-assembly heterogeneities in heterogeneous systems like the BASALA experimental cores.     

次临界反应性测量的空间修正及其应用综述

次临界下的反应性测量技术有着自身的特点,次临界下控制棒的动作、堆芯的次临界度以及外中子源的存在都会对堆芯中子通量的分布产生影响,因此通常情况下堆芯的次临界度只能"监视",无法准确测量。在堆芯模拟软件发展的基础上,国外科研人员提出了次临界下点堆模型的空间修正方法,将这种方法用于动态棒价值测量(DRWM),并在此基础上进一步发展了次临界控制棒价值测量(SRWM),这些技术有的已经被国内核电站使用,但是国内对空间修正的原理及方法鲜有介绍。本文针对这种需求,总结概括了国外商用堆次临界反应性测量的基本原理与方法,并结合反应性测量仪表技术,给出了次临界反应性仪的数据处理流程,这对于推进国内商用堆次临界反应性测量的研究和实际应用具有较为重要的意义。     

A methodology for benefit assessment of using in-core neutron detector signals in core protection calculator system (CPCS) for Korea standard nuclear power plants (KSNPP)

Core Protection Calculator System (CPCS) is a digital computer based safety system generating trip signals based on the calculation of departure from nucleate boiling ratio (DNBR) and local power density (LPD). Currently, CPCS uses ex-core detector signals for core power calculation and it has some uncertainties. In this work, a quantitative economic benefit assessment of using in-core neutron detector signals is carried out. In-core detector signals which directly measure the inside neutron flux of core are applied to CPCS to obtain more accurate power distribution profile, DNBR and LPD to reduce the calculation uncertainties. In order to improve axial power distribution calculation, piecewise cubic spline method is applied. Simulation is also carried out to verify its applicability to power distribution calculation in this work. Simulation result shows that the improved method reduces the calculational uncertainties significantly and it allows larger operational margin. It is also assured that no power reduction is required while Core Operating Limit Supervisory System (COLSS) is out-of-service when the improved method is applied.     

Examination of Actual Neutron Count Rate Data during a Control Rod Drop Testing for Estimation of Control Rod Worth in PWRs

The Modified Neutron Source Multiplication (MNSM) method, which is based on the extraction of the fundamental mode of neutron flux distribution, has been proposed to estimate subcriticality. It has been proven applicable to a small critical assembly and domestic PWRs during criticality approach. In the following study, it is also shown by numerical simulation that it is applicable to estimate the subcriticality using neutron count rate data during the control rod drop testing in PWRs. As the next step, we looked further into the actual data of neutron count rate in order to examine whether the expected signal response was observed for the estimation. It was found that the actual data have shown the expected response, and the control rod worth could have been estimated in the same manner as during criticality approach. A new procedure is also proposed to measure a reference reactivity that is essentially required to evaluate the reactivity of each control rod worth.     

固定棒位法测量控制棒总价值

控制棒价值测量的准确度与效率对核电厂的安全性与经济性具有重要影响。在动态刻棒等反应性测量工作中,本底与中子源对探测器有显著影响,致使根据实测电流计算得到的反应性显著偏离真实值。基于点堆逆动态方程,通过对本底与中子源影响的分析,利用固定棒位状态下的测量数据计算反应性并得到控制棒总价值,给出了一种不受本底与中子源影响的简便的控制棒总价值测量计算方法,并在零功率实验装置上进行验证。结果表明,该方法可有效避免本底和中子源组件对反应性探测的影响,并简化了离线理论计算,其与周期法计算结果的相对偏差在1%以内。     

双面慢化环形燃料反应堆物理实验

环形燃料零功率反应堆是首个双面慢化环形燃料作为核燃料的反应堆。本文采用周期法、落棒法获取环形燃料零功率反应堆的临界参数、控制棒价值、元件价值、含Gd元件的反应性效应等关键参数,对环形燃料零功率反应堆的物理性能进行实验研究,验证环形燃料反应堆堆芯物理设计计算程序。结果表明：根据外推过程确定堆芯临界装载环形燃料元件96根,实心燃料元件172根,此时k_eff为1.000 40,堆芯调节棒价值为-247.5 pcm,安全棒价值为-1 358.4 pcm;元件价值与理论值平均偏差为1.3 pcm,含Gd元件反应性效应与理论值平均相对偏差为8.8%。本文结果为环形燃料的工程化设计程序提供关键数据支撑。     

On-line extraction of the variance caused by burn-up in in-core three-dimensional power distribution

In most of PWRs, the ex-core ion-chambers are the sole real-time sensors to respond to in-core power and its axial offset. However, the calibration coefficient of the ion-chambers depends on the (3D) power distribution and varies with the burn-up. People expect to know the variance in distribution caused by burn-up directly from the signals of ion-chambers. This expectation is not realized as yet, because an ion-chamber almost only responds to its nearest fuel assemblies. The authors then developed a two-step method for burn-up characteristic extraction: the harmonics synthesis method and harmonics’ burn-up grouping. Using the extracted burn-up characteristics, the relationship between the readings of the ex-core ion-chambers and the in-core 3D power distribution is set up. Through the simulation on the heating reactor, the method of burn-up characteristic extraction is verified under engineering conditions. It is possible to on-line extract the variance caused by burn-up in 3D power distribution.     

Borssele PWR noise: Measurements, analysis and interpretation

In the Borssele reactor — a 450 MWe PWR — reactor noise measurements have been performed during four fuel cycles. Measurements were made with a set of ex-core neutron detectors, on one occasion an in-core displacement transducer, and with primary coolant pressure sensors. Digital analysis was applied, where the most powerful tool was the computer programme FAST, which computes auto and cross power spectra for all combinations from a set of many simultaneously recorded signals.

Analyses of neutronic signals show a reactivity noise peak at 9.2 Hz, core barrel motion peaks at about 12 and 15 Hz, a damped oscillation at about 2 Hz. Results are given for begin and end of each fuel cycle. The r.m.s. value of the low frequency noise appears to depend linearly on the boron concentration over a wide range.

Also some results of primary coolant pressure noise are presented, with coherent peaks below 15 Hz and incoherent peaks above.

The second part of the paper describes an alternative way of analyzing and interpreting noise spectra, namely attempts to decompose the neutronic power spectra into physical components, using the information present in the CPSD's of all detector combinations. The components are characterized by their detector position dependency. Effects considered are: uncorrelated noise, global reactivity noise, core motion attenuation noise, and a possible coupling between reactivity and core motion. Results show excellent separation into reactivity and core motion components with possibilities to separate overlapping peaks. Weak peaks become more easily detectable. At low frequencies the decomposition of the spectra is not yet complete, however.     

反应堆堆外核测量系统的实时仿真

堆外核测量系统实时仿真是核电厂全范围培训模拟器的重要组成部分。本文给出一种基于测量原理的功能仿真处理方法,利用堆芯物理仿真计算出堆芯中子通量密度．建立了堆外核测量值与反应堆内三维中子通量密度分布之间的拟合公式．根据反应堆物理计算或功率刻度实验确定拟合系数．可以实时准确仿真堆外核测量系统,满足核电厂全范围培训模拟器的要求．     

动态棒价值测量软件包LIGHT的开发与数值验证

动态棒价值测量是一种快速测量控制棒组价值的方法。基于测量过程和相关的反应堆物理数值计算方法，开发了动态棒价值测量软件包LIGHT。LIGHT可产生进行动态棒价值测量所需的参数，包括静态空间因子、动态空间因子和缓发中子参数。针对基准问题和AP1000核电厂进行了数值计算并进行了比较。分析表明，计算结果具有较高的精度，说明建立的计算模型及开发的程序是正确的。