Feasibility Study on Subcriticality Monitoring with a Digital Reactivity Meter

A conventional digital reactivity meter is based on a simple principle to solve inverse point reactor kinetics equations and it can monitor reactivity continuously on a real time basis. Then, feasibility was studied for a conventional digital reactivity meter to be used as a subcriticality monitor. It was necessary to overcome some problems; for example, the applicability of the point reactor kinetics equations must be verified for the system where neutron distribution is dependent on the subcriticality. We showed that the problems can be solved or can be taken into account. The subcriticality calculated by the reactivity meter might not be accurate for the measurement of the actual value of the subcriticality itself, however, it is accurate enough for the purpose of subcriticality monitoring. We believe that the monitoring on a real time basis is more important for subcriticality monitoring than the accuracy of the value of the monitored subcriticality. Based on the study, we proposed that a digital reactivity meter can be used as a subcriticality monitor.     

Decoupling Control of Nonlinear Coupled Core Reactor

This paper concerns the application of the decoupling theory for a nonlinear system to the power control of the coupled core reactor. By using this theory, we can deal with the power change problem, the regulating problem for a system subject to a large perturbation, etc., which cannot be dealt with by the decoupling theory for a linear system.

But, since this theory assumes tacitly that all the states are measurable, the theory can not be applied directly to the nuclear reactor that has nonmeasurable state variables such as the delayed neutron precursor. In this paper, the above difficulty is overcome by introducing the observer theory for a nonlinear system.

The decoupling controller and observer resulted from these theories are applied to the coupled core reactor and the dynamic characteristic of the reactor is simulated by the digital computer. The simulation shows that the reactor power of each core is controlled satisfactorily in decoupling manner.     

基于蒙特卡罗-离散纵标双向耦合方法的堆坑粒子注量率计算

为有效解决大型复杂核设施屏蔽计算问题,研究了三维蒙特卡罗(MC)-离散纵标（S_N）双向耦合方法,通过自主开发接口程序实现MC粒子概率分布与S_N角通量密度之间的相互转换,实现MC-S_N双向耦合计算。将基于MC-S_N双向耦合方法的程序用于某反应堆堆坑底部粒子注量率计算。利用MC程序建立堆芯及堆坑处的精细模型进行计算,三维S_N程序用于堆芯下表面与压力容器底面之间区域的计算。通过MC-S_N-MC两步耦合计算,给出堆坑通道及小室内的中子和光子注量率。三维MC-S_N双向耦合方法计算结果与单一MCNP程序结果吻合较好,初步验证了该方法是解决大型复杂核装置屏蔽问题的有效工具。     

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.     

基于格子Boltzmann方法的反应堆核-热-流耦合模拟

反应堆堆芯内部存在多种不同物理场之间的相互作用和反馈,对其准确模拟需要考虑这些物理过程之间的耦合。为了降低堆芯核 热 流耦合模拟的实现难度,消除不同物理场之间的外部插值过程,本文构建了核 热 流耦合模拟的格子Boltzmann方法（LBM）,将中子输运（包括SN方程、SP3方程以及扩散方程）、考虑燃料流动效应的缓发中子先驱核守恒方程以及流动传热方程统一到相似的LBM格式下,采用统一的LBM碰撞 迁移过程进行求解,有效降低了堆芯多物理耦合模拟的实现难度。计算结果表明：本文建立的核 热 流耦合LBM模型对不同雷诺数下的流动效应均能准确模拟,同时温度反馈在高温熔盐堆低速流动条件下有较为明显的影响,不能忽略;提高堆芯熔盐流速能够有效地展平功率及温度分布。     

Experimental determination of subcriticality at subcritical PWRs in Korea

A direct subcriticality measurement system (SMS) based on the Feynman-α method has recently been developed by KEPRI. It was applied to six commercial pressurized water reactors in Korea. However, the obtained Feynman curves failed to give proper multiplication factors. The objective of these tests was to investigate the performance of the Feynman method to predict directly the subcriticality of a given subcritical reactor by using the neutron pulse counts only without any reactor perturbation in the large commercial reactors. Recently, two methods developed by Hokkaido University and Westinghouse Electric Corporation. These methods have a defect due to being based on the modified neutron source multiplication method. To overcome this defect and derive operational benefits is necessary to estimate the subcriticality of a subcritical core directly from the neutron pulse counts only. The performance of the developed SMS was verified in the Kyoto University Critical Assembly and applied to eight 1000 MWe Optimized Pressurized Water Reactors (OPR1000) in Korea. The obtained results show that the SMS based on the Feynman method can be a useful tool to estimate the reactivity of a subcritical power reactor. Although the discrimination level of the signal-processing unit in OPR1000 suffers from noise and gamma ray effects, SMS can provide good Feynman curves and effective multiplication factors. However, the SMS has failed to give the reactivity for the entire measured data set. Improving the SMS and investigating the effects of different discriminator level settings at SPU in OPR1000 will be topics for further study.     

Feasibility Study for Evaluation of Control Rod Worth in Pressurized Water Reactors using Neutron Count Rate during a Control Rod Drop Testing

Applicability of the modified Neutron Source Multiplication (NSM) method with extraction of the fundamental mode to subcriticality measurement has been proposed. Following the feasibility verification in the previous study based on numerical analyses, its applicability has been proven in a more realistic situation; in a withdrawal sequence of control rod banks during the PWR startup. Subcriticalities with various control rod insertion configurations were estimated based on the modified NSM method. The subcriticality could be evaluated with a good accuracy even with the mockup experiment where any special treatments for accurate measurement were not taken into account and furthermore the insensitivity of measured signals by reactivity changes and their large fluctuations were seen.

Based on this fact, we further investigated a feasibility to use neutron count rate data obtained during the control rod drop testing, which is carried out before the reactor physics tests at hot zero power condition. When it is proven that these data could be used for the estimation of each control rod worth, the following reactor physics tests could be performed with the advanced knowledge of each control rod worth and procedures for detailed control rod worth measurement could be simplified or eliminated from the reactor physics tests.     

中国实验快堆全厂断电事故多维度热工耦合计算

多维度耦合方法是将传统的一维反应堆热工流体力学程序与三维流体动力学分析软件通过一定的耦合方法结合起来，实现反应堆局部复杂流体现象分析与系统计算的耦合方法。本工作根据中国实验快堆设计和运行经验，开发了基于Rubin和Fluent的耦合程序框架，完成了中国实验快堆全厂断电工况的计算和验证。计算结果表明，耦合方法对全场断电事故的计算结果合理可靠，是对一维系统程序分析方法的有益补充。     

Development of three-dimensional reactor analysis code system for accelerator-driven system,ADS3D and its application with subcriticality adjustment mechanism

In order to perform the parametric survey for an accelerator-driven system (ADS) core with the subcriticality adjustment mechanism, a new calculation code system, ADS3D, was developed on MARBLE which is a comprehensive and versatile framework for reactor analysis. The application of ADS3D was also demonstrated on the neutronics design of ADS operated by control rod (CR) movement. Through the neutronics calculation, it was shown that the maximum proton beam current was decreased from 20.5 to 11.6 mA due to the switch from beam-operated to CR-operated core.     

Indication Lowering of Average Magnitude Type Campbelling System in Low Pulse Rate Region

In the nuclear power calibration process of JOYO, the first experimental fast breeder reactor in Japan, the indication of the Intermediate Range Monitoring System (IRMS), employing Average Magnitude type Campbelling System (AMCS), was calibrated with the reactor power at 45.82 kW. The reactor power was then decreased and the nonlinear indication lowering of the IRMS was observed.

In this paper, we present a derivation of an equation representing the AMCS characteristic and show that the indication lowering occurs when the product of mean arrival rate of pulses and their width is small. The computed values based on the derived equation agreed very well with the observed ones in the JOYO IRMS below 45.82 kW, and it was confirmed that the evaluation method was applicable. Furthermore, it was evident from the evaluation that the indication lowering of the JOYO IRMS above 45.82 kW was negligibly small, and did not affect the reactor power ascension testing. Also, it was proved in a following thermal calibration test above 50 kW that the indication lowering was allowably small indeed in this power region.     

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.     

脉冲中子源法测量铅基零功率反应堆Venus-Ⅱ次临界度

本文利用脉冲中子源法测量了铅基零功率反应堆Venus-Ⅱ在4种燃料棒装载情况下的次临界度,简要介绍了脉冲中子源法测量次临界度的原理、测量系统及实验结果等,通过面积比法分析了各探测器的计数率时间谱,确定了系统次临界度。测量结果表明,当系统有效增殖因数在0.94附近时,不同位置处的探测器测量结果之间呈明显差异。基于MCNP理论模拟计算,分别用空间修正因子和普适的微扰法对面积比测量结果进行必要修正,消除了空间效应对实验结果的影响。在系统有效增殖因数约0.94时,经修正的面积比法能精确给出系统的次临界度。本实验研究为ADS嬗变系统的次临界度精确测量提供了一种有效方法。     

Subcriticality Measurement by Neutron Source Multiplication Method with a Fundamental Mode Extraction

A new neutron multiplication method has been proposed for an accurate measurement of subcriticality. The proposed method consists of two correction processes for (1) extraction of the fundamental mode from measuring data of a neutron detector that contains higher modes as well as the fundamental mode feeding from an external neutron source and (2) spatial corrections for perturbations induced by a reactivity addition in the distributions of the fundamental mode and a neutron importance field. Feasibility of the proposed method has been verified from a numerical study, although under some limitations such that the neutron multiplying system to be analyzed is small-sized and a reactivity change takes place homogeneously in a fuel loaded region. With extraction of the fundamental mode and the spatial corrections, the subcriticality can be estimated accurately even with measuring data highly contaminated with higher modes due to a detector position near to an external point neutron source. For a future application to measurement of control rod bank worth of a nuclear power plant from measuring data during a reactor physical testing, some useful guidelines have been obtained.     

严重事故下反应堆压力容器下封头耦合烧蚀传热分析

核电站严重事故发生后,反应堆压力容器（RPV）固壁在熔池作用下会发生烧蚀、减薄。开展RPV下封头耦合烧蚀传热分析对堆坑注水有效性论证和RPV剩余壁厚确认有重要的理论指导意义。本文以CPR1000反应堆压力容器为研究对象,在FLUENT 17.2平台下,基于动态网格方法和UDF二次开发,构建了综合考虑RPV固壁瞬态烧蚀与导热、RPV内壁热流密度再分布及RPV外壁过冷沸腾的全耦合计算模型,获取了9 000 s内的堆坑两相流场分布和RPV固壁烧蚀温度场,分析确定了最小剩余壁厚和发生位置。结果表明：使用动态网格捕捉壁面烧蚀的方法可行,本文全耦合计算模型在分析RPV固壁瞬态烧蚀过程方面有一定优势。     

Coupled Ablation and Heat Transfer Analysis of Lower Head for Reactor Pressure Vessel under Severe Accident Condition

After a reactor core melts accident, the solid wall of the reactor pressure vessel (RPV) will be inevitably eroded by the melting core which contains large density of heat flux. The analysis of the coupled ablation and heat transfer of the lower head for RPV is of great theoretical significance to the effectiveness demonstration of water injection in reactor pit and the confirmation of the residual wall thickness of RPV. In this work, numerical simulations were carried out based on the RPV model of CPR1000 using the CFD software FLUENT 17.2. Based on dynamic mesh model and user-defined function (UDF) redevelopment, a fully coupling calculation model considering the transient ablation and heat conduction of solid wall of RPV, the redistribution of heat flux density in RPV inner wall and the subcooled boiling of RPV outer wall was established. Both two-phase flow pattern in the reactor pit and temperature field of RPV solid wall ablation within 9 000 s were obtained and the minimum residual wall thickness and the occurrence location were determined by analysis. The results show that it is feasible to use dynamic mesh to capture wall ablation. The fully coupling calculation model has certain advantages in analyzing the transient ablation process of RPV under severe accident.     

Space-Dependent Effect Observed in Subcriticality Measurements for Loosely Coupled-Core System

The results of the subcriticality measurements by various techniques performed for the UTR-KINKI reactor, a light-water-moderated and graphite-reflected coupled-core reactor, are presented. The result of the source-multiplication measurement indicates that the apparent dependence of the subcriticality on the detector position is significantly observed even under a condition 2$ subcritical, and that the location of neutron source remarkably influences the sub- criticality obtained. On the other hand, the spatial dependence in the source-jerk measurement is slight relative to that in the source-multiplication and the rod drop measurements. Furthermore, the result of the Feynman-α measurement suggests that much more samples should be acquired for the reduction of the experimental uncertainty to the same level as that in the above measurements.     

Estimation of sensitivity coefficients of core characteristics based on reduced-order modeling using sensitivity matrix of assembly characteristics

We propose an estimation method of sensitivity coefficients of core neutronics parameters based on a multi-level reduced-order modeling approach. The idea is to use lower-level models to identify the dominant input parameter variations, constrained to the so-called active subspace, which are employed to determine the sensitivity coefficients of the core neutronic parameters. In our implementation, the lower-level model is represented by two-dimensional assembly calculations, which are employed in the preparation of the few-group cross-sections for core-wide calculations. The active subspace basis is estimated using the singular value decomposition of sensitivity matrices of assembly neutronics parameters. In numerical verification calculation, sensitivity coefficients of core characteristics for a typical three-loop PWR equilibrium-cycle are estimated using the proposed method and the direct method. Comparison of these two results shows that the proposed method well reproduces the results obtained by the direct method with lower calculation costs. Through the verification calculations, applicability of the proposed method to practical light water reactor analysis is confirmed.     

On-line subcriticality measurement using a pulsed spallation neutron source

To investigate the applicability of the pulsed neutron source method using a pulsed spallation neutron source for an on-line subcriticality monitoring system of an accelerator-driven system, a subcritical experiment is conducted using the Kyoto University Critical Assembly in combination with the fixed-field alternating gradient accelerator. Reactivity values obtained from different traditional techniques, the area-ratio method and the α-fitting method, are discussed with respect to the applicability to on-line subcriticality monitoring. The results show that the area-ratio method robustly and accurately monitors subcriticality in shallow subcritical states with negative reactivity of up to a few dollars; however, this method faces problems with temporal fluctuations, spatial dispersion, and sensitivity to the proton-beam current with increasing depth of subcriticality. On the other hand, it is shown that the α-fitting method alleviates such problems in deep subcritical states. Moreover, a proposed fitting technique using the maximum-likelihood estimation method based on the Poisson distribution is robust enough to be applicable to on-line subcriticality monitoring for negative reactivity levels of up to roughly nine dollars.     

池式夹带高速区试验研究

发生失水事故后的压水堆内会产生池式夹带现象,这一现象将造成反应堆进一步失水,进而发生堆芯裸露或堆芯熔化等严重事故。Kataoka和Ishii于1983年开发的池式夹带模型在反应堆安全分析中被广泛使用,但十分保守。其中一个重要原因是模型中高速夹带区的试验数据极为有限且不确定性较大,导致该区的模型并不完善。本文介绍空气-水的池式夹带高速区试验,试验本体参考AP1000原型参数,本体内径为380 mm,高为2.2 m,由透明材料制作,供气流速为0.98~5.41 m/s。试验过程中的两相混合液位和夹带液体质量的测量分别使用导波雷达液位计和称重模块。本试验为夹带模型的高速区补充了数据,发展了现有的池式夹带高速区模型,并发现了在夹带高速区出现的夹带饱和现象。