Axially Heterogeneous FBR Core Concept and Its Nuclear Characteristics

This work consists of conceptual design and experimental studies on an axially heterogeneous core (AHC) for large LMFBRs. Trade-off studies were performed to optimize the AHC, from which it was found out that the AHC has the following advantages compared to the conventional homogeneous core (HOC); lower peak linear power, lower peak fast fluence in fuel cladding materials, lower burnup reactivity, lower potential of energetic consequences in hypothetical core disruptive accidents and so on. Aiming at further improvement of the core performance, the AHC core configuration was studied taking control rod operating into account.

Critical experiments of the AHC were performed using the FCA facility at JAERI. The experiments demonstrated satisfactory fundamental nuclear characteristics, such as a flat power distribution. The calculational accuracies for the AHC were found to be nearly the same as those for the HOC.

Through our studies, the AHC with improved safety and economic characteristics was proposed prior to designs in other countries, and the characteristics were demonstrated by experiments. These have provided a technical basis for development of future large LMFBR cores.     

Interpretation of Spatial Kinetics for Rod Drop Experiment in Loosely Coupled-Core Systems

Abstract

The coupled two-core reactor systems with various degrees of spatial coupling were constructed in the Kyoto University Critical Assembly (KUCA) to study the spatial kinetics observed in the control rod drop experiment. By applying the two-mode and the two-point kinetic models to the space-dependent rod worths measured on the basis of the one-point model, the first-harmonic λ-mode eigenvalue separation and the reactivity coupling coefficient were inferred. The present values of these parameters agreed with the results obtained by the reactor noise measurements and the diffusion calculations.

The experimental results show that the magnitudes of the spatial kinetic phenomena including the dependence of the rod reactivity worth on the detector position, the reactivity interaction effect between control rods and the transient flux tilts induced by the rod drop, which have been significantly observed in large thermal and fast power reactors, are inversely proportional to the eigenvalue separation. Applying the two-mode model, the inherent reactivity worths of control rods were also inferred from the space-dependent ones.     

Comparison of Cell Models for Analysis of Heterogeneous Fast Critical Assembly

We have investigated cell calculation models to be used in the analysis of neutronic characteristics of a heterogeneous fast critical assembly. As cell models we have considered a single drawer model with a critical buckling, a single drawer model with group dependent bucklings and a multidrawer model which consists of some fuel and blanket drawers. We have compared the cell averaged cross sections obtained from these cell models with the results of a reference transport calculation and estimated the effects of the cell models on k _eff, reaction rate ratios, reaction rate distributions and sodium void worths in the heterogeneous fast critical assembly ZPPR-13A. The multidrawer model and the single drawer model with group dependent buckling give reasonable cell averaged cross sections and have large effects on k _eff and ²³⁸U fission rate distribution.     

A Proposal of Benchmark Calculation on Reactor Physics for Metallic Fueled and MOX Fueled LMFBR Based upon Mock-up Experiment at FCA

In order to assess the validity of the cross section library for fast reactor physics, a set of benchmark calculation is proposed. The benchmark calculation is based upon mock-up experiments at three FCA cores with various compositions of central test regions, two of which were mock-ups of metallic fueled LMFBR's, and the other was a mock-up of a mixed oxide fueled LMFBR. One of the metallic cores included enriched uranium in the test region, while the others did not.

Physics parameters to be calculated are criticality, reaction rate ratios, plutonium and B₄C sample worth, sodium void reactivity worth, and Doppler reactivity worth of ²³⁸U. Homogenized atomic number densities and various correction factors are given so that anyone can easily perform diffusion calculation in two-dimensional RZ-model and compare the results with the experiments. The validity of the correction factors are proved by changing the calculation method and used nuclear data file.     

Improvement of Correlated Sampling Monte Carlo Methods for Reactivity Calculations

Two correlated Monte Carlo methods, the similar flight path and the identical flight path methods, have been improved to evaluate up to the second order change of the reactivity perturbation. Secondary fission neutrons produced by neutrons having passed through perturbed regions in both unperturbed and perturbed systems are followed in a way to have a strong correlation between secondary neutrons in both the systems. These techniques are incorporated into the general purpose Monte Carlo code MORSE, so as to be able to estimate also the statistical error of the calculated reactivity change.

The control rod worths measured in the FCA V-3 assembly are analyzed with the present techniques, which are shown to predict the measured values within the standard deviations. The identical flight path method has revealed itself more useful than the similar flight path method for the analysis of the control rod worth.     

快堆控制棒组件非均匀效应修正方法研究

控制棒组件是快堆控制系统和安全保护系统的重要组成部分,快堆控制棒价值的准确求解至关重要。基于PASC?5程序的快堆少群均匀化群常数计算中使用直接体积均匀化方式,这会导致控制棒价值严重高估,必须对控制棒组件的非均匀效应进行修正。基于群常数修正的思路,本论研究了体积?通量权重、反应率之比守恒和反应性守恒3种方法在快堆控制棒组件非均匀效应修正中的应用;基于二维特征线程序开发了群常数修正因子计算程序FRHP。通过中国实验快堆算例进行测试验证,修正后的控制棒价值计算结果与MCNP计算的参考结果符合较好,表明3种方法均能对控制棒组件的非均匀效应实现有效修正,其中反应性守恒方法修正效果最好。     

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.     

Experimental Study on Reactivity Worth for Absorber Material in High Conversion Light Water Reactor Using FCA-HCLWR Core Fueled with Enriched Uranium

Experimental study on reactivity worth for absorber material in HCLWR core has been carried out in a series of experiments using the Fast Critical Assembly (FCA) in Japan Atomic Energy Research Institute (JAERI). The central reactivity worth as well as the simulated control rod worth of B₄C with different ¹⁰B content and of Hf was measured in FCA-HCLWR core fueled with enriched uranium. Both reactivity worths of B₄C increase with ¹⁰B content. These increasing trends do not saturate to 90% enriched B₄C. The Hf has the smaller reactivity worth than the 20% B₄C. The experimental values are compared with the calculated ones which obtained from JENDL-2 data and the SRAC system. The calculation predicts well the dependence of reactivity worth on ¹⁰B content and underestimates the reactivity worth ratios of the Hf to the 20% B₄C.     

Effect of Group Collapsing in Perturbation Theory for Sample Worth Analysis

The effect of group collapsing applied to the perturbation theory for sample worth analysis in fast reactor systems is theoretically and numerically examined assuming the validity of the thin sample approximation.

As a result, the calculated worths of scattering predominant materials placed at the center of core are found to be strongly influenced by the group collapsing. The effect on the sample worth when the sample is placed in positions off the core center decreases with increasing distance from the center. It is noted that the reactivity perturbation due to inelastic scattering is also affected significantly by group collapsing especially near the core-blanket interface.

Based on the above observations, it is concluded that the perturbation theory with about 70 energy groups appropriately arranged is necessary to reproduce the experimental values of Na, O and Fe sample reactivity worths with accuracy efficient for ordinary purposes.     

Prediction Uncertainty Analysis of Neutronic Properties of Fast Breeder Reactor by Use of Sensitivity-Based Methodology

The prediction accuracies of key neutronic characteristics including burnup properties evaluated with use of the sensitivity-based methodology have been reviewed for a fast breeder reactor. The bias factor method, the cross section adjustment method and the combined method are used to evaluate the prediction accuracies. The calculation method of sensitivity coefficients used in the uncertainty analysis is discussed. The three methods are compared from the theoretical and numerical points. For the numerical comparison, they are applied to a 1,000 MWe fast breeder reactor. The prediction uncertainties are within the range of 0.7~1.0% for k_eff , 3~5% for control rod worth, 1~2% for ²³⁹Pu fission rate distribution, 12% for burnup reactivity loss and 1.5% for breeding ratio. These values are much smaller than those predicted without any integral data.     

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.     

An Effective Method for Estimating Multiple Control Rod Worths in Large Fast Reactors

A method for estimating the multiple control rod worth in large fast reactors has been developed using the higher order perturbation technique. With this method, physical significance of the interaction effect between multiple control rods can be understood by decomposing it into independent components with different physical processes. Furthermore, a new technique is proposed, whereby the interaction effect between multiple control rods can be estimated from a combination of the interaction effects between two or three control rods depending on the strength of the effect. The validity of the method is examined with the experimental data of PHENIX and numerically for MONJU. The results show that the interaction effect between multiple control rods in prototype fast reactors can be estimated from a combination of the effects between 2 control rods with a good accuracy. The numerical examinations for a 1,000 MWe fast reactor showed that the interaction effect is too large to apply the present method for large fast reactors. To overcome this difficulty, a new concept of “quasi-control-rod” is introduced in the method. With this improved method, the worths of 19 and 18 control rods in the 1,000 MWe fast reactor are estimated with accuracies of ±2%.     

Control-Rod Interference Effects Observed during Reactor Physics Experiments with Nuclear Ship “MUTSU”

Abstract

The control rods in the reactor of the nuclear ship MUTSU are classified into four groups: groups G1 and G2 are located in the central part of the core, while groups G3 and G4 are in the peripheral zone of the core. Several types of mutual interference effects among these control-rod groups were observed during reactor physics experiments with this reactor. During normal hot operations, positive shadowing was dominant between the G1 and G2 groups; the degree of the shadowing effect of one rod group depended on the position of the other rod group. Both positive and negative shadowing effects occurred between an inner rod group (G1 or G2) and an outer group (G3 or G4) depending on the three-dimensional arrangement of the control rods. The rod worths of G1 and G2 increased as a result of slight core burnup, about 1,400 MWd/t, mainly due to the decrease in shadowing effects resulting from a change in control-rod pattern. A three-dimensional diffusion calculation with internal control-rod boundary conditions has proved to be useful for analyzing these various interaction effects.     

Experiments and Analyses on Fuel Expansion and Bowing Reactivity Worth in Mock-up Cores of Metallic Fueled Fast Reactors at FCA

Axial fuel expansion and radial fuel bowing were simulated in mock-up cores of metallic fueled fast reactors at the Fast Critical Assembly (FCA). Reactivity worth caused by the simulation was measured and compared with calculations. Based on these experiments and calculations, the applicability of current calculation methods was discussed for both the first order perturbation theory (FOP) and the exact perturbation theory (EP).

For the axial fuel expansion reactivity worth, both FOP and EP showed 10 to 20% smaller values than the experiment. This underestimation was consistent to a C/E trend of axial distributions of plutonium sample worth. No significant difference was observed between FOP and EP, when transport correction was applied.

For the radial fuel bowing reactivity worth, the FOP showed about 10% larger values than the EP. Near the core central plane, the EP with transport correction showed good agreement with the experiment, while FOP showed overestimation by 14%. At the core axial edge, however, both FOP and EP underestimated the reactivity worth by more than 10%.     

启明星2号轻水堆燃料棒价值实验和模拟研究

本文对启明星2号零功率装置中轻水堆的单根棒价值进行了实验和模拟研究。利用MCNP6程序和5种截面库计算出5组动态参数,将实验所测的倍周期代入倒时方程得到了5种动态参数对应的单根棒价值。采用斜率法计算出5种数据库对应的单根棒价值,并与实验结果进行了比较。结果表明：5组动态参数给出的周期法实验结果存在明显差异,不同数据库下斜率法给出的模拟结果基本一致;采用JENDL-4.0库时,实验值与模拟值吻合最好,相对偏差小于1%。本文推荐选用JENDL-4.0库计算的动态参数处理实验数据,周期法所得的单根棒价值为(0.237 6±0.015 6) mk。获得精确的单根棒价值,将有助于提高后续ADS相关实验的准确性和可靠性。     

Modification to Fissile Element Cross Sections and Their Influence on the Calculated Parameters of Fast Critical Assemblies

Fast cross section sets are prepared for the analysis of fast critical assemblies to test the agreement of calculated and measured integral parameters. Modifications are brought to fissile element cross sections making use of recently measured cross section data, and these updated cross section data are utilized to compare the calculated integral parameters of these assemblies, and to determine the effect brought to the calculated results by the differences between the data. The results are presented for the eigenvalue, central fission ratios and centra] sample reactivity in the ²³⁹Pu fueled assemblies ZPR- 3-48, 49, 50 and ZEBRA-6A, whose spectra simulate those of large fast reactors. In addition, for ZPR- 6-7 and ZPPR-2, which are large fast critical assemblies intended for testing the calcul ational procedures of practical demonstration reactor design, the results of analysis obtained with the updated cross section set are compared with experiments. It is found that the cross section for ²⁴¹Pu recommended here satisfactorily agrees with the experimental reactivity worth.     

热中子研究堆薄板型控制棒价值计算

对通过采用能量相关的内边界条件，在扩散理论的范围内计算薄板型热中子研究堆控制棒价值进行了理论分析，成功地计算了日本原子能研究所JRR-3M的控制棒价值，并与日本的计算结果进行了对比。     

Three-Dimensional Transport Correction in Fast Reactor Core Analysis

Three-dimensional (3-D) transport corrections for K_eff, control rod worths, neutron spectra and power distributions are calculated for the fast critical assemblies ZPPR-9, -10 and -13. The calculations are performed in 7 energy groups using the 3-D and 2-D transport codes TRITAC and TWOTRAN-II. The evaluated 3-D transport corrections are compared with those predicted by a 2-D RZ model and a combined XY, RZ and R model to assess the accuracy of these 2-D models. The RZ model yielded some errors in estimating the transport corrections to K_eff, control rod worths, neutron spectrum and power distribution, while the combined model predicted them with good accuracy.     

核燃料裂变产物对临界影响研究

本文针对钐、钕、钆和银等4种裂变产物在中试厂核临界安全实验装置上开展了临界实验研究。堆芯的易裂变材料为固液两相存在,固体燃料为二氧化铀,液体燃料为硝酸铀酰。固体燃料棒采用六角形方式排布,浸泡在硝酸铀酰溶液中。将临界实验测量结果与蒙特卡罗程序MONK的理论计算结果进行比较。结果表明：理论计算结果与临界实验测量结果符合较好;裂变产物样品引入的负反应性价值非常可观,能谱变化显示裂变产物样品对中子的吸收在热能点以下能区起决定性作用。     

Analysis of Reactivity Coefficients of Chernobyl Reactor by Cell Calculation

A series of cell calculations for the Chernobyl reactor was performed using the SRAC code system to provide its fundamental neutronic characteristics for the accident analysis at JAERI. The calculations are based on a two-step cell modelling. The primary cell is supposed on a unit square graphite block of 25cm × 25cm which contains a fuel assembly or a control channel. The secondary cell IS supposed on a unit of 16 channels where 14 fuel and 2 control channels are located so as to simulate the whole core.

Detailed Investigation on fractional change of reaction rates for each nuclide along with increase of void fraction was carried out. The analysis clarified the mechanism to induce the positive void coefficient, together with its burn-up dependence and the increase due to withdrawal of control rod.

A comparison of the effect of void fraction on the reaction rates in the primary cell between a Monte Carlo code VIM and SRAC shows consistent results within the statistical error.

The calculated results for the composition of discharged fuel, void and other reactivity coefficients, kinetic parameters and their burn-up dependence show satisfactorily good agreement with those reported by the Soviet Union and some institutions.