Measurement of Thermal Neutron Cross Section of 137Cs(n, γ)138Cs Reaction

A calculational model for a modified diffusion coefficient has been developed to incorporate the neutron streaming effect in heterogeneous low-density channels accurately into diffusion theory calculations. The model uses a supercell, and the axial and radial diffusion coefficients of the heterogeneous inner cell are so defined that they can reproduce Benoist's axial and radial diffusion coefficients of the supercell when the diffusion coefficient of the outer cell is given as 1/3 Σ_tr . In the case of the axial diffusion coefficient, the axial buckling effect is taken into account by modifying the neutron path length within the streaming channel in calculating the collision probabilities. This model has been applied to an RZ fast reactor Core model with a gas expansion module (GEM). By using the axial diffusion coefficient obtained with the presented model, calculational error of GEM worth was reduced to less than 1/7 compared to the formula of Rowlands and Eaton.     

Decoding of Thermal Data in Fleischmann & Pons Paper

A uranium-free fast reactor was simulated at FCA in order to examine the prediction accuracy for sodium void effect of plutonium burning fast reactors. Material sample worth for plutonium and B4C was also measured to compare its prediction accuracy with that for the sodium void reactivity worth. It was found that an axial distribution of plutonium sample worth and the central B₄C sample worth for various kinds of ¹⁰B enrichment were precisely calculated by the conventional calculation method for fast reactors with 70-group structure. The sodium void reactivity worth was, however, poorly predicted especially for the non-leakage term. This discrepancy seems to be caused by the peculiar energy breakdown of the non-leakage term in the uranium-free fast reactor.     

Analysis of Sodium Void Reactivity Measured in FCA V-1 Assembly

The analysis of sodium void reactivity measurements has been performed. The measurements were made in the FCA V-1, which is a fast critical assembly intended for physics mock-up of the experimental fast reactor “JOYO”. The voided zones were the central region of the core and channel drawers extending throughout the core height. The calculations were performed using the JAERI set with 70- group structure.

As a result it was found that the conventional two-dimensional calculations underestimate measurements by about 10–40% in the core region. However, if the axial streaming effects are considered, the ratio between calculations and experimental results become about 0.9 for almost all cases of channel void. The streaming effects are calculated with use of Benoist's formula of anisotropic diffusion coefficients.

The heterogeneity effects on the spatial neutron flux distribution are taken into consideration by the collision probability method. The effect is large in the central part of the core (about 20% negative reactivity). The elastic removal cross sections are precisely obtained for the predominant resonances of light elements and compared with the conventional set. The influence on sodium void reactivity is not so large in this assembly.     

Sodium Void Reactivity Worth Calculations for Fast Critical Assemblies without Whole-Lattice Homogenization

In the present paper, we calculate the sodium void reactivity worth of fast critical assemblies without whole-lattice homogenization in order to reduce errors associated with lattice homogenization. Firstly, we solve a neutron transport benchmark problem simulating fast critical assemblies composed of thin material plates with a discrete ordinates transport solver. The discrete ordinates transport solutions agree well with the Monte Carlo reference solutions; hence, we confirm the validity of the deterministic transport calculations for the sodium void reactivity worth of lattice-heterogeneous critical assemblies. Thereafter, the existing experimental data are calculated without whole-lattice homogenization. The result suggests that the lattice homogenization results in the overestimation of the leakage component of sodium void reactivity worth when the leakage component parallel to plate boundaries is dominant. Utilizing the numerical method without whole-lattice homogenization and the nuclear data JENDL-3.3, numerical solutions agree with the experimental data within 3σ of the experimental uncertainties.     

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.     

大型MOX燃料快堆钠空泡反应性微扰理论研究

钠空泡反应性效应是钠冷快堆核设计和安全分析的重要内容。本文基于多群节块扩散法,采用微扰理论推导出钠空泡反应性的计算方法,对1 000 MWe钠冷快堆MOX燃料堆芯的总钠空泡反应性、空间分布、物理分项进行了计算。结果表明,钠空泡反应性主要来源于中子泄漏的增加和能谱的硬化,两者一正一负,且空间分布规律相反,导致钠空泡反应性具有强烈的空间依赖性;对于所计算的MOX燃料堆芯钠空泡反应性高达3 $左右。计算和分析结果阐明了钠空泡反应性的产生机理和分布规律,可为低钠空泡的设计提供参考。     

On the diffusion coefficient calculation in two-step light water reactor core analysis

This paper presents consistent and rigorous accuracy assessments of various methods for calculating the diffusion coefficients in a two-step reactor core analysis of light water reactors (LWRs). The diffusion coefficients are significantly affected by the transport correction and critical spectrum calculations. There are various methods for the transport corrections (inflow/outflow/hybrid corrections) and critical spectrum calculations (B₁/P₁/CASMO-4E methods) so that it is necessary to decide the best combination to achieve a high accuracy in the transport/diffusion two-step analysis. Numerical tests are performed step-by-step to search for the best combination of the methods by comparing each other the transport one-step results, transport/diffusion two-step results, and Monte Carlo results. Numerical test results with a large and a small LWR core show that the combination of inflow transport correction and CASMO-4E critical spectrum calculation is most accurate than the other combinations in terms of eigenvalues and assembly power distributions.     

Effective Homogenization Method for Control Rod Channels

A cell calculation method has been developed for accurately treating neutron transport and heterogeneity effects of control rods (CRs) within the bounds of homogeneous neutron diffusion theory. In this method, CR cell-averaged homogeneous neutron cross sections are calculated by a heterogeneous neutron transport calculation with an annular supercell model, in which a CR assembly is surrounded by a homogeneous fuel region. Then, a neutron diffusion calculation is carried out using the homogeneous neutron cross sections in the same supercell, and the CR cell-averaged radial neutron diffusion coefficients are modified in an iterative manner such that the CR cell-interface neutron current which is obtained by the heterogeneous transport calculation can be reproduced by the homogeneous diffusion calculation. In the case of a 1,000-MWeclass FBR, the center CR worth, which was calculated by an RZ diffusion calculation using the cross sections obtained by the above method, agreed within 1% with that obtained by a heterogeneous transport calculation, proving the validity of the method.     

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%.     

Diffusion coefficients and collision probabilities for annular regions of low optical thickness II: the general case

Collision probability theory has been used to calculate neutronics parameters in nuclear reactors for many years, although it has long been suspected that this technique breaks down in the presence of material voids. In this work, the circumstances under which the breakdown of the probability theory occurs is first carefully determined, to be followed by an excruciatingly detailed explanation showing how to cure the problem mathematically, and how to verify that the remedy is operating properly. Once cured, it becomes possible to more accurately calculate parameters, such as directed diffusion coefficients, that are important to reactor analysis, particularly in the estimation of reactivity coefficients. Such calculations are performed here as a demonstration of the significance of the old and new mathematical methods to problems of practical interest. The most significant parameter investigated is a comparison of void reactivity in the presence of leakage by an experimental version of the lattice cell code WIMS-AECL using the old and new methods. ©     

Cold-state physical characteristics of ÉGP-6 reactors after upgrading

Measurements and calculations important to safety are reported for éGP-6 reactors in the cold state. These data give the sufficient number of manual control rods to be fitted with upgraded RS-AZ drives, and it is shown that the reactor subcriticality can be determined. Measurements have been made on the temperature coefficients of reactivity, the reactivity change when the coolant is lost from the new cooling channels for the control rods, and the reactivity increment caused by using these new channels. Bilibinsk Nuclear Power Station. Translated from Atomnaya énergiya, Vol. 86, No. 2, pp. 94–99, February, 1999.     

Diffusion coefficients for LMFBR cells calculated with MOC and Monte Carlo methods

The present work discusses the calculation of the diffusion coefficient of a lattice of hexagonal cells, with both “sodium present” and “sodium absent” conditions. Calculations are performed in the framework of lattice theory (also known as fundamental mode approximation). Unlike the classical approaches, our heterogeneous leakage model allows the calculation of diffusion coefficients under all conditions, even if planar voids are present in the lattice. Equations resulting from this model are solved using the method of characteristics (MOC). Independent confirmation of the MOC result comes from Monte Carlo calculations, in which the diffusion coefficient is obtained without any of the assumptions of lattice theory. It is shown by comparison to the Monte Carlo results that the MOC solution yields correct values of the diffusion coefficient under all conditions, even in cases where the classic calculation of the diffusion coefficient fails. This work is a first step in the development of a robust method to calculate the diffusion coefficient of lattice cells. Adoption into production codes will require more development and validation of the method.     

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.     

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).     

Experimental verification of the theory of neutron diffusion in a medium with voids

Experiments are described which have been carried out to verify the theory of diffusion of thermal neutrons in a graphite medium. Measurements of the neutron fluxes in continuous graphite media and in a graphite medium with channels verify the theoretical formulas which relate in a medium with empty channels, the effective diffusion coefficients (and the diffusion lengths) of the thermal neutrons with the lattice parameters of the channels, and the corresponding diffusion coefficient (and diffusion length) in a continuous medium.In conclusion, the author wishes to take the opportunity to express his gratitude to V. S. Fursov for his continued interest in this work.     

Analysis of core physics experiments on irradiated BWR MOX fuel in the REBUS program

Critical experiments were performed in the REBUS program on a core loaded with a test bundle including 16 irradiated BWR-type MOX rods of average burnup of 61 GWd/t. The experimental data were analyzed using diffusion, transport, and continuous-energy Monte Carlo calculation codes coupled with nuclear data libraries based on JENDL-3.2 or JENDL-3.3. Biases in effective multiplication factors of the critical cores were ?1.0%Δk for the diffusion calculations (JENDL-3.2), ?0.3%Δk for the transport calculations (JENDL-3.3), and 0.2%Δk for the Monte Carlo calculations (JENDL-3.2). The measured core fission rate and co-activation rate distributions were generally well reproduced using the three types of calculations. The burnup reactivity determined using the measured water level reactivity coefficients was ?2.41 ± 0.08%Δk/kk’, which also agreed with the results of the three type of calculations within the measurement and calculation errors. The most probable isotopic inventories in the irradiated MOX rods was tentatively obtained by using the ratios of the calculation to chemical assay data on a pellet sample, and the burnup reactivity was reanalyzed to split the calculation error into those due to the inventory and reactivity calculations. This approach showed that the inventory calculation error compensated the reactivity calculation error.     

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.     

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.     

Temperature Effects on Reactivity in Light Water Moderated U02 Cores with Soluble Poisons

Experimental and computational studies have been performed on the temperature coefficients of reactivity in light-water moderated and reflected UO₂ cores with soluble poisons such as boron and gadolinium. Experiments were carried out using the Tank-type Critical Assembly (TCA) in Japan Atomic Energy Research Institute (JAERI). Temperature coefficients of the cores with soluble poisons were measured by changing the temperature of the moderator and reflector from the room temperature to about 60°C. The dependence of temperature coefficients on the core configuration and the concentration of soluble poison was studied with the water level worth method. Temperature coefficients were calculated with a diffusion code CITATION included in the SRAC code system and a perturbation code CIPER for comparison with the experimental data. It was found that the temperature coefficients are always negative in the experimental cores (the water to fuel volume ratio (Vm/V_f) of 1.83) containing boron as soluble poison. On the other hand, the temperature coefficients become positive in the cores with gadolinium due to the deviation of the gadolinium absorption cross section from the 1/v law and the neutron spectral shift with the increase in temperature.     

杂质硼在高温气冷堆中的燃耗特性

在球床式高温气冷堆的堆芯和石墨反射层中,不可避免地含有少量杂质硼。硼杂质的存在及其燃耗会对反应堆的反应性产生影响。对于多次通过的球床堆芯,根据燃料元件的运行历史计算所有元件的硼燃耗,对于中子注量率差别较大的反射层,分区计算了硼燃耗。再采用微扰理论,计算燃耗过程中硼反应性价值的变化。计算结果表明,硼杂质燃耗很快,因此,硼杂质对反应性的影响降低很快。