Comparison of measured and calculated reaction rate distributions in an scwr-like test lattice

High resolution gamma-ray spectroscopy measurements were performed on 61 rods of an SCWR-like fuel lattice, after irradiation in the central test zone of the PROTEUS zero-power research reactor at the Paul Scherrer Institute in Switzerland. The derived reaction rates are the capture rate in ²³⁸U (C₈) and the total fission rate (F_tot), and also the reaction rate ratio C₈/F_tot. Each of these has been mapped rod-wise on the lattice and compared to calculated results from whole-reactor Monte Carlo simulations with MCNPX. Ratios of calculated to experimental values (C/E’s) have been assessed for the C₈, F_tot and C₈/F_tot distributions across the lattice. These C/E’s show excellent agreement between the calculations and the measurements. For the ²³⁸U capture rate distribution, the 1σ level in the comparisons corresponds to an uncertainty of ±0.8%, while for the total fission rate the corresponding value is ±0.4%. The uncertainty for C₈/F_tot, assessed as a reaction rate ratio characterizing each individual rod position in the test lattice, is significantly higher at ±2.2%. To determine the reproducibility of these results, the measurements were performed twice, once in 2006 and again in 2009. The agreement between these two measurement sets is within the respective statistical uncertainties.     

Comparisons of Deterministic Neutronic Calculations with Monte Carlo Results for an Advanced BWR Fuel Assembly with Hafnium Control Blades

From the neutronic viewpoint, the optimization of BWR core designs is strongly related to the accurate determination of flux variations inside and around fuel assemblies. These fluctuations, which are mainly due to the high heterogeneity of the fuel and moderator regions, as additionally to the presence of cruciform absorber blades, have a direct impact on reactor safety and performance. Of particular importance is the pin power distribution, leading to the need of assessing the capabilities of design tools in a sufficiently rigorous manner. The basic configuration chosen for the code comparisons corresponds to a SVEA-96 fuel assembly under full-density water moderation conditions, with inserted hafnium absorber blades. The calculational schemes employed are the Monte Carlo code MCNPX2.5, in conjunction with various nuclear data libraries (ENDF/B-VI, JEF2.2, JEFF3.0, JENDL-3.2 and JENDL3.3), and the deterministic codes CASMO4 with JEF2.2, BOXER with JEF1.0 and HELIOS 1.6 with ENDF/B-VI based libraries, respectively. The significant discrepancies observed in k _∞ predictions (>500pcm) are found to be mainly nuclear data related. On the other hand, data library effects have been found to be quite small for the prediction of pin-wise distributions of total fissions (F_tot), ²³⁸U captures (C8), as also of the C₈=F_tot ratio. Significant differences in these reaction rate distributions (up to several percent) have, however, been observed between the Monte Carlo and deterministic calculations, particularly in the vicinity of the hafnium blades and in the gadolinium pins.     

Experimental Validation of Reaction Rate Distributions for a SVEA-96+ BWR Assembly with Hafnium Control Blades

The accurate estimation of reactor physics parameters related to the presence of cruciform absorber blades in boiling water reactors (BWRs) is important for safety assessment and for achieving flexible operation during the cycle. Characteristics that are affected significantly include distributions of the total fission (F_tot) and ²³⁸Ucapture (C₈) rates for controlled regions. Representative experimental investigations have been performed in the framework of the LWR-PROTEUS programme. In particular, the LWRPROTEUS I-2A experiments concerned the neutronics characterisation of a SVEA-96+ BWR assembly controlled with a hafnium (Hf) blade under full-density water moderation conditions. The current paper presents the comparisons of the measured F_tot and C₈ pin-wise distributions with a variety of stochastic and deterministic calculations: (a) MCNPX2.5 using recent nuclear data libraries (JEFF-3.1, ENDF/BVI. 8, and JENDL-3.3), (b) PHOENIX4 using ENDF/B-VI.3, (c) BOXER using JEF-1, (d) CASMO₄ using JEF-2.2, and (e) HELIOS1.6 using ENDF/B-VI.1. The calculation/experiment comparisons show standard deviations from 1.2% (MCNPX2.5) up to 1.9% (BOXER) for the prediction of the F_tot distribution, the highest individual discrepancy (7.6% with BOXER) being seen close to the “Hf-vertex.” The C₈ comparisons show systematically better agreement than those of F_tot, the lowest standard deviations being 1.0% (BOXER) and the highest only 1.4% (HELIOS). In addition, sensitivity studies highlight the greater importance of modelling aspects, compared with that of nuclear data libraries, for the achievement of satisfactory and validated F_tot and C₈ predictions.     

On the accuracy of reactor physics calculations for square HPLWR fuel assemblies

Although the supercritical-pressure or high-performance light water reactor (HPLWR) concept is largely based on the well-established technological experience available with conventional light water reactors, there is still no consensus on various key design features such as an optimal layout for the fuel assembly. This results mainly from the very large density variations of supercritical-pressure water in the core, which render it difficult to ensure reliable values for parameters such as power peaking factors and reactivity worths. The present paper describes studies carried out to compare deterministic and Monte Carlo codes for analysing a representative square HPLWR lattice with uniform 5%-enriched UO₂ fuel. The main purpose has been to assess the prediction accuracies achievable for integral parameters such as the multiplication factor, control absorber effectiveness, moderator/coolant density reactivity feedback and pin power distributions. The results show good agreement between the deterministic and stochastic calculations for the unperturbed lattice. However, for certain perturbed situations involving, for example, local coolant density changes in the assembly or control absorber insertion, the observed discrepancies are large enough to question the basic viability of the reactor physics design, e.g. with respect to the thermal performance.     

基于SCIENCE程序包的IFBA组件模型的可行性研究

表面涂有一薄层硼化锆的一体化燃料可燃吸收体(IFBA)被用作轻水堆UO2燃料组件的反应性控制。法国AREVA公司开发的SCIENCE程序包具有模拟IFBA组件的能力,但其模拟精度需经标定。本文利用APOLLO2-F程序建立IFBA组件模型和不含IFBA组件模型,研究了组件的无限增殖因数k∞及IFBA价值,并与西屋公司结果进行比较。分析了燃料和包壳温度的处理方法以及数据库的差异对结果的影响。利用硼化锆密度修正因子评估IFBA价值偏差对堆芯参数和功率分布等的影响。结果表明:SCIENCE计算的k∞及IFBA价值与西屋公司的结果符合较好,低燃耗区SCIENCE计算的价值偏小2%。装载8个104根IFBA棒组件的堆芯,组件相对功率最大偏差约为1%;硼浓度、功率峰因子FQ和焓升因子FΔH的变化均不到0.1%,可忽略。先导组件采用28根或更少的IFBA棒时,可直接采用SCIENCE程序进行计算。     

Improvement of Monte Carlo Lattice Burnup Calculation Performance with the Correlated Sampling Method

For next generation reactor designs, which are attempting wide variations of assembly configurations, the flexibility Monte Carlo method holds is attractive, but still costly for repetitive design study works. This paper presents an advanced correlated sampling (ACS) method which was developed to speed up Monte Carlo lattice burnup calculations. The ACS method is the combination of the correlated sampling method and a pseudo-scattering technique. All burnup steps are considered as consecutive perturbed problems using the same neutron collision history, which is pre-calculated based on a selected unperturbed problem. Since neutron weights can be adjusted on every collision point, rather than along paths between them, the perturbed calculation is very fast and the neutron collision history is light enough to be stored in memory or physical storage, which is an indispensable feature for consecutive perturbed calculations. The presented theory shows that the ACS method has good potential to work for a wide range of neutron absorption variations, the dominant perturbation in the lattice burnup. In an example calculation on a BWR lattice, the ACS calculation results of 600,000 neutrons/step agree well with the independent Monte Carlo runs of 20,000,000 neutrons/step within 0.1%dk/k in terms of k_? throughout 95 steps (~50GWd/t). Average calculation time of neutron tracking with the former method is 3.4 s/step with 600,000 neutron histories on a single processor of an Alpha21164-600 MHz, and the speed-up factor against the Monte Carlo calculation turns out to be about 100.     

Effect of anisotropic scattering in neutronics analysis of BWR assembly

The anisotropic scattering effect to keff is studied for UO₂ and MOX fueled BWR assemblies. The anisotropic scattering effect increases the assembly k_∞ by 0.44% Δk for the UO₂ assembly with 0% void fraction, and by 0.21% Δk for the MOX assembly with 0% void fraction. This is because the anisotropic scattering effect flattens the intra-assembly thermal flux, and the absorption rate in the surrounding water gap is decreased, but the absorption rates in the MOX fuel rods are increased compared to the UO₂ rods. Therefore, the total decrease in absorption rates in the UO₂ assembly is relatively large, and the k_∞ is increased in the UO₂ assembly. The dependence of the anisotropic scattering effect on the void fraction is investigated, and the significant difference of 0.62% Δk/k is found for the 0% and the 80% void fractions. The BWR assemblies with Gd rods are also considered. Furthermore, the usefulness of the transport cross section is investigated, and it is found that the transport cross section gives reasonable anisotropic scattering effect, though not satisfactory.     

Comparison of 3D reaction rate distributions measured in an Optima2 BWR assembly with MCNPX predictions

As part of a joint research programme between the Paul Scherrer Institute (PSI) and swissnuclear, with the co-operation of the Leibstadt nuclear power plant in Switzerland and fuel suppliers Westinghouse Sweden, measurements and calculations have been made of the axial and radial distributions of fission and ²³⁸U capture rates in the fuel rods of a Westinghouse SVEA-96 Optima2 boiling water reactor assembly. The measurements, made in the zero-energy research reactor PROTEUS at PSI, have been compared with calculations carried out using the Monte Carlo code MCNPX. The results reported are for the regions near the ends of the part-length fuel rods, which are a feature of SVEA-96 Optima2 assemblies. The sudden increase in moderation above the ends of the part-length rods leads to power peaking in the adjacent rods. Careful attention needs to be given to this phenomenon in the deployment of such fuel, the present paper providing experimental evidence for the ability of a stochastic code to predict such effects.     

Coolant void reactivity adjustments in advanced CANDU lattices using adjoint sensitivity technique

Coolant void reactivity (CVR) is an important factor in reactor accident analysis. Here we study the adjustments of CVR at beginning of burnup cycle (BOC) and k_eff at end of burnup cycle (EOC) for a 2D Advanced CANDU Reactor (ACR) lattice using the optimization and adjoint sensitivity techniques. The sensitivity coefficients are evaluated using the perturbation theory based on the integral neutron transport equations. The neutron and flux importance transport solutions are obtained by the method of cyclic characteristics (MOCC). Three sets of parameters for CVR-BOC and k_eff-EOC adjustments are studied: (1) Dysprosium density in the central pin with Uranium enrichment in the outer fuel rings, (2) Dysprosium density and Uranium enrichment both in the central pin, and (3) the same parameters as in the first case but the objective is to obtain a negative checkerboard CVR-BOC (CBCVR-BOC). To approximate the EOC sensitivity coefficient, we perform constant-power burnup/depletion calculations using a slightly perturbed nuclear library and the unperturbed neutron fluxes to estimate the variation of nuclide densities at EOC. Our aim is to achieve a desired negative CVR-BOC of −2 mk and k_eff-EOC of 0.900 for the first two cases, and a CBCVR-BOC of −2 mk and k_eff-EOC of 0.900 for the last case. Sensitivity analyses of CVR and eigenvalue are also included in our study.     

Analysis of VIP-BWR reactor core physics experiments on UO2 and MOX mockup fuel assemblies - part 2: analysis with SIMULATE5

Analysis of the three test cores in the VIP-BWR program was performed in a two-dimensional geometrical model with CASMO5 coupled with the JENDL-4.0-based neutron data library, and reported in the previous paper. Following the study, interpretation of the experiments were carried out in a three-dimensional geometrical model with SIMULATE5 for the code validation study. The nuclear libraries for the SIMULATE5 calculations were generated with CASMO5 with the JENDL-4.0-based neutron data library. The effective multiplication factors of the critical cores ranged from 0.9983 to 1.0023 with measurement uncertainties of 0.0003 to 0.0004 (one σ). The root mean squares of (the calculated/the measured-1) for the fission rates at the core-mid plain of all the measured fuel rods were about 3% for the three cores. It was noticed that the calculations underestimated the fission rates of the UO₂ fuel rods and overestimated those of the MOX fuel rods for the test cores loaded with MOX fuel rods, which was consistent with trends in the preceding analysis studies of the VIP-BWR program and other MOX core experiments, and the biases were confirmed in the calculation results of power distributions in MOX-fueled light water reactor cores.     

Design of an overmoderated fuel and a full MOX core for plutonium consumption in boiling water reactors

The use of uranium–plutonium mixed oxide fuel (MOX) in light water reactors (LWR) is nowadays a current practice in several countries. Generally 1/3 of the reactor core is loaded with MOX fuel assemblies and the other 2/3 with uranium assemblies. Nevertheless the plutonium utilization could be more effective if the full core could be loaded with MOX fuel. In this paper the design of a boiling water reactor (BWR) core fully loaded with an overmoderated MOX fuel design is investigated. The design of overmoderated BWR MOX fuel assemblies based on a 10×10 lattice are developed, these designs improve the neutron spectrum and the plutonium consumption rate, compared with standard MOX assemblies. In order to increase the moderator to fuel ratio two approaches are followed: in the first approach, 8 or 12 fuel rods are replaced by water rods in the 10×10 lattice; in the second approach, an 11×11 lattice with 24 water rods is designed with an active fuel length very close to the standard MOX assembly. The results of the depletion behavior and the main steady state core parameters are presented. The feasibility of a full core loaded with the 11×11 overmoderated MOX fuel assembly is verified. This design take advantage of the softer spectrum comparable to the 10×10 lattice with 12 water rods but with thermal limits comparable to the standard MOX fuel assembly.     

Reactor physics ideas for large scale utilization of thorium in gas cooled reactors

The physics principles for maximizing the fertile to fissile conversion were used in developing reactor concepts for large scale utilization of thorium in thermal and fast reactors (Jagannathan & Pal, 2006; Jagannathan et al., 2008). It is recognized that these principles are very well suited for ‘He’ gas cooled reactors with graphite moderator since both helium gas coolant and the graphite moderator have low neutron absorption characteristics and thus gives better neutron economy. In this paper, these ideas are applied to the High Temperature Test Reactor (HTTR) core of Japan to assess its advantage over the present day gas cooled reactors. HTTR is helium cooled and graphite moderated system. Significant amount of thorium has been loaded in the HTTR core with some minimal changes in the existing core design. The modified design is called HTTR-M core.In the HTTR-M core, the fuel is changed from enriched UO₂ fuel to Pu in ThO₂ fuel. The locations of boron type burnable poison rods within each fuel assembly of HTTR are replaced by one cycle irradiated thoria rods. Also, the B₄C type control assembly around the HTTR core is replaced by fresh seedless thorium assembly. The fertile thoria assembly are scattered uniformly in the HTTR-M core. The equilibrium core of HTTR-M shows very small burnup reactivity swing. The core excess reactivity is ∼18 mk at BOC and reduces to 1 mk at 660 days. It is interesting to note that this small reactivity change is intrinsically achieved by the choice of seed and fertile dimensions and their contents without the use of burnable poison rods or mechanical control rods which are used in HTTR core. The burnup reactivity swing in the latter after using burnable poison is ∼100 mk. The fissile seed inventory ratio (FIR) in a fuel cycle is 0.90 as compared with 0.717 of HTTR core. Since ²³³U is a better fissile nuclide with highest ‘η’ value in thermal range, the above conversion ratio can be regarded as quite good.     

Criticality of the thorium burnup in equilibrium state

The effective neutron multiplication factor (k_eff) as a function of burnup for different volume coolant (CoR) and fuel (FR) to cell ratio is presented. Additionally the Conversion Ratio (CR) of Th-232 to U-233, concentration of U-233, fissile and fission products calculation as a function of burnup are presented. The assembly is a critical reactor which makes volumes of coolant and fuel changes possible. In addition, an analytical model of calculation of k_eff as a function of U-233 and a poison concentration in equilibrium state are presented. One can achieve the criticality of Thorium Breeder Reactor (TBR) for enough high average neutron energy which one can obtain in Fast Breeder Reactor (FBR) only. The maximal value of CR and burnup for case of k_eff ≥ 1 achieves 1.4 and 360 GWd/MTU, correspondently. The calculations were done with a MCNPX 2.7 code using F₂Be, Na and Pb coolants.     

Effect of Low-frequency Power on F, CF2 Relative Density and F/CF2 Ratio in Fluorocarbon Dual-Frequency Plasmas

Effect of low-frequency power on F, CF₂ relative density and F/CF₂ ratio, in C₂F₆, C₄F₈ and CHF₃ dual-frequency capacitively couple discharge driven by the power of 13.56 MHz/2 MHz, was investigated by using optical emission spectroscopy. High F, CF₂ relative density and high F/CF₂ ratio were obtained in a CHF₃ plasma. But for C2F6 and C4F8 plasmas, the F, CF₂ relative density and F/CF₂ ratio all decreased significantly due to the difference in both reactive paths and reactive energy. The increase of LF power caused simultaneous increase of F and CF₂ radical relative densities in C₄F₈ and CHF₃ plasmas, but led to increase of F with the decrease in CF₂ relative densities in C₂F₆ plasma due to the increase of lower energy electrons and the decrease of higher energy electrons in EEDF.     

Reactivity feedbacks of a material test research reactor fueled with various low enriched uranium dispersion fuels

The reactivity feedbacks of a material test research reactor using various low enriched uranium fuels, having same uranium density were calculated. For this purpose, the original aluminide fuel (UAl_x–Al) containing 4.40 gU/cm³ of an MTR was replaced with silicide (U₃Si–Al and U₃Si₂–Al) and oxide (U₃O₈–Al) dispersion fuels having the same uranium density as of the original fuel. Calculations were carried out to find the fuel temperature reactivity feedback, moderator temperature reactivity feedback, moderator density reactivity feedback and moderator void reactivity feedback. Nuclear reactor analysis codes including WIMS-D4 and CITATION were employed to carry out these calculations. It was observed that the magnitudes all the respective reactivity feedbacks from 38 °C to 50 °C and 100 °C, at the beginning of life, of all the fuels were very close to each other. The fuel temperature reactivity feedback of the U₃O₈–Al was about 2% more than the original UAl_x–Al fuel. The magnitudes of the moderator temperature, moderator density and moderator void reactivity feedbacks of all the fuels, showed very minor variations from the original aluminide fuel.     

Measurement of Thermal Utilization Factor in a Square Cell of UO2-H2O Lattice

Thermal neutron distribution in a square lattice of water moderated UO₂ (enriched to 2.596 w/0 in ²³⁵U) was measured with dysprosium micro-foils. Diameters of the fuel pellet and the aluminum cladding tube were 12.5mm and 14.12mm respectively. The pitch of the square lattice was 19.56mm, and the water to fuel volume ratio 1.844. To obtain the integrated flux in the fuel and moderator regions, the solution for the P-1 diffusion equation was used. A disadvantage factor of 1.27±0.02 and a thermal utilization factor of 0.891±0.002 were obtained. The theoretical value of the disadvantage factor obtained by the 30 group integral transport theory in a square call is 1.341 and is larger than the experimental value by a discrepancy exceeding the experimental error. The result is also compared with some approximate calculations.     

基于CASMO5的燃耗历史对乏燃料反应性的影响计算

基于乏燃料贮存领域常用的锕系加裂变产物(APU-2)级燃耗信任制,应用二维组件燃耗计算程序CASMO5,计算了燃耗过程中功率密度和运行历史对乏燃料k∞的影响。结果表明:燃耗计算中,选择堆芯额定功率对应的平均功率密度,同时k∞附加0.002 3的包络裕度,运行历史选择循环内及循环间无停堆额定功率运行,同时k∞附加0.004 5的包络裕度,可满足燃耗信任制中包络性原则。     

Influence of the plasma profile and the antenna geometry on the matching and current distribution control of the ITER ICRF antenna array. Optimization of the decoupling-matching system

The eight triplets of straps of the ITER ICRF antenna array are fed through 8 matching circuits and 4 hybrids to ensure load resilience. Decouplers are used to mitigate the effects of triplet mutual coupling. They also control the array phasing. The electrical constraints on the decouplers for different layouts with heating (H) or current drive (CD) phasing are compared starting from the TOPICA matrix computed for the last antenna plug design and the reference (most pessimistic) plasma profile “2010low” provided by IO. It is shown that this last profile provides a significant decrease of plasma coupling and increase of mutual coupling with respect to the previous reference profile “Sc2short17”. This results in a larger range of decoupler reactance X_dec and voltage V_Xdec needed. This range can be reduced when using 10 decouplers instead of the 7 needed for the same forward power P_Gk+ of the 4 power sources. For H phasing only 4 decouplers could be used but with different P_Gk+ (P_Gk+ ratio up to 1.5–2.5). For CD phasing and same plasma profile the power capability P_tot is increased by 25% with a decoupler layout allowing much smaller poloidal phasing than the 90° provided by the hybrids. A decrease of the distance antenna-plasma profile reduces the normalized decoupler voltage V_Xdec/√P_tot with no significant change of the X_dec range. The recess of the vertical septa between the strap boxes increases the plasma coupling but has the drawback of also increasing the mutual coupling between triplets: the needed range of X_dec and of V_Xdec/√P_tot is increased in proportion.     

The theory of heterogeneous reactors with slugs of finite radius

This paper deals with the theory of a large heterogeneous thermal neutron reactor using cylindrical slugs. The dimensions of the square lattice are much greater than the scattering length of the neutrons fn the moderator. In contrast with the theory of Feinberg and Galanin [1, 2], each slug in this case is not only a neutron sink, but it also has a dipole moment. Accordingly, in addition to the thermal constant, two polarization constants must be given which determined the diffusion length in the lattice, in directions parallel and perpendicular to the axis of the slug. The characteristic equation of the lattice, and the formulas for the diffusion length, are found for the condition of quite small absorption in the moderator, and a very large number of cells in the reactor. As an example, the polarization coefficients are can culated in the P₂-approximation. In the P₁ approximation, the results obtained are the same as the data of [3], with the exception of small correction terms previously calculated incorrectly.Translated from Atomnaya Énergiya, Vol. 15, No. 2, pp. 107–115, August, 1963