3-D Neutron Transport Benchmarks

Three-dimensional (3-D) neutron transport benchmark problems proposed from Osaka University to NEACRP in 1988 have been calculated by many participants and the results have been summarized. The results of k _eff, control rod worth, and region-averaged group fluxes for proposed four core models calculated by various 3-D transport codes have been compared. There was consistency among the results, when necessary corrections were made. The solutions of the four core models are quite useful as benchmarks for checking the validity of 3-D neutron transport codes.     

Development of Three-Dimensional Transport and Diffusion Codes Based on Nodal Method

A basic concept on partitioning and transmutation treatment by neutron reaction was developed in order to Improve the waste management and the disposal scenario of high level waste (HLW). The grouping in partitioning was important factor and closely linked with the characteristics of BIT (burning and/or transmutation) treatment. The selecting and grouping concept in partitioning of HLW was proposed herein, such as Group MA1 (Np, Am, and unrecovered U and Pu), Group MA2 (Cm, Cf etc.), Group A (Tc and I), Group B (Cs and Sr) and Group R (the partitioned remain of HLW), judging from the three criteria for B/T treatment proposed in this study, which is related to (1) the value of hazard index for long-term tendency based on ALI, (2) the relative dose factor related to the mobility or retardation in ground water penetrated through geologic layer, and (3) burning and/or transmutation characteristics for recycle B/T treatment and the decay acceleration ratio by neutron reaction. Group MA1 and Group A could be burned effectively by thermal B/T reactor. Group MA2 could be burned effectively by fast B/T reactor. Transmutation of Group B by neutron reaction is difficult, therefore the development of radiation application of Group B (Cs and Sr) in industrial scale may be an interesting option in the future. Group R, i.e. the partitioned remains of HLW, and also a part of Group B should be immobilized and solidified by the glass matrix. HI_ALI, the hazard index based on ALI, due to radiotoxicity of Group R can be lower than HI_ALI due to standard mill tailing (smt) or uranium ore after about 300 years.     

Effect of Geometrical Approximation on Multiplication Factor in Small Fast Reactor Core

In most of the calculations using analytical methods a reactor core is approximated as cylinder and the reactor parameters are calculated using two-dimensional computer codes. While such calculations are useful in scoping studies in view of azimuthal asymmetry in the actual reactor core these calculations could entail errors of unknown magnitude. The present study reports our estimate of such errors in K _eff with the instance of fast reactor having 22 and 23 fuel subassemblies. The K _eff are calculated using Monte Carlo code KENO and Hansen-Roach cross section set, modelling the core in two different ways, (1) by approximating the core to a cylinder (2-D calculation), (2) by near exact representation of the core (3-D calculation). The difference in K _eff is appreciable between 2-D and 3-D calculations.

Experimental values are adduced in support of these calculations.     

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.     

Coarse-Mesh Three-Dimensional Transport Calculation Method

A coarse-mesh 3-D (X-Y-Z, Hexagonal-Z) discrete ordinates transport calculation method has been developed. This method employs an weighted diamond difference approximation, the weight in which is a function of neutron direction and scalar flux, and can be easily incorpolated into conventional discrete ordinates transport codes. Results obtained in four-group S₄P₀ calculations on simple fast reactors indicate that, though the computer time of this method has increased by 30–50% compared with that of the conventional finite difference method using the same mesh, the errors of k_eff and the power distribution are reduced remarkably.     

Application of Hexagonal Element Scheme in Finite Element Method to Three-Dimensional Diffusion Problem of Fast Reactors

The finite element method is applied in Galerkin-type approximation to three-dimensional neutron diffusion equations of fast reactors. A hexagonal element scheme is adopted for treating the hexagonal lattice which is typical for fast reactors. The validity of the scheme is verified by applying the scheme as well as alternative schemes to the neutron diffusion calculation of a gas-cooled fast reactor of actual scale. The computed results are compared with corresponding values obtained using the currently applied triangular-element and also with conventional finite difference schemes.

The hexagonal finite element scheme is found to yield a reasonable solution to the problem taken up here, with some merit in terms of saving in computing time, but the resulting multiplication factor differs by 1% and the flux by 9% compared with the triangular mesh finite difference scheme. The finite element method, even in triangular element scheme, would appear to incur error in inadmissible amount and which could not be easily eliminated by refining the nodes.     

Generalized Exact Solution of the Slowing Down Equation

The slowing down equation for an infinite homogeneous monoatomic medium is solved exactly. The solution is obtained in analytical form. The calculated collision density is compared with the one obtained by Teichmann and Stefanovi'c respectively. For the special case of hydrogen, the present solution reduces to Bethe's solution.     

Experimental Study of Nuclear Characteristics of Large Axially Heterogeneous Core Using Fast Critical Assembly

The physics characteristics of large axially heterogeneous liquid-metal fast breeder reactors (LMFBRs), particularly the parameters for use in design and safety assessment, were examined using the JAERI fast critical assembly facility, arranged in Assembly XH-1, a partial mock-up of axially heterogeneous LMFBR. The properties measured were (1) criticality, (2) reaction rates and reaction rate ratios, (3) material sample worths, (4) sodium-void worths and (5) B4C control rod worths.

The results were compared with those of prior experiments with assemblies representing conventional homogeneous core. Confirmation was obtained of the typical nuclear characteristics attributed to axially heterogeneous LMFBRs, including flattening of the axial distribution of power and of the differential worth of control rod, as also lower sodium void worth.

Theoretical analyses paralleling the experiments, using JENDL-2 cross section library and JAERI standard calculation code system for fast reactor neutronics, resulted in some discrepancies, particularly for the internal blanket, in respect of plutonium sample worth, fission rate and fission rate ratio.     

Diffusion Calculation Model for Streaming Effects in Low Density Channels in LMFBRs

A study is made of the use of modified diffusion theory to calculate the negative reactivity worth of recently proposed flow activated reactor shutdown devices, in which sodium is voided from purely sodium filled channels located at the boundary between the core and the radial blanket in a Liquid Metal cooled Fast Breeder Reactor (LMFBR). Three-dimensional diffusion theory calculations using various definitions of modified diffusion coefficients in the channels are compared with each other and with three-dimensional transport theory computations. While normal diffusion coefficient is found to be inadequate for these reactivity worth calculations, the various modified diffusion coefficients appear adequate for the considered case. Modelling method of the small thickness of steel wall and interstitial sodium layer of the modules are also studied.     

Measurement and Analysis of Neutron Spectra in Lithium Fluoride and Polytetrafluoroethylene Piles

For the assessment of neutron cross section data for fluorine, angular neutron spectra in the lithium fluoride (LiF) and polytetrafluoroethylene ((CF₂)n) piles were measured in the energy range from a few keV to a few MeV by the time-of-flight method with an electron linac, and the results were compared with those calculated by using nuclear data from JENDL-2 and ENDF/B-IV. Spatial distributions of neutron and X-ray fluxes were also measured in the test piles by the activation method, and the influence of photoneutrons generated in the sample material on the neutron spectrum in each pile was estimated. As a result, it was found that their influence on the neutron spectrum shape below 1 MeV was not so large as was necessary to be taken into account for the present assessment.

The calculated spectra using the JENDL-2 data and the ENDF/B-IV data show generally good agreement with those measured in both piles. However, both calculations underestimate the neutron fluxes around several 100 keV, and overestimate those below 100 keV, when they are normalized in the energy range of 10 keV～1 MeV. Large discrepancies are found between the shapes of the measured and calculated spectra around the resonances of fluorine cross section below 100 keV. The present measurements and analyses suggest that the reevaluations of the inelastic and elastic scattering cross sections below 1MeV and the resonance cross sections below 100 keV are necessary to reduce the observed discrepancies.     

Effect of Polynomial Expansion Order of Intranode Flux Treatment in Nodal SN Transport Calculation Code NSHEX for Large-Size Fast Power Reactor Core Analysis

The nodal discrete ordinates (S_N) transport calculation code for three-dimensional hexagonal geometry NSHEX treats intranode flux distribution using a polynomial series and considers the angular dependence of flux by the SN method. For the improvement of calculation accuracy of NSHEX for practical use to large-size fast reactor plants, the maximum order of the polynomial series is extended from two to six. In order to check the effect of the polynomial expansion order, NSHEX is applied to the intermediate-size fast power reactor core “Monju” and the large-size one “Super Phenix,” including various control rod insertion conditions. From the application, it is found that extension of the polynomial expansion order is effective especially for the large-size core “Super Phenix” under the control-rod-inserted condition.     

Unbiasedness Evaluation of Statistical Error in Staged Monte Carlo Calculation

Fuel rod failure behavior has been studied under a reactivity initiated accident condition in Nuclear Safety Research Reactor (NSRR), JAERI. In the studies, inetallurgical observations showed that the incipient fuel rod failure mode was oxygen-induced embrittlement of the cladding independent of the test conditions such as fuel designs and cooling environments except for pressurized and waterlogged fuels. Development of the oxidation layers and embrittlement of β-Zry were quantitatively evaluated through the metallurgical examinations. A diffusion equation of oxygen was solved under a finite system with moving boundary conditions to obtain the oxygen concentration and evaluate the cladding embrittlement. The calculation showed that the wall thinning due to the cladding melt is needed for the complete embrittlement because the wall thinning enhances the oxygen concentration in the β-Zry, which well explain the experimental results. Therefore the failure threshold energy is determined by the cladding melting temperature. The failure threshold derived from this study is expected to be applicable to predicting the fuel rod failure behavior in computer analyses and also useful to evaluate the failure threshold energy for the new types of fuel rod.     

Evaluation of Reactivity Worth of Air Filled Beam Tubes in a Small Neutron Source Reactor by 3-D Transport Calculations

Four air filled beam tubes are present in the small pool type ²³³U fuelled, BeO and water reflected neutron source reactor KAMINI under construction in IGCAR, Kalpakkam. The positive reactivity insertion possible due to the accidental ingress of surrounding water into these empty beam tubes was estimated using the 3-D transport code TRITAC. To save computer time and also to highlight the effects caused by filling of air gaps with water, a similar but symmetrical core with more beam tubes was also studied in detail. Microscopic cross sections were derived from WIMS library and assembly homogenization was performed using a computer code SMAXY. Condensed eight group cross sections were used in TRITAC.

During the study reported here, need was found for the use of tight flux convergence criterion in TRITAC for getting reliable estimates of air to water worths. From the study of the symmetrical core, it is found that the presence of outer water reflector significantly reduces the air to water worth of these beam tubes. Further, the air to water worth of these beam tubes is quite small when the region where water replaces air is, beyond 15 cm from core boundary. Thus it is inferred that the total air to water worth of all beam tubes in the KAMINI reactor will be small compared to the total delayed neutron fraction of ²³³U.     

Calculational Study of Time-Dependent Neutron Spectra in Ice at Low Temperature

Calculations on the time-dependent neutron spectra in an ice block are reported for the temperature range of 86–16 K.

Three models for the lattice vibrational frequency distributions were applied to calculate scattering kernels. Calculated spectra were compared with measured spectra. It was found that the calculation with the Debye model agrees well with the experiment.

From the present analysis, it was suggested that the Debye temperature θ_D of the low temperature ice can be expressed as θ_D = 208 + 0.3T ₀ where T ₀ is the medium temperature.     

Measurements of Reaction Rates in Zone-Type Cores of Fast Critical Assembly Simulating High Conversion Light Water Reactor

Measurements of reaction rates have been performed in three uranium-fueled zone-type cores of the FCA constructed for a series of experiments on a high conversion light water reactor (HCLWR). These cores possess central test zones of different fuel enrichments and moderator to fuel volume ratios. Radial and axial fission rates of 236U, 239Pu, 238U and 23,Np were measured in each test zone by means of the micro-fission counter traverse. A region where the fundamental mode spectrum is established in the test zone were determined by utilizing these fission rate distributions. Central reaction rate ratios relative to the 235U fission rate were obtained from the measurements by the micro-fission counters and metallic uranium foils to examine changes in the reaction rate ratios among the three cores.

The measured data were analyzed by the SRAC code system on the basis of the nuclear data file JENDL-2. The calculated fission rate distributions agree well with the experimental results for the all cases. The results of reaction rate ratios show that the calculations over- predict the experimental values of the 238U capture/235U fission and 238U fission/235U fission rate ratios in the three cores.     

Vaiidition of ORIGEN Computer Code by Measurements on Nuclear Fuels of JPDR-1

The depletion and production amounts of U, Pu, transplutonium nuclides and fission products (FPs) measured on the fuel of JPDR-1 were corrected to take account of the performance history of irradiation and cooling using the results of three-dimensional nuclear-thermo-hydrodynamic and nuclide depletion and production calculations. Except a few nuclides, the corrected values proved to agree well with the values calculated by the ORIGEN computer code. Further enhancement of calculational accuracy calls for systematic re-evaluation of neutron cross sections on the basis of neutron spectrum in nuclear fuel.     

Analysis of Post Irradiation Experiments in PWR Using New Nuclear Data Libraries

For the precise calculation of the burnup of minor actinide isotopes, a code system-SWAT has been developed. This system analyzes burnup problems with neutron spectrum that depends on the type of a reactor and the irradiation history, using latest evaluated nuclear data files JENDL-3 or ENDF/B-Vl. The post irradiation test in TRINO and the recent experiment in typical PWRs in Japan were analyzed with SWAT. These analyses show that the results of U and Pu for high burnup fuels almost agree with experimental results but those for middle burnup fuels do not agree with them. The results for Am and Cm isotopes still have large discrepancy. The average C/E of ²⁴³Am is –0.79, and that of ²⁴⁴Cm is –0.70 for high burnup (–33,000 MWd/tU) samples.

For middle burnup (–25,000 MWd/tU) samples, the C/E for ²⁴⁴Cm is over 2.0. The discrepancy is partially explained by considering the power peaking history of first cycle and second cycle.