Multigroup Cross Sections Research Articles

The contribution of individual correlated parameters to the uncertainty of integral quantities

Modern libraries of multigroup cross-sections often include covariances of the multigroup data. Data covariances are especially useful in calculating the variance of an important applied quantity z that can be calculated as a function of the data. Frequently, it is also of interest to know the magnitude of the contributions to this variance arising from various subsets of the data. This knowledge can be used, for example, in judging the benefits of performing specific new measurements, calculations, or evaluations on a given data subset. Here we describe a method for determining the contribution of an identified set of parameters to the variance of z that can be applied without difficulty even when the data have general correlations.

Analysis of regularly perturbed lattices and reaction rate distributions from TIC experiments for X7 lattices

Temporary International Collective (TIC) was established in 1972 by an agreement among seven countries, namely, Bulgaria, Czechoslovakia, Germany, Hungary, Poland, Romania and Union of Soviet Socialist Republics. The main objective of TIC was to provide the experimental data for the reactor physics analysis of water cooled and water moderated power reactors (WWER). Extensive experimental work for different core configurations was carried out by TIC countries to investigate the physics behavior of WWER lattices and the results were published in TIC volumes. In this paper, TIC experiments on regularly perturbed cores have been analyzed as part of the validation of indigenous computer codes, EXCEL, TRIHEX-FA and HEXPIN developed at Light Water Reactors Physics Section, B.A.R.C. The few group homogenized parameters of assembly cell or individual lattice cells were obtained by the hexagonal lattice burn-up code EXCEL and the core diffusion calculations were then performed using hexagonal assembly geometric code TRIHEX-FA and the pin-by-pin diffusion code HEXPIN. A transport-diffusion theory correction to the absorber cell cross section by a diffusion iterative technique (DIT) was used to iteratively adjust the absorber cell cross sections such that the transport leakage into the absorber cell is reproduced by diffusion theory. Neutron-nuclear multi-group cross-section libraries in WIMS/D format in 69/172 energy groups have been released by IAEA at the conclusion of WIMS library update project (WLUP). In the present study we have used libraries based on ENDF/B-6, ENDF/B-7, JEFF3.1 and JENDL3.2 evaluated nuclear datasets. Except ENDF/B-6, the trends of the k eff from the remaining three libraries were found to be similar. JEFF3.1 data is being used for most of the design computations of LWR projects in India. Therefore, HEXPIN simulations were performed using the cross section library based on JEFF3.1 data. The calculated results are presented in two categories. In category-1, the calculated k eff values using TRIHEX-FA and HEXPIN are presented for the TIC experiments on Xn lattices. In our earlier work, we have reported that there is a need to perform 3-D core computations for leakage calculations. The improvements in k eff values by using core calculation tools, TRIHEX-FA and HEXPIN, are presented in this paper by comparing the results with zero dimensional buckling model of EXCEL. In category-2, calculated reaction rate distributions for different activation foils are compared with the measured reaction rate distributions from the TIC experiments. Reaction rate distributions have been calculated using cross section library based on JEFF3.1 data.

Collimator System Design for a DT Neutron Beam at the First Target Room of JAEA/FNS

*A new collimator is designed and optimized to produce a new DT neutron beam with a small target at the first target room of the Fusion Neutronics Source facility in Japan Atomic Energy Agency. The characteristics of the collimator are calculated with the DORT code and the FENDL/MG-2.1 multi-group cross section library. It is concluded that the calculated neutron fluence above 14 MeV at the exit of the collimator is 180 times as large as that at the10 cm offset position from the beam axis.

Insufficient Self-Shielding Correction in VITAMIN-B6

*We carried out a simple benchmark calculation test with a multigroup cross-section library VITAMIN-B6 generated from ENDF/B-VI. The model of this test consisted of an iron sphere of 1 m in radius with an isotropic 20 MeV neutron source in the center. Neutron spectra in the sphere were calculated with an Sn code ANISN and VITAMIN-B6 or FENDL/MG-1.1. A calculation with MCNP and ENDF/B-VI was carried out as a reference. The neutron spectra with ANISN and FENDL/MG-1.1 agreed with those with MCNP, while those with ANISN and VITAMIN-B6 were at most 50 % different from those with MCNP. We uncovered that the discrepancy came from insufficient self-shielding correction due to the followings; 1) The smallest background cross section of 56 Fe in VITAMIN-B6 is 1. 2) The weighting flux used in generating VITAMIN-B6 is not adequate. VITAMIN-B6 should be revised for adequate self-shielding correction.

Improvement of Tone's Method with Two-Term Rational Approximation

An improvement of Tone's method, which is a resonance calculation method based on the equivalence theory, is proposed. In order to increase calculation accuracy, the two-term rational approximation is incorporated for the representation of neutron flux. Furthermore, some theoretical aspects of Tone's method, i.e., its inherent approximation and choice of adequate multigroup cross section for collision probability estimation, are also discussed. The validity of improved Tone's method is confirmed through a verification calculation in an irregular lattice geometry, which represents part of an LWR fuel assembly. The calculation result clarifies the validity of the present method.

An Adaptive Energy Mesh Constructor for Multigroup Library Generation for Transport Codes

Users’ demands for multigroup transport calculations are wide and diverse, encompassing routine, rough, and fast calculations as well as very precise simulations. For these reasons, the use of accurate and efficient multigroup cross-section libraries is needed. In this work, we present an adaptive energy mesh constructor (AEMC) that builds a multigroup mesh from predefined requisites of precision and calculation time. For a given self-shielding model and number of groups, AEMC looks for the optimal bounds of a multigroup mesh that minimizes the errors of the multigroup transport solutions for a predefined set of infinite homogeneous medium problems. We have applied this methodology to define two energy meshes for fast sodium reactor applications: a 600-group mesh associated with an extension of the Livolant-Jeanpierre self-shielding method and a 1200-group mesh based on subgroup self-shielding. Tests in homogeneous media prove that the multigroup solutions are almost equivalent to Monte Carlo simulations. Simplified one-dimensional transport calculations confirm the accuracy of the 1200-group mesh and show that this mesh provides a precision similar to that obtained with the well-validated 1968-group ECCO mesh. The same tests reveal that the 600-group mesh optimized for subgroup self-shielding offers a good compromise between simulation time and precision.

NEUTRONICS MODELING AND SIMULATION OF SHARP FOR FAST REACTOR ANALYSIS

This paper presents the neutronics modeling capabilities of the fast reactor simulation system SHARP, which ANL is developing as part of the U.S. DOE’s NEAMS program. We discuss the three transport solvers (PN2ND, SN2ND, and MOCFE) implemented in the UNIC code along with the multigroup cross section generation code MC²-3. We describe the solution methods and modeling capabilities, and discuss the improvement needs for each solver, focusing on massively parallel computation. We present the performance test results against various benchmark problems and ZPR-6 and ZPPR critical experiments. We also discuss weak and strong scalability results for the SN2ND solver on the ZPR-6 critical assembly benchmarks.

Validation of lattice code ‘EXCEL’ with TIC experiments on uniform and regularly perturbed lattices

Temporary International Collective (TIC) was established in 1972 by an agreement among seven countries, namely, Bulgaria, Czechoslovakia, Germany, Hungary, Poland, Romania and Union of Soviet Socialist Republics. The main objective of TIC was to provide the experimental data for the reactor physics analysis of water cooled and water moderated power reactors (WWER). Extensive experimental work for different core configurations was carried out by TIC countries to investigate the physics behaviour of WWER lattices and the results were published in TIC volumes. Two VVER-1000 MWe reactors are currently in an advanced stage of construction and due for commissioning in Kudankulam, Tamil Nadu, India. Indigenous development of in-core fuel management computer codes for the analysis of hexagonal lattice cores is also in an advanced stage to address various design, operation and safety issues of VVER type cores. The validation of the above TIC lattice experiments will help in the identification of deficiencies in reactor physics design computational codes and the associated nuclear data libraries. In this paper, TIC experiments on uniform and regularly perturbed lattices have been analyzed as part of the validation of indigenous computer codes, EXCEL, TRIHEX-FA and HEXPIN developed at Light Water Reactors Physics Section, B.A.R.C. Neutron-nuclear multi-group cross-section libraries in WIMS/D format in 69/172 energy groups have been released by IAEA at the conclusion of WIMS library update project (WLUP). In the present study we have used libraries based on ENDF/B-6, ENDF/B-7, JEFF3.1 and JENDL3.2 evaluated nuclear datasets. The results of the theoretical analyses bring out the performance of the code system and various cross-section libraries.

A feasibility study of ferro-boron as in-core shield material in fast breeder reactors

Shields around core and blankets form major part of reactor assembly in fast reactors as the incident neutron spectrum is hard with negligible thermal component and has anisotropic angular distribution. In this paper, a study is presented on the use of ferro-boron as neutron shield material in pool type fast reactors. The reference case chosen is the Prototype Fast Breeder Reactor (PFBR), a 500 MWe which is sodium cooled, pool type, mixed oxide (MOX) fuelled reactor, which is under construction at Kalpakkam, India. It is shown through 2D transport calculations, carried out using 175 neutron multigroup cross-sections, that this low cost material as shield is capable of satisfying the radiological safety criteria as well as the shields in the reference case. The secondary sodium activity and dose in steam generator building are marginally lower than the reference case. The total shield material weight will be lower by about 50 tonnes and the material cost lower by a factor 5 as compared to PFBR shields comprising of stainless steel and B 4C.

Design Calculations of VPVR/M Research Reactor Spent-Fuel Cask

To support the transport of spent nuclear fuel from Czech research reactors of Russian origin back to the Russian Federation, a special VPVR/M transport cask was designed at SKODA JS, Czech Republic. In 2007, the shipment of 16 VPVR/M casks with EK-10 fuel of 10 wt% 235U, IRT-2M fuel of 80 wt% 235U, and IRT-2M fuel of 36 wt% 235U expended at the LVR-15 research facility since 1957 was realized. The VPVR/M cask was designed for all fuel types used in Russian research reactors of similar designs, which were built in many countries outside of Russia.A revised version of the ORIGEN 2.2 code was used for depletion calculations of 35 types of irradiated fuel. Shielding analyses of the VPVR/M cask were performed using the DORT code with the revised BUGLE-96 multigroup cross-section library based on ENDF/B-VI Release 3. The criticality of the cask loaded with the highest-reactivity fuel was evaluated with the MCNP code using the DLC-200 cross-section data library using the fresh fuel approach.The isotopic inventory of IRT-3M fuel of 36 wt% 235U burned up to 184 MWd/kg U was identified as the bounding value. The sources of gamma rays for shielding calculations, neutron sources for shielding and criticality calculations, and heat sources were consequently evaluated. The original design of the cask was optimized with respect to the minimum weight needed for the conservation of the required shielding properties. In compliance with the regulatory requirements for spent-fuel storage and transport casks, the subcriticality of the system met the criticality safety criterion of keff < 0.95 for all the fuel types evaluated. The cask fulfilled Czech safety criteria as well as International Atomic Energy Agency regulations for subcriticality, shielding, heat cooling, and structure requirements.

Efficient Generation of One-Group Cross Sections for Coupled Monte Carlo Depletion Calculations

Coupled Monte Carlo depletion systems provide a versatile and an accurate tool for analyzing advanced thermal and fast reactor designs for a variety of fuel compositions and geometries. The main drawback of Monte Carlo-based systems is a long calculation time imposing significant restrictions on the complexity and amount of design-oriented calculations. This paper presents an alternative approach to interfacing the Monte Carlo and depletion modules aimed at addressing this problem. The main idea is to calculate the one-group cross sections for all relevant isotopes required by the depletion module in a separate module external to Monte Carlo calculations. Thus, the Monte Carlo module will produce the criticality and neutron spectrum only, without tallying of the individual isotope reaction rates. The one-group cross section for all isotopes will be generated in a separate module by collapsing a universal multigroup (MG) cross-section library using the Monte Carlo calculated flux. Here, the term “universal” means that a single MG cross-section set will be applicable for all reactor systems and is independent of reactor characteristics such as a neutron spectrum; fuel composition; and fuel cell, assembly, and core geometries. This approach was originally proposed by Haeck et al. and implemented in the ALEPH code.Implementation of the proposed approach to Monte Carlo burnup interfacing was carried out through the BGCORE system. One-group cross sections generated by the BGCORE system were compared with those tallied directly by the MCNP code. Analysis of this comparison was carried out and led to the conclusion that in order to achieve the accuracy required for a reliable core and fuel cycle analysis, accounting for the background cross section (σ0) in the unresolved resonance energy region is essential.An extension of the one-group cross-section generation model was implemented and tested by tabulating and interpolating by a simplified σ0 model. A significant improvement of the one-group cross-section accuracy was demonstrated.

Multigroup Coupled Neutron-Gamma Cross-Section Library for Deterministic and Monte Carlo Borehole-Logging Analysis

A special-purpose multigroup cross-section library optimized for nuclides and reactions arising in nuclear oil well logging was prepared for use in deterministic and Monte Carlo transport codes. The library is based on the recent ENDF/B-VI.8 evaluation, which includes among others improved oxygen and chlorine cross sections. A 175-neutron and 45-gamma-ray energy group structure was selected as a way to take into account the requirements of oil well-logging applications. This library is expected to improve the prediction of the neutron and gamma spectra at the detector positions of the logging tool. For the Monte Carlo codes the library can be useful in particular in calculations requiring multigroup cross sections, like adjoint or MIDWAY methods. Furthermore, comparison of deterministic and Monte Carlo calculations using the same or similar cross sections can reveal the uncertainty linked to the computational method and model. The use of the library for the interpretation of the carbon/oxygen neutron logging measurements in boreholes was studied. Preparation and testing of this library, which is available from the Organisation for Economic Co-operation and Development/Nuclear Energy Agency Data Bank, is described.

Isotopic and Energy Groupwise Dependence of Fuel Temperature Coefficient of Reactivity in Natural Uranium-Fueled Pressurized Heavy Water Reactors

We have studied the individual effect of the temperature dependence of the multigroup cross sections of 238U, 235U, 239Pu, 240Pu, and 16O on the calculated fuel temperature coefficient (FTC) by performing detailed sensitivity studies. The thermal contribution and the Doppler contribution of the FTC have been estimated for the above isotopes for the 19-element UO2-fueled heavy water lattice of the pressurized heavy water reactor (PHWR). The groupwise breakdown of the FTC due to 238U resonances has also been obtained. The FTC of Canada deuterium uranium reactor (CANDU)-type pressurized heavy water moderated lattices using UO2 fuel becomes less negative with burnup and changes sign at high burnups. Our studies clearly demonstrate that the positive component of the FTC in natural UO2-fueled PHWRs arises primarily because of the temperature dependence of scattering cross sections of 16O in agreement with the earlier findings of Stammler. In this paper, we have calculated the reactivity due to the change in fuel temperature, and all our discussions are based on this fuel temperature reactivity rather than the FTC itself.

Neutron multigroup cross-sections of moderator materials for cold and ultracold neutron production

A total of 32 sets of multigroup (energy-averaged) cross-sections are developed for liquid 4He, H 2 , D 2 , CH 4 , H 2 O and D 2 O and solid CH 4 at widely different temperatures. The neutron energy range from 10 MeV down to 0.1 μ eV is covered. It is intended to treat both the moderation of fission and spallation neutrons and the production of low-energy neutrons such as thermal ( ∼ 25 meV ) , cold ( ∼ 2 meV ) and ultracold ( < about 0.3 μ eV ) neutrons. The entire energy range is divided into 140 intervals (groups) and the angular distribution of scattering is represented by the expansion in Legendre polynomials up to order 3. The cross-sections characterizing low-energy neutron scattering are calculated using the physical models of molecular dynamics and structure for each moderator material. To demonstrate availability of the cross-section sets, a study is made of ultracold neutron production and storage in a liquid- 4He sphere surrounded with liquid D 2 and D 2 O as reflectors. It is shown that the relevant cross-sections are successful in describing neutron energy spectra for fast and low-energy neutrons and that the study of a liquid- 4He source clarifies neutronic conditions to be required on the high-density storage of ultracold neutrons. The latter results serve physical and quantitative interpretation of the recent experimental measurement of ultracold neutron production in superfluid 4He.

A New Methodology for Adjustment of Iron Scattering Cross Sections Using Time-of-Flight Spectroscopy

Abstract Monte Carlo analysis of a time-of-flight experiment was performed to investigate the iron scattering cross section. Experimental data were utilized to build a Monte Carlo source for simulation of a time-of-flight (ToF) experiment with a spherical iron shell, different source spectra, and different angular beam source alignments. For this study, two pointwise cross section libraries, ENDF/B-VI and JEFF 3.0 are examined. Comparison of calculation and experimental results indicates differences that are larger than experimental and calculation errors. To reduce the observed discrepancy, pointwise data in the ENDF/B-VI iron scattering cross section file were adjusted at a few energy intervals using a utility code developed for this purpose. Adjusted cross sections resulted in closer agreement of calculated results with the experimental Time-of-Flight data. Multigroup cross sections were generated with the adjusted cross sections and results indicate pressure vessel fluence may be underestimated.

Improvement on multi-group scattering matrix in thermal energy range generated by NJOY

This paper describes an improvement pertaining to the multi-group scattering matrix in thermal energy range, which is obtained by the NJOY code. By using the multi-group cross-section obtained by the original NJOY code, neutron spectrum in the thermal energy range shows considerable discrepancy from that of the continuous energy Monte–Carlo code, MCNPX. Extensive investigation of this issue reveals that multi-group scattering matrix generated by the NJOY code does not have enough accuracy in thermal energy range. Root cause is as follows. The scattering matrix in thermal energy range is tabulated at specific incident energy points that are implemented in the THERMR module of the NJOY code. Since the implemented energy grid is not sufficiently fine, numerical integration in the GROUPR module to obtain the multi-group scattering matrix causes considerable error. By increasing the number of incident energy points from 59 (original) to 349 (improved), the accuracy of the multi-group scattering matrix is improved. Consequently, the discrepancy of neutron spectra in thermal energy range between MCNPX and that obtained by the NJOY multi-group cross-section is resolved. The above issue has considerable impact on thermal reactor analyses using multi-group cross-sections generated by the NJOY code and incorporation of the present improvement is recommended.

Validation of the Neutron Fluence Calculation on the VVER-440 RPV Support Structure

Abstract Measurements with activation detectors were carried out on Unit 4 of Kozloduy NPP in order to validate the fluence calculation data for the RPV support structure. Irradiation of iron, copper, and niobium detectors was performed during the 17th fuel cycle. The neutron fluence on the support structure and the activities of irradiated detectors were calculated by the three-dimensional transport code TORT with BGL440 multigroup cross section library. The history of local power distribution in the reactor core was taken into account. The measured and calculated induced activities are in good agreement in the area of the support structure. The calculated fluence evaluation in this area is conservative.

Neutron analysis of spent fuel storage installation using parallel computing and advance discrete ordinates and Monte Carlo techniques

In the United States, the Nuclear Waste Policy Act of 1982 mandated centralised storage of spent nuclear fuel by 1988. However, the Yucca Mountain project is currently scheduled to start accepting spent nuclear fuel in 2010. Since many nuclear power plants were only designed for -10 y of spent fuel pool storage, > 35 plants have been forced into alternate means of spent fuel storage. In order to continue operation and make room in spent fuel pools, nuclear generators are turning towards independent spent fuel storage installations (ISFSIs). Typical vertical concrete ISFSIs are -6.1 m high and 3.3 m in diameter. The inherently large system, and the presence of thick concrete shields result in difficulties for both Monte Carlo (MC) and discrete ordinates (SN) calculations. MC calculations require significant variance reduction and multiple runs to obtain a detailed dose distribution. SN models need a large number of spatial meshes to accurately model the geometry and high quadrature orders to reduce ray effects, therefore, requiring significant amounts of computer memory and time. The use of various differencing schemes is needed to account for radial heterogeneity in material cross sections and densities. Two P3, S12, discrete ordinate, PENTRAN (parallel environment neutral-particle TRANsport) models were analysed and different MC models compared. A multigroup MCNP model was developed for direct comparison to the SN models. The biased A3MCNP (automated adjoint accelerated MCNP) and unbiased (MCNP) continuous energy MC models were developed to assess the adequacy of the CASK multigroup (22 neutron, 18 gamma) cross sections. The PENTRAN SN results are in close agreement (5%) with the multigroup MC results; however, they differ by -20-30% from the continuous-energy MC predictions. This large difference can be attributed to the expected difference between multigroup and continuous energy cross sections, and the fact that the CASK library is based on the old ENDF/B-II library. Both MC and SN calculations were run in parallel on a BEOWULF PC-cluster (eight processors). Timing results indicate that the SN calculation yielded a detailed dose distribution at over 318,426 points in -164 h. Unbiased continuous energy MC required 214 h to calculate dose rates with a 1% relative error in only 18 regions on the surface of the cask. The biased A3MCNP calculations yields dose rates with -0.8% relative error in only 2.5 h on one processor. This study demonstrates that a parallel code, such as the 3-D parallel SN transport code, PENTRAN can solve a complex large problem, such as the storage cask, accurately and efficiently. Moreover, this calculation was performed on a relatively inexpensive PC-cluster. Possible inadequacies of the CASK cross section library still need to be evaluated.

Characterisation of radioactive waste products associated with plant decommissioning

The inventory of radioactivity that must be considered in the decommissioning of a typical 1000 MWe Spanish pressurised water reactor (PWR) was investigated as part of a generic plant decommissioning study. Analyses based on DORT models (in both R-Z and R-theta geometries) were used with representative plant operating history and core power distribution data in defining the expected neutron environment in regions near the reactor core. The activation analyses were performed by multiplying the DORT scalar fluxes by energy-dependent reaction cross sections (based on ENDF/B-VI data) to generate reaction rates on a per atom basis. The results from the ORIGEN2 computer code were also used for determining the activities associated with certain nuclides where multi-group cross section data were not available. In addition to the bulk material activation of equipment and structures near the reactor, the activated corrosion-product (or 'crud') deposits on system and equipment surfaces were considered. The projected activities associated with these sources were primarily based on plant data and experience from operating PWR plants.

05/01337 The experimental investigation of the impact of a particle or a rigid body on a cylindrical shell

HTR-10 is a 10 MWt prototype pebble-bed reactor (PBR) that presents a doubly heterogeneous geometry for neutronics calculations. An appropriate unit-cell treatment for the associated fuel elements is vital for creating problem-dependent multigroup cross sections. Considering four unit-cell options for resonance self-shielding correction in SCALE6, a series of HTR-10 core models were established using the CSAS6 sequence to systematically investigate how they affected the computational accuracy and efficiency of PBR criticality calculations. Three core configurations, which ranged from simplified infinite lattices to a detailed geometry, were examined. Based on the same ENDF/B-VII.0 cross-section library, multigroup results were evaluated by comparing with continuous-energy SCALE6/CSAS6 and MCNP5 calculations. The comparison indicated that the INFHOMMEDIUM results overestimated the effective multiplication factor (keff) by about 2800 pcm, whereas the LATTICECELL and MULTIREGION treatments overestimated keff values with similar biases at approximately 470–680 pcm. The DOUBLEHET results attained further improvement, reducing the keff overestimation to approximately 280 pcm. The comparison yielded two unexpected problems from using SCALE6/CSAS6 in HTR-10 criticality calculations. In particular, the continuous-energy CSAS6 calculations in this study present a non-negligible discrepancy with MCNP5, potentially causing a keff value overestimate of approximately 680 pcm. Notably, using a cell-weighted mixture instead of an explicit model of individual TRISO particles in the pebble fuel zone does not shorten the CSAS6 computation time in the high-fidelity HTR-10 model because of the presence of graphite balls and the complex modeling of peripheral reflectors.