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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Nuclear data uncertainty analysis for the generation IV gas-cooled fast reactor

For the European 2400 MW Gas-cooled Fast Reactor (GoFastR), this paper summarizes a priori uncertainties, i.e. without any integral experiment assessment, of the main neutronic parameters which were obtained on the basis of the deterministic code system ERANOS (Edition 2.2-N). JEFF-3.1 cross-sections were used in conjunction with the newest ENDF/B-VII.0 based covariance library (COMMARA-2.0) resulting from a recent cooperation of the Brookhaven and Los Alamos National Laboratories within the Advanced Fuel Cycle Initiative. The basis for the analysis is the original GoFastR concept with carbide fuel pins and silicon-carbide ceramic cladding, which was developed and proposed in the first quarter of 2009 by the 'French alternative energies and Atomic Energy Commission', CEA. The main conclusions from the current study are that nuclear data uncertainties of neutronic parameters may still be too large for this Generation IV reactor, especially concerning the multiplication factor, despite the fact that the new covariance library is quite complete; These uncertainties, in relative terms, do not show the a priori expected increase with bum-up as a result of the minor actinide and fission product build-up. Indeed, they are found almost independent of the fuel depletion, since the uncertainty associated with {sup 238}U inelastic scattering results largely dominating. This finding clearly supports the activities of Subgroup 33 of the Working Party on International Nuclear Data Evaluation Cooperation (WPEC), i.e. Methods and issues for the combined use of integral experiments and covariance data, attempting to reduce the present unbiased uncertainties on nuclear data through adjustments based on available experimental data. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2010

A Simplified HTTR Diffusion Theory Benchmark

The Georgia Institute of Technology (GA-Tech) recently developed a transport theory benchmark based closely on the geometry and the features of the HTTR reactor that is operational in Japan. Though simplified, the benchmark retains all the principal physical features of the reactor and thus provides a realistic and challenging test for the codes. The purpose of this paper is twofold. The first goal is an extension of the benchmark to diffusion theory applications by generating the additional data not provided in the GA-Tech prior work. The second goal is to use the benchmark on the HEXPEDITE code available to the INL. The HEXPEDITE code is a Green’s function-based neutron diffusion code in 3D hexagonal-z geometry. The results showed that the HEXPEDITE code accurately reproduces the effective multiplication factor of the reference HELIOS solution. A secondary, but no less important, conclusion is that in the testing against actual HTTR data of a full sequence of codes that would include HEXPEDITE, in the apportioning of inevitable discrepancies between experiment and models, the portion of error attributable to HEXPEDITE would be expected to be modest. If large discrepancies are observed, they would have to be explained by errors in the data fed into HEXPEDITE. Results based on a fully realistic model of the HTTR reactor are presented in a companion paper. The suite of codes used in that paper also includes HEXPEDITE. The results shown here should help that effort in the decision making process for refining the modeling steps in the full sequence of codes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Automated convergence detection in Monte Carlo criticality calculations using student's bridge statistics based on K{sub eff} or Shannon entropy

Monte Carlo (MC) criticality calculations are based on an iterative method. It requires a converged fission source distribution before beginning tallying the effective multiplication factor (K{sub eff}) or other quantities of interest. However, it is pretty difficult to locate on the run, the end of the source convergence and scores may be biased by an initial transient. This paper deals with a method that locates and suppresses the transient due to the initialization in an output series, applied here to K{sub eff} and Shannon entropy. It relies on modeling stationary series by an order 1 auto regressive process and applying statistical tests based on a Student Bridge statistics. It should be noticed that the initial transient suppression only aims at obtaining stationary output series and cannot guarantee any kind of convergence. The truncation method is applied on both K{sub eff} and Shannon entropy on three test cases. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2011

Study of a multi-beam accelerator driven thorium reactor

The primary advantages that accelerator driven systems have over critical reactors are: (1) Greater flexibility regarding the composition and placement of fissile, fertile, or fission product waste within the blanket surrounding the target, and (2) Potentially enhanced safety brought about by operating at a sufficiently low value of the multiplication factor to preclude reactivity induced events. The control of the power production can be achieved by vary the accelerator beam current. Furthermore, once the beam is shut off the system shuts down. The primary difference between the operation of an accelerator driven system and a critical system is the issue of beam interruptions of the accelerator. These beam interruptions impose thermo-mechanical loads on the fuel and mechanical components not found in critical systems. Studies have been performed to estimate an acceptable number of trips, and the value is significantly less stringent than had been previously estimated. The number of acceptable beam interruptions is a function of the length of the interruption and the mission of the system. Thus, for demonstration type systems and interruption durations of 1sec < t < 5mins, and t > 5mins 2500/yr and 50/yr are deemed acceptable. However, for industrial scale power generation without energy storage type systems and interruption durations of t < 1sec., 1sec < t < 10secs., 10secs < t < 5mins, and t > 5mins, the acceptable number of interruptions are 25000, 2500, 250, and 3 respectively. However, it has also been concluded that further development is required to reduce the number of trips. It is with this in mind that the following study was undertaken. The primary focus of this study will be the merit of a multi-beam target system, which allows for multiple spallation sources within the target/blanket assembly. In this manner it is possible to ameliorate the effects of sudden accelerator beam interruption on the surrounding reactor, since the remaining beams will still be supplying source neutrons. The proton beam will be assumed to have an energy of 1 GeV, and the target material will be natural lead, which will also be the coolant for the reactor assembly. Three proton beam arrangements will be considered, first a single beam (the traditional arrangement) with an entry at the assembly center, two more options will consist of three and six entry locations. The reactor fuel assembly parameters will be based on those of the S-PRISM fast reactor proposed by GE, and the fuel composition and type will be based on that proposed by Aker Solutions for use in their accelerator driven thorium reactor. The following table summarizes the parameters to be used in this study. The isotopic composition of the fertile material is 100% Th-232, and the plutonium isotopic distribution corresponds to that characteristic of the discharge from a typical LWR, following five years of decay. Thus, the isotopic distribution for the plutonium is; Pu-238 2.5%, Pu-239 53.3%, Pu-240 25.1%, Pu-241 11.8%, and Pu-242 7.3%.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2012

Benefits of the delta K of depletion benchmarks for burnup credit validation

Pressurized Water Reactor (PWR) burnup credit validation is demonstrated using the benchmarks for quantifying fuel reactivity decrements, published as 'Benchmarks for Quantifying Fuel Reactivity Depletion Uncertainty,' EPRI Report 1022909 (August 2011). This demonstration uses the depletion module TRITON available in the SCALE 6.1 code system followed by criticality calculations using KENO-Va. The difference between the predicted depletion reactivity and the benchmark's depletion reactivity is a bias for the criticality calculations. The uncertainty in the benchmarks is the depletion reactivity uncertainty. This depletion bias and uncertainty is used with the bias and uncertainty from fresh UO{sub 2} critical experiments to determine the criticality safety limits on the neutron multiplication factor, k{sub eff}. The analysis shows that SCALE 6.1 with the ENDF/B-VII 238-group cross section library supports the use of a depletion bias of only 0.0015 in delta k if cooling is ignored and 0.0025 if cooling is credited. The uncertainty in the depletion bias is 0.0064. Reliance on the ENDF/B V cross section library produces much larger disagreement with the benchmarks. The analysis covers numerous combinations of depletion and criticality options. In all cases, the historical uncertainty of 5% of the delta k of depletion ('Kopp memo') was shown to be conservative for fuel with more than 30 GWD/MTU burnup. Since this historically assumed burnup uncertainty is not a function of burnup, the Kopp memo's recommended bias and uncertainty may be exceeded at low burnups, but its absolute magnitude is small. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2011

An Approach for Validating Actinide and Fission Product Burnup Credit Criticality Safety Analyses-Isotopic Composition Predictions

The expanded use of burnup credit in the United States (U.S.) for storage and transport casks, particularly in the acceptance of credit for fission products, has been constrained by the availability of experimental fission product data to support code validation. The U.S. Nuclear Regulatory Commission (NRC) staff has noted that the rationale for restricting the Interim Staff Guidance on burnup credit for storage and transportation casks (ISG-8) to actinide-only is based largely on the lack of clear, definitive experiments that can be used to estimate the bias and uncertainty for computational analyses associated with using burnup credit. To address the issues of burnup credit criticality validation, the NRC initiated a project with the Oak Ridge National Laboratory to (1) develop and establish a technically sound validation approach for commercial spent nuclear fuel (SNF) criticality safety evaluations based on best-available data and methods and (2) apply the approach for representative SNF storage and transport configurations/conditions to demonstrate its usage and applicability, as well as to provide reference bias results. The purpose of this paper is to describe the isotopic composition (depletion) validation approach and resulting observations and recommendations. Validation of the criticality calculations is addressed in a companion paper at this conference. For isotopic composition validation, the approach is to determine burnup-dependent bias and uncertainty in the effective neutron multiplication factor (keff) due to bias and uncertainty in isotopic predictions, via comparisons of isotopic composition predictions (calculated) and measured isotopic compositions from destructive radiochemical assay utilizing as much assay data as is available, and a best-estimate Monte Carlo based method. This paper (1) provides a detailed description of the burnup credit isotopic validation approach and its technical bases, (2) describes the application of the approach for representative pressurized water reactor and boiling water reactor safety analysis models to demonstrate its usage and applicability, (3) provides reference bias and uncertainty results based on a quality-assurance-controlled prerelease version of the Scale 6.1 code package and the ENDF/B-VII nuclear cross section data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2011

Monte Carlo Criticality Methods and Analysis Capabilities in SCALE

This paper describes the Monte Carlo codes KENO V.a and KENO-VI in SCALE that are primarily used to calculate multiplication factors and flux distributions of fissile systems. Both codes allow explicit geometric representation of the target systems and are used internationally for safety analyses involving fissile materials. KENO V.a has limiting geometric rules such as no intersections and no rotations. These limitations make KENO V.a execute very efficiently and run very fast. On the other hand, KENO-VI allows very complex geometric modeling. Both KENO codes can utilize either continuous-energy or multigroup cross-section data and have been thoroughly verified and validated with ENDF libraries through ENDF/B-VII.0, which has been first distributed with SCALE 6. Development of the Monte Carlo solution technique and solution methodology as applied in both KENO codes is explained in this paper. Available options and proper application of the options and techniques are also discussed. Finally, performance of the codes is demonstrated using published benchmark problems.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2015

Irradiation campaign in the EOLE critical facility of fiber optic Bragg gratings dedicated to the online temperature measurement in zero power research reactors

The control of temperature during operation of zero power research reactors participates to the overall control of experimentation conditions and reveals itself of a major importance more especially when measuring small multiplication factor variations. Within the framework of the refurbishment of the MASURCA facility, the development of a new temperature measurement system based on the optical fiber Bragg grating (FBG) technology is under consideration. In a first step, a series of FBGs is irradiated in the EOLE critical facility with the aim to select the most appropriate. Online temperature measurements are performed during a set of irradiations that should allow reaching a fast neutron fluence of some 10{sup 14} n.cm{sup -2}. The results obtained, more especially the Bragg wavelength shifts during the irradiation campaign, are discussed in this paper and compared to data from standard PT100 temperature sensors to highlight possible radiation effects on sensor performances. Work to be conducted during the second step of the project, aiming to a feasibility demonstration using a MASURCA assembly, is also presented. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2017

Extension of the DIF3D Code for Molten Salt Reactor Analysis

The molten salt reactor (MSR) with the fuel dissolved into the liquid salt has been selected as one of the six Generation-IV reactors due to its excellent characteristics in the aspects of sustainability, economy, passive safety, and resource utilization. In a MSR, the fuel salt is circulated throughout the whole system and thus some of delayed neutron precursors generated in the core decay in position of low importance or even out of the core. As a result, the multiplication factor (k-eff) of MSR is smaller than that of a reactor of stationary fuel when all the other conditions are same. Therefore, the neutronics code developed for stationary fuel cannot be applied directly to MSR analysis. In this paper, we describe the extension and application of the DIF3D code to MSR neutronics analysis. The DIF3D code system is a multi-group steady-state neutron diffusion and transport theory solver. It provides three flux solution options: finite-difference diffusion theory, nodal diffusion theory, and variational nodal transport theory methods. Eigenvalue, adjoint, fixed source and criticality (concentration) search problems are permitted. The DIF3D code has recently been modified to model the flowing fuel. To verify the new capability of DIF3D, the MSFR [4] core was analyzed with a wide range of velocity field of fuel salt and time spent outside of the core.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2017

An assessment of total depletion uncertainties for a GBC-32 dry storage cask with PLUS7 fuels using Monte Carlo sampling and two-way ANOVA F-test

It is important to accurately evaluate depletion uncertainties that exist due to the limitations of a computer code on accuracy in a nuclear depletion calculation for criticality safety analysis. In this work, the bias and bias uncertainty in the effective neutron multiplication factor (k{sub eff}) for the generic 32 PWR-assembly burnup credit (GBC-32) cask system were assessed using the Monte Carlo uncertainty sampling method for three different burnups and the isotopic biases and uncertainties obtained with the calculated and measured isotopic concentrations. The PLUS7 used nuclear fuel assemblies discharged from the Hanbit Nuclear Power Plant Unit 3 were assumed to be loaded into the GBC-32 cask. In addition, the statistical F-test in the two-way analysis of variance (ANOVA) was suggested to efficiently estimate the statistically converged total depletion uncertainty in k{sub eff}, with a significant reduction of computing efforts in the Monte Carlo criticality calculations, and it was applied to the GBC-32 cask system after a sensitivity analysis was performed to select the important nuclides having significant contributions to the total depletion uncertainty. With the statistical F-tests in the two-way ANOVA, 100 criticality calculations were needed to get a statistically converged total depletion uncertainty for 10 and 30 GWD/MTU, while 120 criticality calculations were needed for 50 GWD/MTU. (authors)

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2011

MONTE-CARLO BURNUP CALCULATION UNCERTAINTY QUANTIFICATION AND PROPAGATION DETERMINATION

MONTEBURNS is a Monte-Carlo depletion routine utilizing MCNP and ORIGEN 2.2. Uncertainties exist in the MCNP transport calculation, but this information is not passed to the depletion calculation in ORIGEN or saved. To quantify this transport uncertainty and determine how it propagates between burnup steps, a statistical analysis of a multiple repeated depletion runs is performed. The reactor model chosen is the Oak Ridge Research Reactor (ORR) in a single assembly, infinite lattice configuration. This model was burned for a 25.5 day cycle broken down into three steps. The output isotopics as well as effective multiplication factor (k-effective) were tabulated and histograms were created at each burnup step using the Scott Method to determine the bin width. It was expected that the gram quantities and k-effective histograms would produce normally distributed results since they were produced from a Monte-Carlo routine, but some of results do not. The standard deviation at each burnup step was consistent between fission product isotopes as expected, while the uranium isotopes created some unique results. The variation in the quantity of uranium was small enough that, from the reaction rate MCNP tally, round off error occurred producing a set of repeated results with slight variation. Statistical analyses were performed using the {chi}{sup 2} test against a normal distribution for several isotopes and the k-effective results. While the isotopes failed to reject the null hypothesis of being normally distributed, the {chi}{sup 2} statistic grew through the steps in the k-effective test. The null hypothesis was rejected in the later steps. These results suggest, for a high accuracy solution, MCNP cell material quantities less than 100 grams and greater kcode parameters are needed to minimize uncertainty propagation and minimize round off effects.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2010

Deterministic Modeling of the High Temperature Test Reactor with DRAGON-HEXPEDITE

The Idaho National Laboratory (INL) is tasked with the development of reactor physics analysis capability of the Next Generation Nuclear Power (NGNP) project. In order to examine the INL’s current prismatic reactor analysis tools, the project is conducting a benchmark exercise based on modeling the High Temperature Test Reactor (HTTR). This exercise entails the development of a model for the initial criticality, a 19 fuel column thin annular core, and the fully loaded core critical condition with 30 fuel columns. Special emphasis is devoted to physical phenomena and artifacts in HTTR that are similar to phenomena and artifacts in the NGNP base design. The DRAGON code is used in this study since it offers significant ease and versatility in modeling prismatic designs. DRAGON can generate transport solutions via Collision Probability (CP), Method of Characteristics (MOC) and Discrete Ordinates (Sn). A fine group cross-section library based on the SHEM 281 energy structure is used in the DRAGON calculations. The results from this study show reasonable agreement in the calculation of the core multiplication factor with the MC methods, but a consistent bias of 2-3% with the experimental values is obtained. This systematic error has also been observed in other HTTR benchmark efforts and is well documented in the literature. The ENDF/B VII graphite and U 235 cross sections appear to be the main source of the error. The isothermal temperature coefficients calculated with the fully loaded core configuration agree well with other benchmark participants but are 40% higher than the experimental values. This discrepancy with the measurement partially stems from the fact that during the experiments the control rods were adjusted to maintain criticality, whereas in the model, the rod positions were fixed. In addition, this work includes a brief study of a cross section generation approach that seeks to decouple the domain in order to account for neighbor effects. This spectral interpenetration is a dominant effect in annular HTR physics. This analysis methodology should be further explored in order to reduce the error that is systematically propagated in the traditional generation of cross sections.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2017

Equipment for subcriticality monitoring by pulse method - 240

At the present time methods and means of determining, evaluating, and monitoring the effective neutron multiplication factor or the subcriticality are becoming very important for validating and monitoring nuclear safety in connection with the accumulation of a large number of spent fuel assemblies and the transition to a more tight mode of their storage arrangement in the spent-fuel pools of NPP. Pulse method is an effective subcriticality monitoring tool for subcritical reactors and spent nuclear fuel storages. This method is based on the use neutron generator, fission chambers and instrumentation for data acquisition and processing. The measurement and control equipment was designed. It allows: neutron pulses generation with specified parameters; neutron flux response monitoring by measuring the count rate at predetermined set of sequential time intervals; data transmitting to the personal computer; data processing and subcriticality calculation; self diagnostics and health monitoring; data recording, archiving and storage. The special device is proposed to check the electronic equipment. This device simulates a signal of a neutron detector counting rate after neutron generator pulses appear. The paper presents hardware structure and composition, specification and software of the control unit, which provides neutron generator operation, data acquisition and processing. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2011

Conceptual design of minor actinides burner with an accelerator-driven subcritical system.

In the environmental impact study of the Yucca Mountain nuclear waste repository, the limit of spent nuclear fuel (SNF) for disposal is assessed at 70,000 metric tons of heavy metal (MTHM), among which 63,000 MTHM are the projected SNF discharge from U.S. commercial nuclear power plants though 2011. Within the 70,000 MTHM of SNF in storage, approximately 115 tons would be minor actinides (MAs) and 585 tons would be plutonium. This study describes the conceptual design of an accelerator-driven subcritical (ADS) system intended to utilize (burn) the 115 tons of MAs. The ADS system consists of a subcritical fission blanket where the MAs fuel will be burned, a spallation neutron source to drive the fission blanket, and a radiation shield to reduce the radiation dose to an acceptable level. The spallation neutrons are generated from the interaction of a 1 GeV proton beam with a lead-bismuth eutectic (LBE) or liquid lead target. In this concept, the fission blanket consists of a liquid mobile fuel and the fuel carrier can be LBE, liquid lead, or molten salt. The actinide fuel materials are dissolved, mixed, or suspended in the liquid fuel carrier. Therefore, fresh fuel can be fed into the fission blanket to adjust its reactivity and to control system power during operation. Monte Carlo analyses were performed to determine the overall parameters of an ADS system utilizing LBE as an example. Steady-state Monte Carlo simulations were studied for three fission blanket configurations that are similar except that the loaded amount of actinide fuel in the LBE is either 5, 7, or 10% of the total volume of the blanket, respectively. The neutron multiplication factor values of the three configurations are all approximately 0.98 and the MA initial inventories are each approximately 10 tons. Monte Carlo burnup simulations using the MCB5 code were performed to analyze the performance of the three conceptual ADS systems. Preliminary burnup analysis shows that all three conceptual ADS systems consume about 1.2 tons of actinides per year and produce 3 GW thermal power, with a proton beam power of 25 MW. Total MA fuel that would be consumed in the first 10 years of operation is 9.85, 11.80, or 12.68 tons, respectively, for the systems with 5, 7, or 10% actinide fuel particles loaded in the LBE. The corresponding annual MA fuel transmutation rate after reaching equilibrium at 10 years of operation is 0.83, 0.94, or 1.02 tons/year, respectively. Assuming that the ADS systems can be operated for 35 full-power years, the total MAs consumed in the three ADS systems are 30.6, 35.3, and 37.2 tons, respectively. For the three configurations, it is estimated that 3.8, 3.3, or 3.1 ADS system units are required to utilize the entire 115 tons of MA fuel in the SNF inventory, respectively.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2013

Minimising the error in eigenvalue calculations involving the Boltzmann transport equation using goal-based adaptivity on unstructured meshes

This article presents a method for goal-based anisotropic adaptive methods for the finite element method applied to the Boltzmann transport equation. The neutron multiplication factor, k{sub eff}, is used as the goal of the adaptive procedure. The anisotropic adaptive algorithm requires error measures for k{sub eff} with directional dependence. General error estimators are derived for any given functional of the flux and applied to k{sub eff} to acquire the driving force for the adaptive procedure. The error estimators require the solution of an appropriately formed dual equation. Forward and dual error indicators are calculated by weighting the Hessian of each solution with the dual and forward residual respectively. The Hessian is used as an approximation of the interpolation error in the solution which gives rise to the directional dependence. The two indicators are combined to form a single error metric that is used to adapt the finite element mesh. The residual is approximated using a novel technique arising from the sub-grid scale finite element discretisation. Two adaptive routes are demonstrated: (i) a single mesh is used to solve all energy groups, and (ii) a different mesh is used to solve each energy group. The second method aims to capture the benefit from representing the flux from each energy group on a specifically optimised mesh. The k{sub eff} goal-based adaptive method was applied to three examples which illustrate the superior accuracy in criticality problems that can be obtained.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

Adaptive Sparse-Grid Stochastic Collocation Uncertainty Quantification Convergence for Multigroup Diffusion

Advanced methods in uncertainty quantification for numerical models in computational physics continue to gain acceptance in nuclear modeling. Previously, the efficiency of sparse-grid stochastic collocation in comparison with Monte Carlo for uncertainty quantification through convergence studies was demonstrated. An adaptive method for anisotropic sparse grid collocation and its convergence compared to previous efforts is considered. The physical system in consideration is a two-dimensional quarter-core reactor, consisting of 5 materials distributed in 121 regions. The two-group neutron diffusion criticality approximation is solved. Vacuum boundaries are applied on the top and right, and reflecting boundaries on the bottom and left. The material cross sections, neutron multiplication factors, and diffusion coefficients are potential sources of uncertainty. Uniformly-distributed uncertainty within 5% of the reference values is introduced for material properties. The distribution of the uncertain parameters make up the uncertainty space Γ included in R{sup N}, where N is the number of uncertain parameters. The input parameter uncertainties are independently distributed. As expected, the convergence of Monte Carlo on the benchmark as a function of computational solves is nearly linear and lethargic compared to the other methods. The static isotropic index set, in which each input dimension is treated with equal importance, converges much more efficiently than Monte Carlo, but lacks the benefit of emphasizing some dimensions over others. The anisotropic case is most efficient, where first-order sensitivity information was used to determine anisotropic weights for polynomials to use in the polynomial chaos expansion. Interestingly, the adaptive algorithm converges slightly less efficiently than the anisotropic case, while still performing better than the isotropic case. Because the adaptive case has to determine the importance of each input dimension, it occasionally predicts inaccurately and wastes computation solves compared to the more ideal anisotropic case. However, in circumstances when an ideal anisotropy is not understood a priori, the adaptive algorithm may be optimally efficient in representing the original model. Given the potential loss of efficiency when using a poorly-chosen anisotropic weighting, the adaptive algorithm may be an effective choice for initial uncertainty quantification in problems with a low-dimensionality input space. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2015

Quantification of calculation accuracy for code systems in burn-up credit applications by recalculations of experimental data - 14480

For application in criticality safety, numerical code systems require profound validation against experimental data. In terms of burn-up credit, this refers to the inventory determination as well as the subsequent criticality calculation. Within this framework, a dedicated, conservative estimation of uncertainties, bias and bias uncertainties for the resulting calculated multiplication factor k{sub eff} is indispensable. However, measures to reduce excess conservatism may become desirable, depending on the application case. For this reason GRS implemented a methodology to validate a calculation code system for criticality safety analyses for systems with irradiated nuclear fuel. The work at hand demonstrates this methodology by means of the GRS home-built inventory determination system KENOREST and ORNL's well-known SCALE 6 CSASS criticality safety calculation sequence. A number of 40 radiochemical analysis samples taken from SFCOMPO and elsewhere have been calculated to derive isotopic correction factors in different ways, depending on the required level of conservatism and the calculational efforts to be carried out. This includes bounding methods as well as different Monte Carlo sampling approaches. Furthermore, from the ICSBEP a number of 515 critical benchmark experiment configurations comprising water moderated low enriched UO{sub 2} fuel rods and water moderated mixed oxide (MOX) fuel rods have been selected and evaluated. Important absorber and structure materials are also covered. Various trending and sensitivity and uncertainty analysis methods have been applied, again to derive conservative estimates on the various contributions to k{sub eff} uncertainties. The overall methodology is applicable to low enriched, water moderated PWR uranium dioxide fuels in a burn-up range of about 10 to 60 GWd/tHM, and validates the reactivity contributions of the major uranium and plutonium isotopes. The methodology itself has no limitation which requires the exclusion of further isotopes as e.g. fission products. However, its application is constrained by the experimental database being publicly available. After the potential provision of an extended database in the future, the range of applicability can easily be extended to more nuclides. In addition, it is not limited to the code systems being used here but can also be applied using different numerical tools. For a generic PWR spent fuel pool rack and different enrichment and burn-up combinations, the impact of the current level of validation on k{sub eff} is demonstrated and quantified. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

Application of Variance Reduction Techniques in RMC Burnup and Thermal-Hydraulic Coupled Calculation

In reactor analog simulation, the Monte Carlo method has relatively high fidelity since it can reduce calculation errors resulting from using approximation methods by describing complex geometry and neutron energy spectra. The Monte Carlo method is, in essence, a stochastic simulation of the neutron transport process, and statistical uncertainty of all the computed results must be provided. In large-scale reactor computation, this method can accurately estimate integral quantities such as the effective multiplication factor (K{sub eff}), and it can limit the uncertainty within an acceptable range via reasonably selecting simulation particles. Nevertheless, it faces great challenges in estimating local quantities like neutron flux and fission power, with uncertainty of estimators beyond acceptance. To decrease the uncertainty of local quantities by increasing simulation particles may cost much time and reduce efficiency. The main reasons are as follows. Firstly, the scale of reactors is so large that common pressurized water reactors have tens of thousands of lattice cells; secondly, uneven distribution of neutron flux and fission power causes uneven distribution of uncertainty. Smith K. puts forward the 95/95 principle to estimate whether uncertainty calculated with Monte Carlo Code satisfies the requirement. According to the principle, with a confidence level of 95%, statistical errors of power density in more than 95% of the regions should be less than 1%. To meet the requirement of the principle, the uniform fission site (UFS) method is raised currently. UFS aims at redistributing fission sources to uniformize the fission source sampling, which can make statistical variance distribution more uniform. This method, which is easy to use, will not obviously increase computation time. Many studies show that UFS has a good variance reduction effect in Monte Carlo criticality calculation, but less attention is paid to its performance in burnup calculation and thermal-hydraulic coupled calculation. Uncertainty arising from the Monte Carlo method has a large impact on burnup calculation and thermal-hydraulic coupled calculation. Variance propagates between burnup steps and between iterative steps of coupled calculation, which causes asymmetry of results of the physical symmetrical regions and instability of coupled iterative convergence errors. To further verify the effect of UFS, this study uses it in the RMC (the Reactor Monte Carlo code) burnup calculation module and the neutronics/thermohydraulics coupled calculation module, and conducts two-dimensional pressurized water reactor burnup calculation and BEAVRS benchmark thermalhydraulic coupled calculation. In this way, it verifies the improvement effect of UFS on variance propagation. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗