Results 1 - 10 of 55
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[en] Bayesian methods are known for treating the so-called data re-assimilation. The Bayesian inference applied to core physics allows us to get a new adjustment of nuclear data using the results of integral experiments. This theory leading to reassimilation encompasses a broader approach. In previous papers, new methods have been developed to calculate the impact of nuclear and manufacturing data uncertainties on neutronics parameters. Usually, adjustment is performed step by step with one parameter and one experiment by batch. In this document, we rewrite Orlov theory to extend to multiple experimental values and parameters adjustment. We found that the multidimensional system expression looks like can be written as the mono-dimensional system in a matrix form. In this extension, correlation terms appears between experimental processes (manufacturing and measurements) and we discuss how to fix them. Then formula are applied to the extension to the Boltzmann/Bateman coupled problem, where each term could be evaluated by computing depletion uncertainties, studied in previous papers. (authors)
[en] Random sampling methods are used for nuclear data (ND) uncertainty propagation, often in combination with the use of Monte Carlo codes (e.g., MCNP). One example is the Total Monte Carlo (TMC) method. The standard way to visualize and interpret ND covariances is by the use of the Pearson correlation coefficient: ρ = cov(x,y)/σx*σy, where x or y can be any parameter dependent on ND. The spread in the output, σ, has both an ND component, σND, and a statistical component, σstat. The contribution from σstat decreases the value of ρ, and hence it underestimates the impact of the correlation. One way to address this is to minimize σstat by using longer simulation run-times. Alternatively, as proposed here, a so-called fast correlation coefficient is used: ρfast = [cov(x,y) - cov(xstat,ystat)]/[√(σx2 - σxstat2)*√(σy2-σystat2)]. In many cases, cov(xstat,ystat) can be assumed to be zero. The paper explores 3 examples: a synthetic data study, correlations in the NRG High Flux Reactor spectrum, and the correlations between integral criticality experiments. It is concluded that the use of ρ underestimates the correlation. The impact of the use of ρfast is quantified, and the implication of the results is discussed. (authors)
[en] This paper presents verification of the PARTISN5.97 code for several one-dimensional benchmark problems with analytic keff eigenvalue and eigenfunction solutions to the neutron transport equation in several geometries. Verification checks that the implemented code precisely reflects the intended calculations and that these calculations have been executed correctly, while validation compares the accuracy of these calculated results usually with experimental data. The motivation for this analysis was in verification of the sophisticated transport theory algorithms when applied to keff calculation of the slab, cylindrical, and spherical geometries with one-media and one-energy group, including anisotropic scattering. The infinite slab with finite thickness problem was also extended to two-energy group problem using anisotropic P1 scattering matrix. The selected benchmarks were chosen to cover problems with simple geometry, few energy groups, and simplified (linearly anisotropic) scattering models, for which analytical solution exits. The macroscopic neutron cross sections, giving reasonable representation of materials used, were extracted from the literature results so they are not general-purpose cross sections for predicting criticality experiments, but are rather used to verify algorithm performance. Various characteristics of deterministic code numerics can also be investigated using these benchmark problems, e.g. space and angle representation, Legendre expansion order, convergence acceleration techniques, and so on. For that purpose, we have used PARTISN5.97 code package, which is a modular computer program designed to solve the time-independent or dependent multigroup discrete ordinates (SN) form of the Boltzmann transport equation in several different geometries. The SN form of approximation is used for treating the angular variation of the particle distribution, while several spatial differencing options use computational mesh which may consist of either a standard orthogonal mesh or a block adaptive orthogonal mesh. Both inner and outer iterations can be accelerated using the diffusion or transport synthetic acceleration methods. The obtained PARTISN5.97 eigenvalue results showed a good agreement with referenced analytical benchmark test set.(author).
[en] We investigated a multi-layer structure for a broadband coherent perfect absorber (CPA). The transfer matrix method (TMM) is useful for analyzing the optical properties of structures and optimizing multi-layer structures. The broadband CPA strongly depends on the phase of the light traveling in one direction and the light reflected within the structure. The TMM simulation shows that the absorption bandwidth is increased by 95% in a multi-layer CPA compared to that in a single-layer CPA.
[en] Highlights: • A conjoint variational formulation based on discontinuous finite elements approach for PN neutron transport equation has been presented. • The spatial dependence of the even-parity and odd-parity angular flux has been modeled by discontinuous finite element method. • A new computer code, DISFENT, has been developed which have capability to solve neutron transport equation in 1D and 2D geometry. • An adaptive mesh-refinement approach for the discontinuous finite element solution has been implemented. - Abstract: A family of variational principles based on discontinuous finite element for solving the transport equation is considered. Furthermore in this paper the adaptive h-refinement approach based on conjoint variational formulation has been presented. The conjoint maximum principle derived, not only ensures global particle conservation for the whole system but also a local neutron balance for every element and every moment of directional. The spatial dependence of the even-parity and odd-parity angular flux has been modeled using discontinuous finite element method. The efficacy of the method is assessed by comparing the number of required meshes which is necessary using continuous finite element method to indicate what savings can be achieved by discontinuous finite element strategy. In order to calculate the average element flux by this method, a new computing code, DISFENT, has been developed which has capability to solve neutron transport equation in 2D geometry. Coarser meshes efficiency tested along with several well-known neutron transport problems and the numerical results are presented to confirm theoretical results and demonstrate the performance of the proposed method while is coupled with adaptive refinement.
[en] The 3-D steady-state SN neutron-gamma transport theory code ATES3 developed at BARC can be utilized for external source problems such as shielding analysis. A brief description on the use of ATES3 and its validation for international shielding type benchmarks problems is presented in the paper. (author)
[en] Kinetic equations appear in a lot of domains from astrophysics to nuclear energy, to semi-conductor technology or spatial flights. In the CEA (Alternative Energies and Atomic Energy Commission) the Boltzmann equation was studied and as this kinetic equation cannot be solved directly, the approximation of the diffusion equation applied to neutron transport was developed for dimensioning the first nuclear reactor cores. (A.C.)
[en] Evaluating uncertainties on nuclear parameters such as reactivity is a major issue for conception of nuclear reactors. These uncertainties mainly come from the lack of knowledge on nuclear and technological data. Today, the common method used to propagate nuclear data uncertainties is Total Monte Carlo but this method suffers from a long computation time. Moreover, it requires as many calculations as uncertainties sought. An other method for the propagation of the nuclear data uncertainties consists in using the standard perturbation theory (SPT) to calculate reactivity sensitivity to the concerned nuclear data. In such a method, sensitivities are combined with a priori nuclear data covariance matrices such as the COMAC set developed by CEA. The goal of this work is to calculate sensitivities by SPT with the full core diffusion code CRONOS2 for propagation uncertainties at the core level. In this study, COMAC nuclear data uncertainties have been propagated on the BEAVRS benchmark using a two-step APOLLO2/CRONOS2 scheme, where APOLLO2 is the lattice code used to resolve the Boltzmann equation within assemblies using a high number of energy groups, and CRONOS2 is the code resolving the 3D full core diffusion equation using only four energy groups. A module implementing the SPT already exists in the APOLLO2 code but computational cost would be too expensive in 3D on the whole core. Consequently, an equivalent procedure has been created in CRONOS2 code to allow full-core uncertainty propagation. The main interest of this procedure is to compute sensitivities on reactivity within a reduced turnaround time for a 3D modeled core, even after fuel depletion. In addition, it allows access to all sensitivities by isotope, reaction and energy group in a single calculation. Reactivity sensitivities calculated by this procedure with four energy groups are compared to reference sensitivities calculated by the iterated fission probability (IFP) method in Monte Carlo code. For the purpose of the tests, dedicated covariance matrix have been created by condensation from 49 to 4 groups of the COMAC matrix. In conclusion, sensitivities calculated by CRONOS2 agree with the sensitivities calculated by the IFP method, which validates the calculation procedure, allowing analysis to be done quickly. In addition, reactivity uncertainty calculated by this method is close to values found for this type of reactor. (authors)
[en] Both the availability and the quality of covariance data improved over the last years and many recent cross-section evaluations, such as JENDL-4.0, ENDF/B-VII.1, JEFF-3.3, etc. include new covariance data compilations. However, several gaps and inconsistencies still persist. Although most modern nuclear data evaluations are based on similar (or even same) sets of experimental data, and the agreement in the results obtained using different cross-sections is reasonably good, larger discrepancies were observed among the corresponding covariance data. This suggests that the differences in the covariance matrix evaluations reflect more the differences in the (mathematical) approaches used and possibly in the interpretations of the experimental data, rather than the different nuclear experimental data used. Furthermore, 'tuning' and adjustments are often used in the process of nuclear data evaluations. In principle, if adjustments or 'tunings' are used in the evaluation of cross-section then the covariance matrices should reflect the cross-correlations introduced in this process. However, the presently available cross-section covariance matrices include practically no cross-material correlation terms, although some evidence indicate that tuning is present. Experience in using covariance matrices of different origin (such as JEFF, JENDL, ENDF, TENDL, SCALE, etc.) in sensitivity and uncertainty analysis of vast list of cases ranging from fission to fusion and from criticality, kinetics and shielding to adjustment applications are presented. The status of the available covariance and future needs in the areas including secondary angular and energy distributions is addressed. (author)
[en] Highlights: • Neutron lattice Boltzmann method is presented for neutron transport problem. • Neutron diffusion equation is recovered via Chapman-Enskog expansion. • Neutron relaxation time is discussed and the influencing factors are studied. • Streaming-based SAMR technique is studied for LBM. - Abstract: Simulation of neutron transport problem is the kernel of nuclear reactor physics, whose application, however, is limited by the exorbitant computational cost and complex geometry structure. This paper presents a lattice Boltzmann method (LBM) for multi-group neutron transport process and proposes a streaming-based block-structured adaptive-mesh-refinement (SSAMR) technique. The neutron lattice Boltzmann equation is deduced from the neutron transport equation and the macroscopic neutron diffusion equation can be recovered from neutron lattice Boltzmann equation via the Chapman-Enskog expansion, which makes the kinetic significance of lattice Boltzmann equation clearly. The significance of relaxation time for neutron LBM is further discussed for the first time, and the factors affecting the neutron relaxation process are studied deeply also. After establishing the neutron LBM, the SSAMR technique is applied to efficiently utilizing the computational resources of proposed LBM. To simply achieve the data communication between different meshes and eliminate the discontinuity of scalar neutron flux, a data exchange technique based on the streaming process of LBM is adopted. Simulation results show that the proposed LBM can be applied to solving neutron transport process in all dimensions, and the SSAMR technique can not only effectively reduce the computational cost, but also be easily implemented. This work may provide some new perspectives for solving the neutron transport process and a powerful thought for large and complex engineering calculation.