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[en] A linear-algebraic form of the equations of the method of characteristics, which is used to approximate the neutron transport equation, is obtained. It is shown on the basis of the obtained linear-algebraic form that the discrete form of the conjugate equation differs from the algebraically discrete problem constructed by linear-algebraic transformations of the discrete form of the normal problem. The reason for the discrepancy lies in the approximation of the volumes of the spatial cells in covering the working region by a network of characteristics. It is shown by means of test calculations that when the network of characteristics is refined the solution of the conjugate transport equation converges to the solution of the algebraically conjugate problem.
[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] 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] An algorithm for calculation of prompt fission neutron lifetimes in a nuclear reactor by the Monte Carlo method is described. Evaluation of the importance function is carried out with solution of the neutron transport equation without solving the adjoint equation. The results of the prompt neutron lifetime calculations performed within some critical experiments are presented and compared with the experimental results.
[en] The TITAN hybrid deterministic transport code is applied to the simulation of particle streaming in a nuclear power plant duct. A simple model is used consisting of a concrete duct emerging from the pressure vessel with an isotropic surface source with a U-235 fission spectrum located at the pressure vessel end. Multiple methods of simulating the duct using the TITAN code are considered to demonstrate the flexibility of the code and the advantages of TITAN's algorithms. These methods include a discrete ordinates (SN) calculation, a characteristics method calculation, and the use of a fictitious quadrature set with simplified ray-tracing. The TITAN code's results are compared with MCNP5 solutions. While all TITAN solutions are obtained in a shorter computation time than the MCNP5 solution, the TITAN solution with the fictitious quadrature set shows the largest speedup. (authors)
[en] By using the one-group and one-dimensional neutron transport equation, we discussed the effect of stochasticity on the criticality size and reactivity of a slab reactor. In our analysis we used a sufficiently simple stochasticity to obtain the exact results. It is shown that the stochasticity increased the reactivity and decreased the critical thickness and our conclusions agreed with the previous conclusions.
[en] This workshop was met by 30 participants. One major issue was how to assign an 'a priori' uncertainty to the trial spectrum used in spectrum adjustment techniques, or, more specifically, the need for a more rigorous and automated coupling of uncertainties into the radiation transport codes that are used to generate the a priori (trial) spectrum that is used in neutron spectrum adjustment approaches. Another important issue for the reactor dosimetry community is the lack of gamma dosimeters that facilitate the determination of the gamma spectrum in reactors. Many metrics for radiation effects are sensitive to photon as well as neutron damage mechanisms. There was discussion on the need for new multi-group neutron/gamma cross section libraries. While processing codes such as NJOY have been used to generate multi-group libraries based on most recent nuclear data evaluations, the energy group structure for the current collapsed-group cross section libraries has been tailored for use in light water reactors. It is not clear that this energy structure is appropriate for all applications supporting advanced reactor concepts. There was also discussion about support for continuous energy or point cross section libraries
[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.