[en] Here in this paper, two-level methods for solving transport problems in one-dimensional slab geometry based on the quasi-diffusion (QD) method are developed. A linear discontinuous finite element method (LDFEM) is derived for the spatial discretization of the low-order QD (LOQD) equations. It involves special interface conditions at the cell edges based on the idea of QD boundary conditions (BCs). We consider different kinds of QD BCs to formulate the necessary cell-interface conditions. We develop two-level methods with independent discretization of the high-order transport equation and LOQD equations, where the transport equation is discretized using the method of characteristics and the LDFEM is applied to the LOQD equations. We also formulate closures that lead to the discretization consistent with a LDFEM discretization of the transport equation. The proposed methods are studied by means of test problems formulated with the method of manufactured solutions. Numerical experiments are presented demonstrating the performance of the proposed methods. Lastly, we also show that the method with independent discretization has the asymptotic diffusion limit.

[en] This paper addresses the use of experimental data for calibrating a computer model and improving its predictions of the underlying physical system. A global statistical approach is proposed in which the bias between the computer model and the physical system is modeled as a realization of a Gaussian process. The application of classical statistical inference to this statistical model yields a rigorous method for calibrating the computer model and for adding to its predictions a statistical correction based on experimental data. This statistical correction can substantially improve the calibrated computer model for predicting the physical system on new experimental conditions. Furthermore, a quantification of the uncertainty of this prediction is provided. Physical expertise on the calibration parameters can also be taken into account in a Bayesian framework. Finally, the method is applied to the thermal-hydraulic code FLICA 4, in a single-phase friction model framework. It allows significant improvement of the predictions of FLICA 4. (authors)

[en] We provide experimental data on the initiation of persistent fission chains obtained at different supercritical states, using the fast burst reactor Caliban. In many previous papers, theory has been compared mostly with initiation experiments at various super-prompt critical states, whereas very few experimental data have been published on delayed supercritical states. To fill the lack of data, we have conducted three studies on the reactor at reactivities far below 0.7 $, which is one of the lowest states ever published for a similar assembly. We give a justification of the use of the gamma function to fit experimental results for the temporal distributions of waiting times and compare experiments with numerical simulations obtained with a punctual zero-dimensional Monte Carlo code and a punctual deterministic initiation code. (authors)

[en] Before the definitive shutdown of the prototype Phenix, a final set of experiments was performed to gather important data about the operation and safety of sodium-cooled fast reactors (SFRs). Among the accident sequences that are to be taken into account, inadvertent withdrawal of a control rod is considered. During operation at nominal power, such a sequence induces a general power increase and local deformations of the power shape. Afterward, local fuel temperature increases can thereby lead to fuel melting and clad failure. The quasi-static control rod withdrawal test was specially designed to gather local power data on fissile assemblies and to complete validation databases of neutronic codes. The maximal deformation of the power shape reached ±12% and was obtained when two control rods were shifted in opposite directions. The test analysis was conducted with the neutronics code ERANOS-2.2. Comparisons between calculated and measured values were satisfying. Most of the discrepancies in power estimation can be explained by measurement problems (heat transfer, sodium mixing). The association of ERANOS-2.2 and the nuclear library JEFF-3.1, presently used for the pre design phase of the ASTRID reactor, constitutes an acceptable predictive tool for local and integral parameter estimations in SFRs, specifically in the evaluation of the control rod withdrawal incident. (authors)

[en] This paper describes the methodology developed and implemented in the Virtual Environment for Reactor Applications Core Simulator (VERA-CS) to perform high-fidelity, pressurized water reactor (PWR), multicycle, core physics calculations. Depletion of the core with pin-resolved power and nuclide detail is a significant advance in the state of the art for reactor analysis, providing the level of detail necessary to address the problems of the U.S. Department of Energy Nuclear Reactor Simulation Hub, the Consortium for Advanced Simulation of Light Water Reactors (CASL). VERA-CS has three main components: the neutronics solver MPACT, the thermal-hydraulic (T-H) solver COBRA-TF (CTF), and the nuclide transmutation solver ORIGEN. This paper focuses on MPACT and provides an overview of the resonance self-shielding methods, macroscopic-cross-section calculation, two-dimensional/one-dimensional (2-D/1-D) transport, nuclide depletion, T-H feedback, and other supporting methods representing a minimal set of the capabilities needed to simulate high-fidelity models of a commercial nuclear reactor. Results are presented from the simulation of a model of the first cycle of Watts Bar Unit 1. The simulation is within 16 parts per million boron (ppmB) reactivity for all state points compared to cycle measurements, with an average reactivity bias of <5 ppmB for the entire cycle. Comparisons to cycle 1 flux map data are also provided, and the average 2-D root-mean-square (rms) error during cycle 1 is 1.07%. To demonstrate the multicycle capability, a state point at beginning of cycle (BOC) 2 was also simulated and compared to plant data. The comparison of the cycle 2 BOC state has a reactivity difference of +3 ppmB from measurement, and the 2-D rms of the comparison in the flux maps is 1.77%. Lastly, these results provide confidence in VERA-CS’s capability to perform high-fidelity calculations for practical PWR reactor problems.

[en] The purpose of this letter is to review earlier studies into the effects of intracell adjoint flux heterogeneity on small samples' reactivity worth (and, therefore, also on the central worth discrepancy). Discusses integral transport theory methods and first-order perturbation theory methods

[en] The average total prompt neutron multiplicity ν-bar of ²⁵²Cf spontaneous fission is investigated as a function of the total kinetic energy TKE and the mass split of the fragments through the code FIFRELIN. This Monte Carlo device, already described in a previous work, aims at simulating the neutron evaporation from fission fragments. The observables n and TKE and the light fragment mass AL are recorded from a sample of 10⁷ fission events. The analyzed results show a value for the inverse of the slope [δν-bar(TKE)/δTKE]^-1 equal to -11.0 MeV/n. In addition to this, the average number of neutrons per fission ν-bar(TKE, A_L) is determined for every possible TKE and A_L. For every fragment mass ratio, differences in behavior between ν-bar(TKE, A_L) versus TKE and ν-bar(TKE) with no discrimination made with regard to A_L are observed. Those differences are explained by the TKE dependency of fission yield. The approximation consisting of ignoring this TKE dependency of mass yield when calculating the ν-bar(TKE) slope is discussed. We estimate that such a calculation could lead to a significant bias on the absolute value of δν-bar(TKE)/δTKE and could explain the discrepancies between calculations found in the literature. (authors)

[en] In reactor physics, calculation schemes with deterministic codes are validated with respect to a reference Monte Carlo code. The remaining biases are attributed to the approximations and models induced by the multigroup theory (self-shielding models and expansion of the scattering law on Legendre polynomials) to represent physical phenomena (resonant absorption and scattering anisotropy). This work focuses on the relevance of a polynomial expansion to model the scattering law. Since the outset of reactor physics, the latter has been expanded on a truncated Legendre polynomial basis. However, the transfer cross sections are highly anisotropic, with nonzero values for a small range of the scattering angle. The finer the energy mesh and the lighter the scattering nucleus, the more exacerbated is the peaked shape of these cross sections. As such, the Legendre expansion is less well suited to represent the scattering law. Furthermore, this model induces negative values, which are nonphysical. Piecewise-constant functions have been used to represent the multigroup scattering cross section. This representation requires a different model for the diffusion source. Thus, the finite-volume method for angular discretization has been developed and implemented in the PARIS environment. This method is adapted for both the Legendre moments and the piecewise-constant functions representations. It provides reference deterministic results that validate the standard Legendre polynomial representation with a P3 expansion. (authors)

[en] In this paper we describe some recent developments in the Method of Characteristics (MOC) for three-dimensional (3D) extruded geometries in the nuclear reactor analysis code APOLLO3. We discuss the parallel strategies implemented for the transport sweep of the MOC solver in the OpenMP framework, and introduce the 3D version of the DPN operator that is customarily used in APOLLO2 to accelerate MOC convergence. In order to provide good physical results, we have also coupled the MOC with the self-shielding environment of APOLLO3. We describe, in particular, the coupling techniques necessary to implement a full subgroup cross-section self-shielding method and a specialized version of the Tone self-shielding technique. In this framework, we use part of the tracking method used for the 3D calculation to provide the two-dimensional Collision Probability Method (CPM) coefficients necessary to produce the self-shielding calculations. We will show some important computational speedups also in the CPM of APOLLO3 with respect to the APOLLO2 CPM equivalent implementation, including the parallelization issue. Finally, we will compare our approach toward a Monte Carlo calculation of a fast breeder reactor hexagonal assembly representing a fertile-fissile interface. (authors)

[en] The precise value of the thermal capture cross section of 238U is uncertain, and evaluated cross sections from various sources differ by more than their assigned uncertainties. A number of the original publications have been reviewed to assess the discrepant data, corrections were made for more recent standard cross sections and other constants, and one new measurement was analyzed. Due to the strong correlations in activation measurements, the gamma-ray emission probabilities from the beta decay of 239Np were also analyzed. As a result of the analysis, a value of 2.683 +- 0.012 barns was derived for the thermal capture cross section of 238U. A new evaluation of the gamma-ray emission probabilities from 239Np decay was also undertaken