[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 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 current design studies on sodium-cooled fast reactors (SFRs) are breaking with the past since they are guided by a new set of design criteria arising from the objectives of Generation IV reactors. The new safety requirements lead to designing reactors with breakeven breeding cores because in terms of reactivity control, they minimize the need to limit the consequences of an inadvertent control rod withdrawal event. Furthermore, as the reactivity control needs are low, a breakeven core enables the use of absorbing materials with reduced efficiency (natural boron, hafnium, etc..), which may be less costly than enriched boron. However, control rods designed with low absorbing materials may present the disadvantage of a non negligible loss of efficiency due to their consumption under irradiation. This paper presents a methodology to accurately calculate and to analyze the impact of this consumption on reactivity control. (authors)

[en] Advanced fast reactor concepts, such as the CFV core (French acronym of 'Coeur a Faible effet de Vide Sodium', meaning 'low sodium void effect core'), are characterized by a heterogeneous axial core arrangement, with an inner fertile zone and a sodium plenum above the fuel. Such concepts represent a strong challenge for accurate predictions of the control-rod anti-reactivity effects, and the surrounding local fuel pin power. Classical equivalence procedures, which were developed for axially homogeneous cores, are put to the test when applied to such axially heterogeneous cores. In this work, we investigate the influence of variations in the local neutron spectra, for different control-rod environments, with the objective of understanding the impact of spectral variations in control-rod homogenization. This was conducted by considering a simple one-dimensional model of the equivalence procedure in which a transition zone between the fuel and control rod was introduced to represent different control-rod environments. Two types of situations were studied, one corresponding to softened neutron spectrum environments, for which the impact in the homogenized control-rod cross section was found to be smaller than 5%. The second situation was with wide elastic scattering resonances in the control-rod environment, which could locally lead to differences of up to 15% in the resulting equivalent cross sections. The reactivity effect of these changes was calculated to be less than 2%. In some cases, the numerical stability of the equivalence procedure was adversely affected, mainly in high energy groups, due to the softening of the neutron spectra. (authors)

[en] Advanced sodium-cooled fast reactors with improved safety features such as the French Advanced Sodium Technological Reactor for Industrial Demonstration (ASTRID) CFV (French acronym of Coeur a Faible effet de Vide sodium, meaning low sodium void effect core) core concept are characterized by an axial heterogeneous core that will present a challenge for the homogenization procedures used today, taking into account all the different axial material transitions. Reliable modeling of the control rod and accurate prediction of the control rod worth are essential to determining the shutdown margins and to ensuring safe operation. In this work (part II of two companion papers), two different homogenization schemes are compared. One is based on the traditional reactivity-equivalence procedure in two dimensions, and the other is a newly implemented three-dimensional (3-D) version of the reactivity-equivalence procedure, with approximations based on the results in the companion paper. The deterministic results are compared with a Monte Carlo reference. Both cross-section sets from the two homogenization schemes yielded results within the requested ±5% error margin in reactivity. The largest discrepancy was found for the classical procedure for the case with a slightly inserted control rod (normal operating conditions). Both cross-section sets yielded similar power profiles in the fuel subassembly neighboring the control rod within the 2σ Monte Carlo standard deviation. Neither of the cross-section sets was able to predict the large gradients in capture rates close to the internal control rod interfaces. The study showed that the traditional two-dimensional (2-D) reactivity-equivalence procedure produces homogenized cross sections that yield reliable results in a CFV-type core. One exception from this was found for slightly inserted control rods, where the effect of the follower-absorber interface could not be fully captured by the 2-D scheme, and for such cases, 3-D modeling is recommended. (authors)

[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] 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)