Using the Few-Group Approximation for Calculating Some Neutron-Physical Characteristics of VVER-1000 Core by Means of the MCU Monte-Carlo Code

The main purpose of this work is to study the possibility of using the few-group approximation for calculation of some neutron-physical characteristics of VVER-1000 core by means of special version of MCU code. The Monte-Carlo method for VVER-1000 core neutron-physical characteristics calculation using the few-group approximation with an estimate of neutron cross sections “by location“ was provided and tested in this research. The reduction of calculation time due to the transition from a pointwise model of representation of cross sections to the few-group approximation and methodical error of this approach were evaluated. Optimal number of energy groups was determined. It was found that consideration of the scattering anisotropy leads to a significant decrease in methodical error. Ways of further reduction of methodical error were worked out.

Neutron Cross Section Generation for PWR MOX Fuel Assemblies with SCALE and Serpent

In this study, the SCALE/TRITON code (based on deterministic method) and the Serpent 2 code (based on Monte Carlo method) were utilized to prepare the group constants of the pressurized water reactor (PWR) mixed-oxide (MOX) fuel assemblies for transient analyses of PWR MOX fueled cores in normal operation and control rod ejection accident condition with 3D reactor kinetics codes. The PWR MOX fuel assemblies were modeled with TRITON and Serpent, and their infinite neutron multiplication factors (k-inf) versus burnup and respective two-group neutron cross sections were calculated and compared against the available benchmark data obtained with the HELIOS code. The comparative results generally show a good agreement between TRITON and Serpent with HELIOS within 643 pcm for the k-inf values and within 5% for the two-group neutron cross sections. Therefore, it indicates that the TRITON and Serpent models developed herein for the PWR MOX fuel assemblies can be applied to group constant generation to be further used in transient analyses of PWR MOX fueled cores.

CANDU Reactor.Physics Analysis Methods and Computer Codes

Reactor physics aims to understand accurately the reactivity and the distribution of all the reaction rates (most importantly of the power), and their rate of change in time, for any reactor configuration. To do this, the multiplication factor (or, equivalently, reactivity) and the neutron-flux distribution under various operating conditions and at different times need to be calculated repeatedly. Most of the other parameters of interest (such as neutron reaction rates, power, heat deposition, etc.) are derived from them. They are governed by the geometry, the material composition and the nuclear data (i.e., the neutron cross sections, their energy dependence, the energy spectra and the angular distributions of secondary particles, etc.). For radiation-shielding calculations, additional photon interactions and coupled neutron-photon interaction data are required.

MODELING NUCLEAR DATA UNCERTAINTIES USING DEEP NEURAL NETWORKS

A new concept using deep learning in neural networks is investigated to characterize the underlying uncertainty of nuclear data. Analysis is performed on multi-group neutron cross-sections (56 energy groups) for the GODIVA U-235 sphere. A deep model is trained with cross-validation using 1000 nuclear data random samples to fit 336 nuclear data parameters. Although of the very limited sample size (1000 samples) available in this study, the trained models demonstrate promising performance, where a prediction error of about 166 pcm is found for keff in the test set. In addition, the deep model’s sensitivity and uncertainty are validated. The comparison of importance ranking of the principal fast fission energy groups with adjoint methods shows fair agreement, while a very good agreement is observed when comparing the global keff uncertainty with sampling methods. The findings of this work shall motivate additional efforts on using machine learning to unravel complexities in nuclear data research.

Dual number automatic differentiation as applied to two-group cross-section uncertainty propagation

This work addresses the problem of propagating uncertainty from group-wise neutron cross-sections to the results of neutronics diffusion calculations. Automatic differentiation based on dual number arithmetic was applied to uncertainty propagation in the framework of local sensitivity analysis. As an illustration, we consider a two-group diffusion problem in an infinite medium, which has a solution in a closed form. We employ automatic differentiation in conjunction with the sandwich formula for uncertainty propagation in three ways. Firstly, by evaluating the analytical expression for the multiplication factor using dual number arithmetic. Then, by solving the diffusion problem with the power iteration algorithm and the algebra of dual matrices. Finally, automatic differentiation is used to calculate the partial derivatives of the production and loss operators in the perturbation formula from the adjoint-weighted technique. The numerical solution of the diffusion problem is verified against the analytical formulas and the results of the uncertainty calculations are compared with those from the global sensitivity analysis approach. The uncertainty values obtained in this work differ from values given in the literature by less than 1?10?5.

Dual number automatic differentiation as applied to two-group cross-section uncertainty propagation

This work addresses the problem of propagating uncertainty from group-wise neutron cross-sections to the results of neutronics diffusion calculations. Automatic differentiation based on dual number arithmetic was applied to uncertainty propagation in the framework of local sensitivity analysis. As an illustration, we consider a two-group diffusion problem in an infinite medium, which has a solution in a closed form. We employ automatic differentiation in conjunction with the sandwich formula for uncertainty propagation in three ways. Firstly, by evaluating the analytical expression for the multiplication factor using dual number arithmetic. Then, by solving the diffusion problem with the power iteration algorithm and the algebra of dual matrices. Finally, automatic differentiation is used to calculate the partial derivatives of the production and loss operators in the perturbation formula from the adjoint-weighted technique. The numerical solution of the diffusion problem is verified against the analytical formulas and the results of the uncertainty calculations are compared with those from the global sensitivity analysis approach. The uncertainty values obtained in this work differ from values given in the literature by less than 1?10?5.