On the Self-Shielding in the Unresolved Resonance Range

Resonance behavior is a feature of nuclear reaction cross sections. Resonance density increases with increasing incident particle energy and they begin to overlap, until they can no longer be resolved experimentally, but they still contribute to self-shielding and must be accounted for. This is usually done by representing them with statistical average parameters according to methods and approximations described in standard text-books. Self-shielding factors are commonly used in deterministic transport codes, while statistical Monte Carlo codes use probability tables or multi-band parameters. An exercise was conducted at the International Atomic Energy Agency (IAEA) to validate codes and methods for generating data that account for self-shielding in deterministic and Monte Carlo codes. A simple numerical model problem was defined, considering a sphere of 1 m radius with a 20 MeV isotropic neutron source at the center. The chosen material for testing was 139La from the ENDF/B-VIII.0 library, which clearly showed anomalous behavior.

Complex Models of Ordering Multi-Sequences with Fuzzy Parameters

Purpose. The aim of the article is to develop complex constructive mathematical models of ordering processes for multi-sequences of elements with fuzzy parameters. At the same time, the following requirements for fuzzy ordering of multi-sequences with complexity evaluation (FOMSCE) were established: accounting fuzzy estimates of the formation operations complexity, the need to define fuzzy classes for ordering the initial elements, as well as building individual fuzzy models for the processes of receiving orders from different sources. Methodology. To solve the problems of optimal planning of non-deterministic processes of clinical monitoring of the patients’ treatment, the formation of complex constructive mathematical models of the processes of ordering multi-sequences of elements with fuzzy FMLCPM parameters was applied. For forming models of FOMSCE tasks, a methodology is used to create models with multilayer structures. To implement fuzzy problems, methods and procedures for discretizing a system of fuzzy quantities using sets of α-levels are applied. Findings. The article proposes an approach to solving the problems of analysis and optimal planning of the processes of clinical monitoring of the patients’ treatment, represented as flow control in service systems under uncertainty. For its formalization and implementation, complex multilayer constructive-production models for ordering multi-sequences with fuzzy parameters have been developed. Originality. The work has developed constructive-production methods for modeling complex systems, presented in the form of a multilayer model FMLCPM, which are designed for the processes of ordering multi-sequences of elements with fuzzy parameters. In FMLCPM, layer models are proposed that provide accounting for fuzzy estimates of the complexity of ordering operations, classification of fuzzy parameters of output elements, the formation and analysis of individual fuzzy models of the processes of receipt of orders in service systems. Practical value. The practical value of the results obtained lies in the spectrum development of applications of the problems of optimal planning of the processes in the service systems, presented as an ordering of multi-sequences with fuzzy parameters. The complex models of FOMSCE processes developed in the article are suitable and effective for formalizing the tasks of analysis and optimal planning of clinical monitoring processes, as well as a wide range of other tasks for monitoring non-deterministic transport processes, logistics and service systems.

A HIGH-FIDELITY SIMULATION OF THE C5G7 BENCHMARK BY USING THE PARALLEL ENTER CODE

In simulation of advanced nuclear reactors, requirements like high precision, high efficiency and convenient to multi-physics coupling are putting forward. The deterministic transport method has the advantage of high efficiency, capable of obtaining detailed flux distribution and efficient in multi-physics coupling, but its accuracy is limited by the homogenized reaction cross-section data and core modelling exactness. The traditional two-steps homogenization strategy may introduce substantial deviation during the assembly calculation. It is possible to conduct a whole core deterministic transport simulation pin-by-pin to achieve higher accuracy, which eliminates the assembly homogenization process. The C5G7 benchmarks were proposed to test the ability of a modern deterministic transport code in analyzing whole core reactor problems without spatial homogenization. Different deterministic code that developed by different methods were applied to the benchmark simulation and some of them solved the benchmark accurately. However, there still exist some drawbacks in the given calculation processes which carried out by some other deterministic transport codes and we could find that the fuel pin cell in the assembly were not exactly geometrically modelled owing to the limit of the code. Consequently, the calculation precision could be improved by utilizing a high-fidelity geometry modelling. In this paper, the C5G7 benchmarks with different control rod position and different configuration were calculated by the finite element SN neutron transport code ENTER [1], and the results were presented after massively parallel computation on TIANHE-II supercomputer. By introducing a large scale high-fidelity unstructured meshes, high fidelity distributions of power and neutron flux were gained and compared with the results from other codes, excellent consistency were observed. To sum up, the ENTER code can meet those new requirements in simulation of advanced nuclear reactors and more works and researches will be implemented for a further improvement.

K-MEANS CLUSTERING OF NEUTRON SPECTRA FOR CROSS SECTION COLLAPSE

The process of generating cross sections for whole-core analysis typically involves collapsing cross sections against an approximate spectrum generated by solving problems with reduced scope (e.g., 2D slices of a fuel assembly). Such spectra vary with the location of a material region and with other state parameters (e.g., burnup, temperature, soluble boron concentration), resulting in a burdensome and potentially time consuming process to store and load spectra. Commonly, this is resolved by manually determinining material regions for which the cross sections can be collapsed with a single weighting flux, requiring a combination of domain knowledge, engineering judgment, and trial and error. Exploring new reactor concepts and solving increasingly complicated problems with deterministic transport methods will therefore benefit greatly from an automated approach to grouping spectra independent of problem geometry or reactor type. This paper leverages a data analytics technique known as k-means clustering to group regions with similar weighting spectra into individual clusters, within each of which an average weighting flux is applied. Despite the clustering algorithm being agnostic to the physics of the problem, the approach results in a nearly 98% decrease in number of spectra regions with minimal impact to the accuracy.

DEVELOPMENT OF A COUPLED SUBPLANE CAPABILITY IN MPACT

Recent efforts in the development of the deterministic transport code MPACT have been devoted to preparing the 2D/1D subplane method to be a production-level capability, as well as leveraging a multilevel coarse mesh finite difference (CMFD) approach to substantially reduce the runtime of target problems. For example, as compared to the previous default 2D/1D solver in MPACT on a standard quarter core model, the new solver reduces in core-hour requirements by ~5–6×. Previous work focused solely on cases without multiphysics feedback, which is obviously important for analyzing the more realistic problems of operating reactors. The work presented in this article focuses on efforts to incorporate thermal hydraulics (TH) coupling through CTF by leveraging what are termed as subgrid solvers, which effectively treat material heterogeneities within subplane regions. Previous efforts have targeted using subgrid solvers for control rods and spacer grids; in this work, they are applied to account for the material property heterogeneities with regards to temperature/density distributions. This will allow the fidelity of coupling to be maintained while still reaping the performance benefits. These new developments are demonstrated on two problems: (1) a single assembly case with feedback, known as Progression Problem 6a, and (2) a 3×3 cluster of assemblies with feedback based on Progression Problem 4a. The results demonstrate notable performance improvement potential for cases with TH feedback, but this approach is more dependent on the iteration process.

ANALYSIS AND COMPARISON OF APOLLO3® AND TRIPOLI-4® NEUTRON NOISE SOLVERS

Neutron noise analysis addresses the description of small time-dependent flux fluctuations in reactor cores, induced by small global or local perturbations of the macroscopic cross sections due to density fluctuations of the coolant, to vibrations of fuel elements, control rods, or structural materials. The general noise equations are obtained by assuming small perturbations around a steady-state neutron flux and by subsequently taking the Fourier transform in the frequency domain. Recently, new neutron noise solvers have been implemented in diffusion and transport theory in APOLLO3®, the multi-purpose deterministic transport code developed at CEA, and a new stochastic solver has been implemented for the neutron noise analysis in the frequency domain in the Monte Carlo code TRIPOLI-4®, also developed at CEA. In this paper, we compare the two solvers for the case of fuel pin oscillations in a simplified UOX fuel assembly, in view of proposing the examined configurations as a benchmark for neutron noise calculations.

Determining the capacity of a bunker as a part of the handling system with combined transport

Introduction. Significant share of the costs for deep quarries is the cost of rock mass reloading from the “assembly transport” to the main transport make up a considerable proportion in open pit development costs. Portable handling systems with bunkers are used, the parameters of which are determined by several methods. Methodology. In this work, when determining the capacity of the bunker, two approaches have been considered: deterministic – transport systems operate at nominal conditions; probabilistic – transport systems operate with their inherent unevenness. The methodology adopted is based on the geometry of the bunker in the configuration of the “inverted obelisk”, as the most productive system. Formulas to calculate the technological and geometric capacity of the bunker have been proposed. The proposed method parameters design takes into account assembly (automobile) transport arrival rate, which is described by the Poisson distribution and railway transport arrival rate described by the distribution of Erlang. Several numerical examples reveal practical application for bunker parameters determination. 112 "Izvestiya vysshikh uchebnykh zavedenii. Gornyi zhurnal". No. 4. 2020 ISSN 0536-1028 Results. The significance of the required additional bunker volumes has been justified in order to make up for cyclic transport vehicles irregular operation within combined transport complexes.

Analisis Model Optimasi Stokastik pada Masalah Transportasi Stokastik

Transportasi adalah suatu proses pemindahan manusia atau barang dari suatu tempat ke tempat lain dengan menggunakan suatu alat bantu kendaraan. Dalam masalah transportasi biasanya membahas mengenai meminimalkan biaya atau meminimalkan waktu. Tulisan ini mempresentasikan suatu model transportasi dengan adanya variabel ketidakpastian. Model yang terbentuk dari variabel ketidakpastian disebut dengan model transportasi stokastik. Solusi optimal diperoleh dengan merubah model transportasi stokastik ke dalam model transportasi deterministik. Transportation is a process of moving people or goods from place to place by using a vehicle aids. In transportation problems usually discuss about cost or time. This paper presents a transport model in the uncertain of variables. The model formed from the variable of uncertainty is called the stochastic transport model. The optimal solution is obtained by changing the stochastic transport model into a deterministic transport model.