Nam Zin Cho (KAIST)

The reactor design requires accurate calculations of the multiplication factor and power (or flux) distribution in various configurations of the reactor core. These calculations are computationally demanding, since a typical reactor is multidimensional, heterogeneous, and cross sections for many nuclides are of resonance-type. The established procedure in current practice is a two-level procedure consisting of the whole-core (global) nodal diffusion calculation and the assembly (local) lattice calculations based on deterministic multi-group transport methods that are used to provide the diffusion nodal parameters.
In spite of the advantages in handling continuous energy and complex geometry, direct application of the Monte Carlo method to whole-core calculation is still problematic, in particular for cores of large size that are loosely-coupled.
This talk presents and discusses two recently proposed methods: 1) whole-core Monte Carlo calculation “accelerated” by CMFD-type deterministic low-order equation and its improvement by “anchoring” the conventional fission source distribution in Monte Carlo, and 2) global-local iterative framework in which the global whole-core calculation is done by a multi-group diffusion nodal method, while the local lattice calculation is performed by a continuous-energy Monte Carlo method with non-zero leakage boundary condition.
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Advanced Homogenization and Energy Condensation Methods in Reactor Physics

Farzad Rahnema (Georgia Institute of Technology)

Current industry methods for reactor core calculations involve a two step process in which lattice (assembly) depletion transport methods are used to prepare energy collapsed and spatially homogenized fuel assembly cross sections for whole core low order transport (e.g., diffusion theory) calculations. Since the boundary condition (core environment) is not known a priori, an infinite medium (zero current) condition is used in the lattice calculations. Clearly, this approximation would lead to undesirable errors in cores in which large flux gradient are present across the fuel assemblies. This is the case in cores that have high heterogeneity, strong local absorbers and/or small size. In this presentation, we discuss advanced transport-based energy re-condensation and re-homogenization methods that address the core environment (boundary condition) issue.
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Transport methods with APOLLO2 and advanced MOC applications

Igor Zmijarevic (CEA)

The modern reactor core designs need precise and efficient transport calculations. A detailed analysis based on transport solutions at the level of fuel assembly is to some extent applied also to that of the whole reactor. Starting from the accurate, spatially dependent, effective cross sections produced by the selfshielding methodology, a variety of numerical techniques has been applied to the solution of the transport equation.
In this talk we discuss the different approaches, ranging from the best estimate, straightforward assembly and/or reactor calculations, to those used in industrial application based on homogenization and flux reconstruction techniques. The latter methods may involve different transport solvers, such as the conventional collision probabilities method with interface current approximation, discrete ordinates with homogeneous or heterogeneous mesh cells, and the method of characteristics.
The emphasis will be given to the recently developed, higher order discretization schemes for the method of characteristics and the short characteristics schemes with the heterogeneous mesh cells taking into account exact fuel pin geometry. The indispensable part of these implementations is an efficient acceleration of iterative solutions. The representative applications will be shown through the examples of assembly and core calculations.
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The Quasidiffusion Method for Solving Neutron Transport Problems in Reactor-Physics Applications

Dmitriy Y. Anistratov (North Carolina State University)

To perform nuclear reactor simulations, it is necessary to formulate and solve multiphysical system of equations which includes the transport equation that is a background for mathematical models of neutron propagation in matter. In this talk, we present an approach for solving neutron transport problems that is based on the Quasidiffusion method. The main idea behind it is to reduce the dimensionality of the original problem by formulating equivalent low-order transport problems. The structure and properties of the resulting low-order equations are good for (i) acceleration of transport iterations, (ii) spatial homogenization and (iii) solving multiphysical problems in which the transport equation is coupled with, for example, burnup and reactor kinetics equations. Various aspects of these pieces of computational reactor-physics methodologies will be discussed in the talk.
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Stochastic techniques for reactor core calculations

Richard Sanchez (CEA, Saclay)

This presentation will cover two applications of stochastic techniques to core calculations: a) Treatment of the double heterogeneity (DH) problem and b) modeling of the pebble-bed modular reactor (PBMR).
The DH problem concerns applications to calculations of MOX and Gadolinia poisoned fuels, as well as any grain-matrix configuration. Basically, the method consists of a homogenization - dehomogenization technique and can be used with any kind of calculation method, but has been developed for the collision probability and long characteristic methods.
Regarding the modeling of the PBMR, a reactor with a double stochasticity (localization of the pebbles in the core and of the TRISO particles in the pebbles), I shall present a macro stochastic computational model for interactive fuel homogenization for core depletion calculations. The model is based on crude assumptions on the pebble distribution in the core and relays on a set of geometric probabilities with the possibility of representing pebble clustering.
A major emphasis of the presentation will be on the limitations and validity of the models.
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