# Neutron noise calculations in a hexagonal geometry and comparison with analytical solutions

## Abstract

This paper presents the development of a neutronic and kinetic solver for hexagonal geometries. The tool is developed based on the diffusion theory with multi-energy groups and multi-groups of delayed neutron precursors allowing the solutions of forward and adjoint problems of static and dynamic states, and is applicable to both thermal and fast systems with hexagonal geometries. In the dynamic problems, the small stationary fluctuations of macroscopic cross sections are considered as noise sources, and then the induced first order noise is calculated fully in the frequency domain. Numerical algorithms for solving the static and noise equations are implemented with a spatial discretization based on finite differences and a power iterative solution. A coarse mesh finite difference method has been adopted for speeding up the convergence. Since no other numerical tool could calculate frequency-dependent noise in hexagonal geometry, validation calculations have been performed and benchmarked to analytical solutions based on a 2-D homogeneous system with two-energy groups and one-group of delayed neutron precursor, in which point-like perturbations of thermal absorption cross section at central and non-central positions are considered as noise sources. (authors)

- Authors:

- Dept. of Applied Physics, Div. of Nuclear Engineering, Chalmers Univ. of Technology, SE-412 96, Gothenburg (Sweden)

- Publication Date:

- Research Org.:
- American Nuclear Society, Inc., 555 N. Kensington Avenue, La Grange Park, Illinois 60526 (United States)

- OSTI Identifier:
- 22105878

- Resource Type:
- Conference

- Resource Relation:
- Conference: PHYSOR 2012: Conference on Advances in Reactor Physics - Linking Research, Industry, and Education, Knoxville, TN (United States), 15-20 Apr 2012; Other Information: Country of input: France; 11 refs.

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; 22 GENERAL STUDIES OF NUCLEAR REACTORS; ALGORITHMS; ANALYTICAL SOLUTION; COMPARATIVE EVALUATIONS; CROSS SECTIONS; DELAYED NEUTRON PRECURSORS; DIFFUSION; FINITE DIFFERENCE METHOD; FLUCTUATIONS; FREQUENCY DEPENDENCE; GEOMETRY; GROUP THEORY; NEUTRONS; NOISE; PERTURBATION THEORY; TWO-DIMENSIONAL CALCULATIONS; VALIDATION

### Citation Formats

```
Tran, H. N., and Demaziere, C.
```*Neutron noise calculations in a hexagonal geometry and comparison with analytical solutions*. United States: N. p., 2012.
Web.

```
Tran, H. N., & Demaziere, C.
```*Neutron noise calculations in a hexagonal geometry and comparison with analytical solutions*. United States.

```
Tran, H. N., and Demaziere, C. Sun .
"Neutron noise calculations in a hexagonal geometry and comparison with analytical solutions". United States.
```

```
@article{osti_22105878,
```

title = {Neutron noise calculations in a hexagonal geometry and comparison with analytical solutions},

author = {Tran, H. N. and Demaziere, C.},

abstractNote = {This paper presents the development of a neutronic and kinetic solver for hexagonal geometries. The tool is developed based on the diffusion theory with multi-energy groups and multi-groups of delayed neutron precursors allowing the solutions of forward and adjoint problems of static and dynamic states, and is applicable to both thermal and fast systems with hexagonal geometries. In the dynamic problems, the small stationary fluctuations of macroscopic cross sections are considered as noise sources, and then the induced first order noise is calculated fully in the frequency domain. Numerical algorithms for solving the static and noise equations are implemented with a spatial discretization based on finite differences and a power iterative solution. A coarse mesh finite difference method has been adopted for speeding up the convergence. Since no other numerical tool could calculate frequency-dependent noise in hexagonal geometry, validation calculations have been performed and benchmarked to analytical solutions based on a 2-D homogeneous system with two-energy groups and one-group of delayed neutron precursor, in which point-like perturbations of thermal absorption cross section at central and non-central positions are considered as noise sources. (authors)},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2012},

month = {7}

}