### Abstract

This report reviews various method for the calculation of the neutron-flux- and power distribution in an nuclear reactor. The nodal expansion method (NEM) is especially described in much detail. The nodal expansion method solves the diffusion equation. In this method the reactor core is divided into nodes, typically 10 to 20 cm in each direction, and the average flux in each node is calculated. To obtain the coupling between the nodes the local flux inside each node is expressed by use of a polynomial expansion. The expansion is one-dimensional, so inside each node such three expansions occur. To calculate the expansion coefficients it is necessary that the polynomial expansion is a solution to the one-dimensional diffusion equation. When the onedimensional diffusion equation is established a term with the transversal leakage occur, and this term is expanded after the same polynomials. The resulting equation system with the expansion coefficients as the unknowns is solved with weighted residual technique.

The nodal expansion method is built into a computer program (also called NEM), which is divided into two parts, one part for steady-state calculations and one part for dynamic calculations. It is possible to take advantage of symmetry properties of the reactor core. The program is very flexible with regard to the number of energy groups, the node size, the flux expansion order and the transverse leakage expansion order. The boundary of the core is described by albedos. The proqram and input to it are described.

The program is tested on a number of examples extending from small theoretical ones up to realistic reactor cores. Many calculations are done on the wellknown IAEA benchmark case. The calculations have tested the accuracy and the computing time for various node sizes and polynomial expansions. In the dynamic examples various strategies for variation of the time step-length have been tested.

The nodal expansion method is built into a computer program (also called NEM), which is divided into two parts, one part for steady-state calculations and one part for dynamic calculations. It is possible to take advantage of symmetry properties of the reactor core. The program is very flexible with regard to the number of energy groups, the node size, the flux expansion order and the transverse leakage expansion order. The boundary of the core is described by albedos. The proqram and input to it are described.

The program is tested on a number of examples extending from small theoretical ones up to realistic reactor cores. Many calculations are done on the wellknown IAEA benchmark case. The calculations have tested the accuracy and the computing time for various node sizes and polynomial expansions. In the dynamic examples various strategies for variation of the time step-length have been tested.

Original language | English |
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Place of Publication | Roskilde |
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Publisher | Risø National Laboratory |

Number of pages | 206 |

ISBN (Print) | 87-550-1169-1 |

Publication status | Published - 1985 |

Series | Denmark. Forskningscenter Risoe. Risoe-R |
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Number | 496 |

ISSN | 0106-2840 |

### Keywords

- Risø-R-496
- Risø-R-496(EN)
- Computerized simulation
- N codes
- Neutron flux
- Polynomials
- Power distribution
- Reactor cores
- Reactor kinetcs
- Series expansion
- Three-dimensional calculators

### Cite this

Christensen, B. (1985).

*Three-Dimensional Static and Dynamic Reactor Calculations by the Nodal Expansion Method*. Roskilde: Risø National Laboratory. Denmark. Forskningscenter Risoe. Risoe-R, No. 496