Three-Dimensional Static and Dynamic Reactor Calculations by the Nodal Expansion Method

Brian Christensen

    Research output: Book/ReportReportResearchpeer-review

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    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.
    Original languageEnglish
    Place of PublicationRoskilde
    PublisherRisø National Laboratory
    Number of pages206
    ISBN (Print)87-550-1169-1
    Publication statusPublished - 1985
    SeriesDenmark. Forskningscenter Risoe. Risoe-R
    Number496
    ISSN0106-2840

    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
    Christensen, Brian. / Three-Dimensional Static and Dynamic Reactor Calculations by the Nodal Expansion Method. Roskilde : Risø National Laboratory, 1985. 206 p. (Denmark. Forskningscenter Risoe. Risoe-R; No. 496).
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    Christensen, B 1985, Three-Dimensional Static and Dynamic Reactor Calculations by the Nodal Expansion Method. Denmark. Forskningscenter Risoe. Risoe-R, no. 496, Risø National Laboratory, Roskilde.

    Three-Dimensional Static and Dynamic Reactor Calculations by the Nodal Expansion Method. / Christensen, Brian.

    Roskilde : Risø National Laboratory, 1985. 206 p. (Denmark. Forskningscenter Risoe. Risoe-R; No. 496).

    Research output: Book/ReportReportResearchpeer-review

    TY - RPRT

    T1 - Three-Dimensional Static and Dynamic Reactor Calculations by the Nodal Expansion Method

    AU - Christensen, Brian

    PY - 1985

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    N2 - 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.

    AB - 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.

    KW - Risø-R-496

    KW - Risø-R-496(EN)

    KW - Computerized simulation

    KW - N codes

    KW - Neutron flux

    KW - Polynomials

    KW - Power distribution

    KW - Reactor cores

    KW - Reactor kinetcs

    KW - Series expansion

    KW - Three-dimensional calculators

    M3 - Report

    SN - 87-550-1169-1

    T3 - Denmark. Forskningscenter Risoe. Risoe-R

    BT - Three-Dimensional Static and Dynamic Reactor Calculations by the Nodal Expansion Method

    PB - Risø National Laboratory

    CY - Roskilde

    ER -

    Christensen B. Three-Dimensional Static and Dynamic Reactor Calculations by the Nodal Expansion Method. Roskilde: Risø National Laboratory, 1985. 206 p. (Denmark. Forskningscenter Risoe. Risoe-R; No. 496).