# Whole-core comparisons of subelement and fine-mesh variational nodal methods

## Abstract

The availability of nodal codes capable of performing whole-core transport calculations accentuates the issue of the errors incurred in first using infinite lattice results at the fuel assembly level to obtain homogenized cross sections. Such errors can be eliminated by employing homogenization only at the fuel pin cell level to obtain self-shielded pin cell cross sections and then performing whole-core transport calculations with each fuel pin cell represented as an explicit homogenized node. In principle, spherical harmonic or simplified spherical harmonic calculations can be performed using the VARIANT variational nodal code with one node per fuel pin cell. Such calculations, however, are expensive for two reasons: the large number of pin cell nodes [typically 289 fuel pins/fuel assembly and 157 or more assemblies per pressurized water reactor (PWR) core] and the slow convergence of the response matrix algorithms for the optically thin cells. To circumvent these difficulties, a finite subelement formulation of the variational nodal method was recently implemented. It is here generalized to perform whole-core PWR calculations without the need for homogenization at the fuel assembly level. In it, the orthogonal polynomials that represent the spatial distribution within each node of the conventional variational nodal methods are replaced bymore »

- Authors:

- Northwestern Univ., Chicago, IL (United States)
- Argonne National Lab., IL (United States)

- Publication Date:

- OSTI Identifier:
- 678129

- Report Number(s):
- CONF-990605-

Journal ID: TANSAO; ISSN 0003-018X; TRN: 99:009114

- Resource Type:
- Journal Article

- Journal Name:
- Transactions of the American Nuclear Society

- Additional Journal Information:
- Journal Volume: 80; Conference: 1999 annual meeting of the American Nuclear Society (ANS), Boston, MA (United States), 6-10 Jun 1999; Other Information: PBD: 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 21 NUCLEAR POWER REACTORS AND ASSOCIATED PLANTS; VARIATIONAL METHODS; NODAL EXPANSION METHOD; FUEL PINS; PWR TYPE REACTORS; FINITE ELEMENT METHOD; HETEROGENEOUS REACTOR CORES; NEUTRON TRANSPORT

### Citation Formats

```
Lewis, E.E., Palmiotti, G., and Taiwo, T.A.
```*Whole-core comparisons of subelement and fine-mesh variational nodal methods*. United States: N. p., 1999.
Web.

```
Lewis, E.E., Palmiotti, G., & Taiwo, T.A.
```*Whole-core comparisons of subelement and fine-mesh variational nodal methods*. United States.

```
Lewis, E.E., Palmiotti, G., and Taiwo, T.A. Wed .
"Whole-core comparisons of subelement and fine-mesh variational nodal methods". United States.
```

```
@article{osti_678129,
```

title = {Whole-core comparisons of subelement and fine-mesh variational nodal methods},

author = {Lewis, E.E. and Palmiotti, G. and Taiwo, T.A.},

abstractNote = {The availability of nodal codes capable of performing whole-core transport calculations accentuates the issue of the errors incurred in first using infinite lattice results at the fuel assembly level to obtain homogenized cross sections. Such errors can be eliminated by employing homogenization only at the fuel pin cell level to obtain self-shielded pin cell cross sections and then performing whole-core transport calculations with each fuel pin cell represented as an explicit homogenized node. In principle, spherical harmonic or simplified spherical harmonic calculations can be performed using the VARIANT variational nodal code with one node per fuel pin cell. Such calculations, however, are expensive for two reasons: the large number of pin cell nodes [typically 289 fuel pins/fuel assembly and 157 or more assemblies per pressurized water reactor (PWR) core] and the slow convergence of the response matrix algorithms for the optically thin cells. To circumvent these difficulties, a finite subelement formulation of the variational nodal method was recently implemented. It is here generalized to perform whole-core PWR calculations without the need for homogenization at the fuel assembly level. In it, the orthogonal polynomials that represent the spatial distribution within each node of the conventional variational nodal methods are replaced by a 17 x 17 array of continuous, piecewise bilinear finite element trial functions with the unknowns representing the even-parity flux at the corners of each fuel pin cell. The group source is constructed from the pin cell averages of the four vertex values of the scalar flux. Lagrange multiplier terms representing the odd-parity flux couple the fuel assemblies. The coupling consists of spatial polynomials (typically quadratic) at each assembly interface, obviating the need for infinite lattice approximations and allowing flux gradients across the assemblies to be more faithfully represented. At the same time, since each assembly represents a node in the global finite subelement transport calculation, the response matrices model optically thick regions and result in rapid convergence of the iterative algorithms.},

doi = {},

journal = {Transactions of the American Nuclear Society},

number = ,

volume = 80,

place = {United States},

year = {1999},

month = {9}

}