Resonance treatment using pin-based pointwise energy slowing-down method

doi:10.1016/j.jcp.2016.11.007

Journal of Computational Physics

Volume 330, 1 February 2017, Pages 134-155

https://doi.org/10.1016/j.jcp.2016.11.007 Get rights and content

Abstract

A new resonance self-shielding method using a pointwise energy solution has been developed to overcome the drawbacks of the equivalence theory. The equivalence theory uses a crude resonance scattering source approximation, and assumes a spatially constant scattering source distribution inside a fuel pellet. These two assumptions cause a significant error, in that they overestimate the multi-group effective cross sections, especially for ²³⁸U. The new resonance self-shielding method solves pointwise energy slowing-down equations with a sub-divided fuel rod. The method adopts a shadowing effect correction factor and fictitious moderator material to model a realistic pointwise energy solution. The slowing-down solution is used to generate the multi-group cross section. With various light water reactor problems, it was demonstrated that the new resonance self-shielding method significantly improved accuracy in the reactor parameter calculation with no compromise in computation time, compared to the equivalence theory.

Introduction

Equivalence theory has been widely used for resonance treatment methods [1], [2]. The equivalence theory gives a reasonable solution within a short computation time. Because of this many lattice physics codes adopt the equivalence theory to generate the effective cross-section (XS) [3], [4]. There have been a lot of research into equivalence theory to improve the accuracy of multi-group effective XS and the applicability for general geometry [1], [5], [6].

Recently, Cao reported that the multi-group ²³⁸U absorption XS from the equivalence theory tends to be overestimated [7]. He concluded that the flux from the narrow resonance (NR) approximation in the equivalence theory is problematic, and suggested an improved resonance treatment method using a pre-generated look-up table of integrated flux like the multi-group effective XS. Yamamoto focused on the reaction rate preservation between the ultrafine group calculation and the multi-group effective XS calculation with multi-term rational approximation, and suggested an improved derivation [8]. The two researches were performed to correct an overestimation of ²³⁸U absorption XS.

The overestimation of the ²³⁸U effective XS is addressed in this paper. This work figures out that resonance scattering causes the overestimation. In the equivalence theory, the resonance scattering source is approximated by the intermediate resonance (IR) approximation, and the resonance scattering XS is usually neglected in the resonance treatment process. However, for the nuclides (i.e., ²³⁸U) which have very large resonance scattering XSs, the equivalence theory causes a significant error in the effective XS because of the following reasons. First, the expression for the effective XS is derived from the multi-term rational approximation along with the NR or IR approximation. The derivation is formulated based on the IR approximation, but the final effective XS is calculated as a linear combination of the effective XSs generated from multiple dilution systems. This discrepancy between the derivation and usage of the XS look-up table can cause an error in the effective XS. Second, the equivalence theory cannot treat the spatial distribution of the effective XS inside the fuel pellet. Since the theory is based on the averaged effective XS of the fuel lump, the spatial self-shielding and spatial distribution of the scattering source cannot be considered properly. There are several methods which can consider spatial self-shielding inside the fuel pellet [9], [10], [11]. However, as the methods are based on the pellet-averaged effective XS [10] or the pellet-averaged escape probability approximation [9], [11] with the IR approximation, the resonance scattering source cannot be accounted for accurately.

This paper suggests a new resonance self-shielding method using the pointwise energy slowing-down solution in order to resolve the two problems described above. The new method computes the collision probabilities inside the fuel pellet as a function of the total XS, and then solves pointwise energy slowing-down equations based on the pin-cell. The shadowing effect correction factor and fictitious moderator are introduced to derive a realistic pointwise energy slowing down equation. The multi-group effective XS is calculated using the pointwise flux spectrum. The new method is verified with various light water reactor (LWR) problems and shows significant improvements in the accuracy of the effective XS and the multiplication factor.

Section snippets

Overestimation of ²³⁸U cross sections

The conventional equivalence theory is summarized in Section 2.1, and numerical test results are described in Section 2.2 to show the overestimation of ²³⁸U XS with the equivalence theory. From Section 2.3 to Section 2.5, further tests are performed with the pointwise energy approaches to find reasons of the overestimation ²³⁸U XS.

New resonance self-shielding method

In Section 2, the limitations of the equivalence theory are discussed. There is an error in the derivation of equivalence theory with the multi-term rational approximation. Furthermore, one region assumption inside the fuel, which is typically used in the equivalence theory, causes a significant error in the final effective XS. Therefore, a new resonance self-shielding method is required to correct the errors in the equivalence theory. In Section 3.1, the limitations of existing spatially

Verification

PSM is verified by solving various LWR problems. In Section 4.1, PSM and the contemporary resonance self-shielding methods are compared to a pin-cell problem, and the optimum calculation option of PSM is decided. In Section 4.2, more realistic LWR problems are analyzed with various resonance treatment methods. In Section 4.3, the computation efficiency of PSM is analyzed and compared to the equivalence theory. In all comparisons, reference results are generated by MCNP6, and the STREAM code is

Discussion

In Section 4, PSM is tested with various LWR problems, showing high accuracies in the eigenvalue and resonance XSs. However, it should be noted that PSM uses the following assumptions. First, PSM assumes constant material composition and temperature inside a fuel pellet. This is because $P_{i j}^{iso} (Σ_{t, i}^{⁎})$ is generated as a function of the total XS of the fuel lump to avoid energy dependent collision probability calculations. Traditionally, the UO₂ fuel is treated as a single region, and the

Conclusions

A new resonance self-shielding method, PSM, has been developed to eliminate the limitations of the conventional equivalence theory based methods. There are two limitations related to the assumptions in the resonance scattering source. First, the IR approximation in the equivalence theory used for the derivation of the multi-group effective XS, makes it possible to express the flux energy distribution in a heterogeneous system as a combination of those of multiple homogeneous systems. However,

Acknowledgements

This work was supported by the U.S. Department of Energy (DOE) under Contract number DE-AC02-06CH11357 and Korea Energy Technology Evaluation and Planning (KETEP) funded by the Korean Government Ministry of Trade, Industry and Energy (No. 20131610101850).

References (25)

C.C. Stoker et al.
Spatially dependent resonance cross sections in a fuel rod
Ann. Nucl. Energy
(1996)
D. Lee et al.
The impact of ²³⁸U resonance elastic scattering approximations on thermal reactor Doppler reactivity
Ann. Nucl. Energy
(2009)
Y. Li et al.
Resonance elastic scattering and interference effects treatments in subgroup method
Nucl. Eng. Technol.
(2016)
S. Choi et al.
Impact of inflow transport approximation on light water reactor analysis
J. Comput. Phys.
(2015)
D. Knott et al.
Lattice physics computations
R.J.J. Stamm'ler et al.
Methods of Steady-State Reactor Physics in Nuclear Design
(1983)
J. Rhodes et al.
CASMO-5 development and applications
D.J. Powney et al.
Overview of the WIMS 9 Resonance Treatment
(2004)
S. Choi et al.
Resonance self-shielding methodology of new neutron transport code STREAM
J. Nucl. Sci. Technol.
(2015)
S. Choi et al.
Resonance self-shielding method using resonance interference factor library for practical lattice physics computations of LWRs
J. Nucl. Sci. Technol.
(2015)

L. Cao et al.

An improved resonance self-shielding calculation method based on equivalence theory

Nucl. Sci. Eng.

(2015)

A. Yamamoto et al.

Improved derivation of multigroup effective cross section for heterogeneous system by equivalence theory

Nucl. Sci. Eng.

(2011)

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Resonance treatment using pin-based pointwise energy slowing-down method

Abstract

Introduction

Section snippets

Overestimation of 238U cross sections

New resonance self-shielding method

Verification

Discussion

Conclusions

Acknowledgements

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Nucl. Sci. Eng.

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Overestimation of ²³⁸U cross sections