Research Papers

A Reduced Basis Approach for Modeling the Movement of Nuclear Reactor Control Rods

[+] Author and Article Information
Alberto Sartori

Nuclear Engineering Division, Department of Energy,
Politecnico di Milano,
Milano 20156, Italy
e-mail: alberto.sartori@polimi.it

Antonio Cammi

Nuclear Engineering Division, Department of Energy,
Politecnico di Milano,
Milano 20156, Italy
e-mail: antonio.cammi@polimi.it

Lelio Luzzi

Nuclear Engineering Division, Department of Energy,
Politecnico di Milano,
Milano 20156, Italy
e-mail: lelio.luzzi@polimi.it

Gianluigi Rozza

SISSA MathLab, International School for Advanced Studies,
Trieste 34136, Italy
e-mail: gianluigi.rozza@sissa.it

1Corresponding author.

Manuscript received November 24, 2014; final manuscript received October 25, 2015; published online February 29, 2016. Assoc. Editor: Asif Arastu.

ASME J of Nuclear Rad Sci 2(2), 021019 (Feb 29, 2016) (8 pages) Paper No: NERS-14-1062; doi: 10.1115/1.4031945 History: Received November 24, 2014; Accepted November 02, 2015

This work presents a reduced order model (ROM) aimed at simulating nuclear reactor control rods movement and featuring fast-running prediction of reactivity and neutron flux distribution as well. In particular, the reduced basis (RB) method (built upon a high-fidelity finite element (FE) approximation) has been employed. The neutronics has been modeled according to a parametrized stationary version of the multigroup neutron diffusion equation, which can be formulated as a generalized eigenvalue problem. Within the RB framework, the centroidal Voronoi tessellation is employed as a sampling technique due to the possibility of a hierarchical parameter space exploration, without relying on a “classical” a posteriori error estimation, and saving an important amount of computational time in the offline phase. Here, the proposed ROM is capable of correctly predicting, with respect to the high-fidelity FE approximation, both the reactivity and neutron flux shape. In this way, a computational speedup of at least three orders of magnitude is achieved. If a higher precision is required, the number of employed basis functions (BFs) must be increased.

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Grahic Jump Location
Fig. 4

Delaunay triangulation (continuous line) and Voronoi tessellation (dotted line) of the initial set (a), of the next iteration (b), and at last iteration (c)

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Fig. 1

Map of the TRIGA Mark II reactor core (a), and x-z model employed for the RB method (b)

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Fig. 5

Energy of the POD modes

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Fig. 6

High-fidelity FE spatial flux distribution (cm−2s−1)

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Fig. 7

Neutron flux distribution (cm−2s−1) provided by the ROM, as function of N. (a) N=10, (b) N=20, (c) N=40, (d) N=60, and (e) N=80

Grahic Jump Location
Fig. 8

Spatial error between the ROM and the FE solution (a.u.), as function of N. (a) N=10, (b) N=20, (c) N=40, (d) N=60, and (e) N=80

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Fig. 2

RB triangulation of the reference domain

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Fig. 3

RB triangulation of the original domain Ωo(μ)



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