A POD reduced order model for criticality problems in reactor physics varying control rod settings
Heaney Claire  1, *@  , Andrew Buchan  1@  , Christopher Pain  1@  , Simon Jewer  2@  
1 : Imperial College London
Department of Earth Science and Engineering, South Kensington Campus, Imperial College London, SW7 2AZ -  United Kingdom
2 : Defence Academy, HMS Sultan
Gosport -  United Kingdom
* : Corresponding author

Problems in reactor physics give rise to complex, coupled and multidimensional systems that are challenging to solve from a computational point of view. In this paper a reduced order model is applied to the equations that govern the criticality of a nuclear reactor. The behaviour of the neutrons is modelled by the multigroup diffusion equation, which, for criticality, takes the form of a generalised eigenvalue problem. The operation of a reactor involves the positioning of control rods. They can be lowered into the reactor to decrease the neutron population and removed to increase the neutron population. The likelihood of whether or not neutron fission or absorption occurs is governed by the fission and absorption cross-sections which are temperature dependent. To solve an eigenvalue problem with every control rod setting of interest for a given temperature distribution would be time consuming, which is why we propose the use of reduced order modelling.

An offline phase involves solving the eigenvalue problem for a range of control rod configurations and a range of temperatures. Known as a snapshot, the eigenvector solution for each choice of parameters is gathered into a matrix. A singular value decomposition is applied to the matrix which yields a set of basis functions. A certain number of the basis functions are used to project the matrices associated with the discrete generalised eigenvalue problem onto a lower dimensional space.

As the projected matrices are of a much smaller size, the online phase of solving the reduced order generalised eigenvalue problem is much faster than solving the full problem. We show results where the reduced order model produces highly accurate solutions for Pressurised Water Reactor assemblies operating under general conditions with varying control rod position and varying temperature distributions for both fuels and coolants. Our results demonstrate that the reduced order model is able to reproduce the snapshot solutions very accurately (as would be expected). Furthermore, we show that for a control rod configuration and temperature not used in the snapshots, then the solution, compared to a full model simulation, is also accurate.

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