To compute the effective coefficients, we employ 2D periodic cells representing the case of nuclear reactors in which the fuel rods are arranged in a square lattice, as in the case of Light Water Reactors (LWRs). Other numerical parameters were kept by default. One iterative Newton method was implemented with: initial damping factor = 1 and minimum damping factor = 1 × 10 − 4. The iterative matrix solution was solved with the MUMPS solver (Multifrontal Massively Parallel Sparse Direct), which allows the solution of large systems. For all the numerical computations, we used triangular elements and ensured independent-mesh results.
#Axial symmetry not applicable on 2d boundaries comsol 5.3 software#
This software works within the finite element method framework and it contains advanced numerical routines to handle challenger peculiarities as periodic boundary conditions, average value constraints, and adaptive grid mesh refinement procedures. The closure problems were solved numerically using the commercial software Comsol Multiphysics 5.2. Also, high neutron absorption rates decrease the number of neutrons moving in the moderator and the same conclusions are obtained when poor neutron dissipation happens, for instance, when fuel rods are used instead of spherical fuel particles.Īlfonso Prieto-Guerrero, Gilberto Espinosa-Paredes, in Linear and Non-Linear Stability Analysis in Boiling Water Reactors, 2019 5.3.4 Neutron effective coefficients
One of these scenarios occurs at early times considering that at the beginning of the reactor operation, the moderator contacts the fuel particles for the first time.
In general, it was found that the coefficient a v κ has larger values for those scenarios where fewer neutrons are traveling through the moderator. It was observed that using 3D cells also decreases the estimation of the neutronic interfacial coefficient, indicating that using nuclear rods in nuclear reactors favors the escaping of neutrons. The maximum (initial) and steady-state values of κ increase when Φ increases and for small moderator volume fractions. The general trend indicates that the steady state is achieved at shorter times for increasing values of Φ. The time to reach the steady state depends on the neutron absorption rate in the moderator.
8.10, the neutronic interfacial coefficient has the maximum value at early times and eventually reaches the steady state.
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