Abstract: A discrete ordinates method has been developed to approximate the neutron transport equation for the computation of the lambda modes of a given configuration of a nuclear reactor core. This method is based on discrete ordinates method for the angular discretization, resulting in a very large and sparse algebraic generalized eigenvalue problem. The computation of the dominant eigenvalue of this problem and its corresponding eigenfunction has been done with a matrix-free implementation using both, the power iteration method and the Krylov-Schur method. The performance of these methods has been compared solving different benchmark problems with different dominant ratios.

Abstract: In order to reproduce and study the neutron noise transients present in the nuclear reactor core, it is compulsory to develop a suitable tool. Unfortunately, this kind of capacity is not originally considered in the time-domain neutron diffusion codes so, a complex methodology have to be developed in each code. Thus, with the aim of endowing the U.S. Nuclear Regulatory Commission (NRC) neutron diffusion code of reference, PARCSv3.2, with the capability for reproducing this type of transients, a complete methodology, involving changes in the source code and the development of new auxiliary tools, has been created in order to ensure accurate reproductions of the core behaviour under the existence of a neutron noise source. This approach is performed for reproducing two representative sources of sinusoi-dal oscillations existing at a nuclear reactor core: a point-wise source, corresponding to the fluctuation created by an absorber of variable length, and a traveling perturba-tion, simulating a perturbation in the thermal-hydraulic data along an entire channel. Besides, one of the main limitations of reproducing this type of problem is the big size data needed, since we need to solve sometimes-long transients with small time steps for an entire nuclear reactor core. In addition, an analysis of the proficiency of the most consolidated numerical schemes available in PARCSv3.2 and the dependence on cell size for this kind of transients are applied to a real case of study in order to understand better their influ-ence in neutron noise transients.

Abstract: In this paper, we summarize on an approach which couples the multi-scale method with the homogenization theory to develop engineering models for three unique granular filtration cases, namely, effective rapid filtration to remove turbidity particles, adsorption and biofilm absorption of natural organic matters. These cases differ in their microscale Peclet and Damköhler numbers due to varying hydraulic loading rates, sizes of solutes and removal mechanisms to achieve the purification step. By first coupling the fluid and solute problems, we systematically derive the homogenized effective equations for the effective rapid filtration process while introducing an appropriate boundary condition to account for the particles’ deposition occurring on the spheres’ boundaries within a pre-scribed face-centred cubic (FCC) periodic cell. Validation of the derived homogenized equation for this case is achieved by comparing the predictions with our experimentally-derived values for the normalized pressure gradient acting upon the experimental filter. The same approach can subsequently be extended to the latter two cases by changing the involved time scale. Experimental works for validating these models are currently underway. Most importantly, we identify a need to include a computational approach to resolve for the concentration parameter within the periodic cell at higher orders. The computational values will then be introduced back into the respective homogenized equations for further predictions which are to be compared with the obtained experimental values under varying real-world conditions. This proposed hybrid methodology is currently in progress.

Abstract: High efficient methods are required for the computation of several lambda modes associated with the neutron diffusion equation. Multiple iterative methods have been used to solve this problem. In this work, three different block methods are studied to solve this problem. The first method is a procedure based on the modified block Newton method. The second one is an eigensolver based on subspace iteration and accelerated with Chebyshev polynomials. Finally, a block inverse-free preconditioned Krylov subspace method is analyzed. Two benchmark problems are studied illustrating the convergence properties and the competitiveness of the methods proposed.