Flux-limited Diffusion Coefficient Applied to Reactor Analysis

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Keller, Steven Ede
Rahnema, Farzad
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A new definition of the diffusion coefficient for use in reactor physics calculations is evaluated in this thesis. It is based on naturally flux-limited diffusion theory (FDT), sometimes referred to as Levermore-Pomraning diffusion theory. Another diffusion coefficient more loosely based on FDT is also evaluated in this thesis. Flux-limited diffusion theory adheres to the physical principle of flux-limiting, which is that the magnitude of neutron current is not allowed to exceed the scalar flux. Because the diffusion coefficients currently used in the nuclear industry are not flux-limited they may violate this principle in regions of large spatial gradients, and because they encompass other assumptions, they are only accurate when used in the types of calculations for which they were intended. The evaluations were performed using fine-mesh diffusion theory. They are in one spatial dimension and in 47, 4, and 2 energy groups, and were compared against a transport theory benchmark using equivalent energy structures and spatial discretization. The results show that the flux-limited diffusion coefficient (FD) outperforms the standard diffusion coefficient in calculations of single assemblies with vacuum boundaries, according to flux- and eigenvalue-errors. In single assemblies with reflective boundary conditions, the FD yielded smaller improvements, and tended to improve only the fast-group results. The results also computationally confirm that the FD adheres to flux-limiting, while the standard diffusion coefficient does not.
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