An integral transport theory boundary condition applied to close-packed lattice cells with investigations into a heuristic flux convergence method

Graduation date: 1983Spatial flux profiles were calculated in idealized,\ud optically-thin ( 1 mfp) cell systems using integral\ud transport theory. Numerical accuracy improvement and\ud convergence efficiency in computing these spatial flux\ud profiles was the primary concern. Toward these ends, kernel\ud volume-averaging techniques for curvilinear cell systems, a\ud reflective angular-dependent edge source boundary condition\ud for optically-thin cell systems and an iterative heuristic\ud convergence method were developed.\ud To the optically-thin cell systems (slab, cylindrical,\ud and spherical), an angular-dependent edge source boundary\ud condition (equivalent to a Double-PN (PNN) boundary\ud condition) was applied to improve the flux profile shape and\ud disadvantage factor. The spatial flux profile is composed\ud of the volume-source flux profile (black-body boundary\ud condition) plus a normalized flux from an edge source. The\ud edge source represents a reflecting boundary by reinserting neutrons that leak from the cell under the more easily\ud computed black-body conditions. For an optically-thick\ud system (greater than a few mfp's), an isotropic edge flux\ud (zero current boundary condition or P∞ ) is sufficient to\ud produce an accurate flux profile. However, in an\ud optically-thin system, the zero current boundary condition\ud begins to break down and a "dip" in the flux profile near\ud the cell edge and a reduced moderator flux are observed.\ud The anisotropy of the volume-source leakage is assumed to be\ud poorly represented by a re-entrant isotropic edge flux.\ud In order to "correct" the flux profile, the angular\ud moments of the volume-source leakage neutrons can be more\ud accurately approximated by two or more edge sources of\ud different angular emission distributions. However, complete\ud matchup of the angular moments of the volume-source leakage\ud neutrons to the re-entrant edge source neutrons would result\ud in the undesireable mirror boundary condition for\ud curvilinear systems subject to the classical "ray effect"\ud (overestimation of the disadvantage factor). Thus, the\ud diffuse few-moment condition (i.e. the P₁₁ or an isotropic\ud edge flux and cosine-directed edge flux combination) that\ud was developed seems to be an accurate and workable\ud compromise between the inaccuracies of the simple\ud zero-current boundary condition\ud (P∞ and those of a "mirror\ud reflecting" system