Graduate Thesis Or Dissertation
 

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

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