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Transport Effects in the P3 Treatment of Cylindrical Rods in a Square Lattice

T. E. Dudley, P. B. Daitch

Nuclear Science and Engineering

Volume 25 / Number 1 / May 1966 / Pages 75-84


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The monoenergetic transport equation is solved in the P3 approximation for a cylindrical rod in a square cell. Reflecting boundary conditions applied on the boundary of the cell represent exactly the geometry of cylindrical rods in an infinite square-lattice array. By comparison with Monte Carlo calculations, the P3 calculations appear to approach the exact transport solution at about the same rate in two dimensions as in one dimension. For the cases investigated, the scalar flux in the central absorbing rod is rather independent of the angular position. This appears to be the reason for the success of the Wigner-Seitz equivalent cylindrical cell, with various outer boundary conditions, in predicting flux disadvantage factors. Flux traverses in the square cell and in the Wigner-Seitz equivalent cylindrical cell are also illustrated.

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