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Perturbation Theory Based on a Nodal Model

Temitope A. Taiwo, A. F. Henry

Nuclear Science and Engineering

Volume 92 / Number 1 / January 1986 / Pages 34-41


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The standard point kinetics equations and formally exact expressions for reactivity, prompt neutron lifetime, and effective delayed neutron fractions are derived from the matrix form of the nodal code QUANDRY. Perturbation theory expressions for reactivity based both on the standard quadratic-transverse-leakage form of QUANDRY and on the coarse-mesh finite difference (CMFD) form, made accurate by the use of discontinuity factors, are derived. With three-dimensional CMFD QUANDRY transient calculations taken as numerical standards, the accuracy of several standard point kinetics methods as well as the improved quasi-static method is tested. Results suggest that point kinetics methods are poor for rod ejection calculations, even if a precalculated table of rod worth versus position is used to infer the reactivity contribution of the moving rods. For transients not involving rod motion, the point kinetics equations are more accurate. Use of core-averaged (rather than node-dependent) temperature coefficients, however, can produce significant errors. The quasistatic scheme appears to yield acceptably accurate results but, for the tests run, consistently required more computing time than needed for the full three-dimensional solutions.

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