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Application of the Natural Mode Approximation to Space-Time Reactor Problems

Larry R. Foulke, Elias P. Gyftopoulos

Nuclear Science and Engineering

Volume 30 / Number 3 / December 1967 / Pages 419-435


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A space-dependent reactor kinetics approximation, called the Natural Mode Approximation (NMA), has been applied to the calculation and interpretation of reactor dynamic experiments. The NMA is based on a modal expansion technique where the space- and time-dependent reactor variables are approximated by a series of products of time-dependent coefficients and space-dependent expansion modes. The modes are the eigenvectors of a linear operator derived from the complete set of equations describing the reactor system at an initial reference condition. A pair of computer codes, MUDMO-II and SYNSIG, are used to synthesize approximate modes in two-dimensional systems without feedback. An oscillation test is proposed which may be used to verify key parameters of the NMA. The experimental technique is described and applied to both numerical and actual measurements. In addition, it is shown how a natural mode expansion may be used to interpret standard dynamic experiments when the observations are functions of space and time. The results of calculations of kinetic problems are compared with those of independent calculations which are considered to be exact. Good agreement is established. It is shown that the flux tilting following a localized perturbation is a sensitive function of the relative magnitudes of the measurable parameters of the NMA. The novel idea of “correction modes” is introduced which increases the accuracy of a low-order NMA without appreciable increase in computation time.

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