Kinetics of Nuclear System Solution Methods for the Space-Time Dependent Neutron Diffusion Equation

Werner, W.

doi:10.1007/978-1-4613-9913-1_4

Cited by 9 publications

(4 citation statements)

References 31 publications

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“…The finite-element method has also been applied to the neutron diffusion equations [K1,LI,R5,W7,H8,A3]. Finite-element methods have a number of advantages over finite-difference methods.…”

Section: Numerical Solution Of the Group Diffusion Equationsmentioning

confidence: 99%

“…In modal methods, the expansion functions are the eigenvectors of some operator [Sl 3,D5,W7]. These eigenvectors or "modes" should form a complete set.…”

Section: Numerical Solution Of the Group Diffusion Equationsmentioning

confidence: 99%

“…Simplifying assumptions are necessary. They are made either in the modeling equations themselves, or in the discretization and numerical procedures used to solve them [HS,Dll,NI,W7,VII. In reactor static as well as transient analyses, the standard approach consists in solving the neutronic and thermal-hydraulic problems in tandem (using "coupled codes"). First, approximate values of fuel temperature, coolant temperature, and coolant density distributions are specified.…”

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confidence: 99%

“…Significant advances have been made in the past fifteen years in the development of methods for reactor-transient analyses [H7,Sl7,W7,A3,H9]. This progress, when combined with elaborate algorithms and numerical solution techniques, should make it possible to perform real-time calculations of three-dimensional neutron flux shapes on desktop (rather than mini-) computers in the near future, even for moderately fast transients.…”

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confidence: 99%

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A semi-experimental nodal synthesis method for the on-line reconstruction of three-dimensional neutron flux-shapes and reactivity

Jacqmin¹

1991

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The safety and optimal performance of large, cornmercial, light-water reactors require the knowledge at ali time of the neutron-flux distribution in the core. In principle, this information can be obtained by solving the timedependent neutron diffusion equations. However, this approach is complicated and very expensive. Sufficiently accurate, real-time calculations (time scale of approximately one second) are not yet possible on desktop computers, even with fast-running, nodal kinetics codes.A semi-experimental, nodal synthesis method which avoids the solution of the time-dependent, neutron diffusion equations is described. The essential idea of this method is to approximate instantaneous nodal group-fluxes by a linear combination of K, precomputed, three-dimensional, static expansion-functions. The time-dependent coefficients of the combination are found from the requirement that the reconstructed flux-distribution agree in a least-squares sense with the readings of J (___K) fixed, prompt-responding neutron-detectors. Possible numerical difficulties with the least-squares solution of the illconditioned, J-by-K system of equations are brought under complete control by the use of a singular-value-decomposition technique. This procedure amounts to the rearrangement of the original, linear combination of K expansion functions into an equivalent, more convenient, linear combination of R (< K) orthogonalized "modes" of decreasing magnitude. Exceedingly small modes are zeroed to eliminate any risk of rout, doff-error amplification, and to assure consistency with the limited accuracy of the data. Additional modes are zeroed when it is desirable to limit the sensitivity of the results to measurement noise.Numerical tests of this fitted-synthesis method demonstrate that best results are obtained when the synthesis is allowed to be discontinuous ha time. In this discontinuous ,.aode of operation, only a small subset of the library of expansion functions is retained at any instant in the synthesis formula. These expansion functions are flux shapes obtained for reactor conditions (control-rod positions, power level, ...) closely bracketing the actual, instantaneous state of the core.A model of a commercial pressurized-water reactor assumed to be equipped with fixed neutron-flux detectors is used to test the method. Comparisons with reference solutions show that, if the neutron detectors are sufficiently numerous and reasonably distributed throughout the core, and if their characteristics are perfectly known, nodal group-fluxes can be reconstructed in real-time with maximum errors of only a few percent, even for very severe transients involving control-rod motions and thermal-hydraulic feedback effects. Reactivity can be inferred by inverse kinetics with an accuracy of better than one miUibeta. PREFACEThis document is the final report of a two-year project carried out with the support of the DOE Office of Energy Research through Grant No. DEFG07-89ER 12888. The objective of the research was to develop and test a method for de...

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“…The finite-element method has also been applied to the neutron diffusion equations [K1,LI,R5,W7,H8,A3]. Finite-element methods have a number of advantages over finite-difference methods.…”

Section: Numerical Solution Of the Group Diffusion Equationsmentioning

confidence: 99%

“…In modal methods, the expansion functions are the eigenvectors of some operator [Sl 3,D5,W7]. These eigenvectors or "modes" should form a complete set.…”

Section: Numerical Solution Of the Group Diffusion Equationsmentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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