A semi-experimental nodal synthesis method for the on-line reconstruction of three-dimensional neutron flux-shapes and reactivity
The safety and optimal performance of large, commercial, light-water reactors require the knowledge at all time of the neutron-flux distribution in the core. In principle, this information can be obtained by solving the time-dependent 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 ({ge}K) fixed, prompt-responding neutron-detectors. Possible numerical difficulties with the least-squares solution of the ill-conditioned, 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 ({le}K) orthogonalized modes'' of decreasing magnitude. Exceedingly small modes are zeroed to eliminate any risk of roundoff-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.
- Research Organization:
- Massachusetts Inst. of Tech., Cambridge, MA (United States). Dept. of Nuclear Engineering
- Sponsoring Organization:
- USDOE; USDOE, Washington, DC (United States)
- DOE Contract Number:
- FG07-89ER12888
- OSTI ID:
- 5956230
- Report Number(s):
- DOE/ER/12888-T1; ON: DE92004450
- Resource Relation:
- Other Information: Thesis (Ph.D.)
- Country of Publication:
- United States
- Language:
- English
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21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS
NEUTRON FLUX
THREE-DIMENSIONAL CALCULATIONS
BWR TYPE REACTORS
COMPUTER CALCULATIONS
GEOMETRY
LEAST SQUARE FIT
NEUTRON DIFFUSION EQUATION
NEUTRON TRANSPORT THEORY
NUCLEAR REACTION KINETICS
PROGRESS REPORT
PWR TYPE REACTORS
Q CODES
REACTOR CORES
COMPUTER CODES
DIFFERENTIAL EQUATIONS
DOCUMENT TYPES
ENRICHED URANIUM REACTORS
EQUATIONS
KINETICS
MATHEMATICS
MAXIMUM-LIKELIHOOD FIT
NUMERICAL SOLUTION
POWER REACTORS
RADIATION FLUX
REACTION KINETICS
REACTOR COMPONENTS
REACTORS
THERMAL REACTORS
TRANSPORT THEORY
WATER COOLED REACTORS
WATER MODERATED REACTORS
220100* - Nuclear Reactor Technology- Theory & Calculation
210100 - Power Reactors
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210200 - Power Reactors
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