THE SPACE-TIME NEUTRON KINETICS BY A VARIATIONAL METHOD WITH APPLICATION TO POWER REACTOR DYNAMICS

Technical Report · Wed Dec 26 04:00:00 EST 1962

OSTI ID:4715228

Dougherty, D E

By use of the semidirect variational method, the time and space dependent neutron kinetic equations were reduced to a system of integro- differential equations in the time domain. The state vector of these equations defines the time-dependent coefficients for a set of space modes given by a modal expansion of the neutron flux. The accuracy of this method of analysis is arbitrary, and solutions are available for reactor configurations as complex as the present state of the art allows steady-state determinations. To avoid the difficult task of determining orthogonal eigenfunctions for a modal expansion in a complex geometry, nonorthogonal Green's Function modes are developed from an approximate solution of the integral form of the multigroup kinetic equations. Since an exact steady-state solution of the one-group diffusion model is available for a bare two-region slab reactor, this solution was compared with the results obtained by both orthogonal and nonorthogonal modal expansions. The basis of comparison was the asymptotic region buckling for a critical (steady- state) tworegion reactor, following a perturbation of the reactor material properties in either of the core regions. A twoterm expansion by Green's Function modes was clearly superior to an expansion in which the first two orthogonal modes for asymmetric perturbations of the core properties were used. Combining power coefficient dynamics with the reduced space-dependent neutron kinetic equations yields a state equation that is in general nonlinear. By linearizing these equations and using the transfer function formalism, the transformed equation of state for the modal coefficients for a generalized power coefficient is obtained. Illustrative calculations were made for a simple secondorder temperature and xenon poisoning power coefficient. A stability criterion was derived for the spatial flux distribution of an annular core model. Reasonably good agreement was obtained between the calculated stability margin and period of the spatial flux oscillations observed in the Shippingport Pressurized Water Reactor. Also calculated was the response of the spatial flux distribution in an annular core to both step and harmonic reactivity changes. 34 references. (auth)

• Research Organization: Knolls Atomic Power Lab., Schenectady, N.Y.
• DOE Contract Number: W-31-109-ENG-52
• NSA Number: NSA-17-021317
• OSTI ID: 4715228
• Report Number(s): KAPL-2217
• Country of Publication: United States
• Language: English

Related Subjects

BIBLIOGRAPHY
BUCKLING
CONFIGURATION
DIFFERENTIAL EQUATIONS
EQUATIONS
GROUP THEORY
NEUTRON FLUX
NEUTRONS
NUMERICALS
POISONING
POWER PLANTS
PRESSURE
REACTIVITY
REACTOR CORE
REACTOR TECHNOLOGY
REACTORS
SHIPPINGPORT
TEMPERATURE
TEMPERATURE COEFFICIENT
TRANSFER FUNCTIONS
TRANSPORT THEORY
WATER MODERATOR
ZONES