Analysis of non-linear feedback in space-time reactor dynamics of finite-element methods

Thesis/Dissertation · Sat Jan 01 04:00:00 EST 1983

OSTI ID:6352426

Salehi, M A

The object of this thesis is to study the space-time behavior of neutrons in a nuclear reactor in the presence of feedback effects in one and two-group diffusion equation models. Mathematical models for slab and circular region cores are formulated which account for one delayed neutron group, fuel and coolant temperatures and xenon concentration. The feedback is expressed through linear temperature and xenon concentration coefficients of the core parameters. The resulting system of strongly coupled, non-linear, mixed (partial and ordinary) differential equations are transformed to a system of stiff ordinary differential equations by a Galerkin formulation of the equations using the finite element method for space discretization. This system is stiff because of the large difference in the time constants of the neutron population and temperature change and other form of feedbacks. Thus suitable stiff integration methods have to be used for the semi-discrete form of the finite element equations. Conditions for the dynamic studies with feedback can be specified that simulate certain departures from steady state. Here we assume that the reactor is initially in a critical condition at t = 0. The reactivity is increased in a step function insertion which causes a departure of the reactor from steady state behavior. Transients in both thermal and fast reactors are analyzed, and the results compared with those obtained in previous studies and in so called benchmark problems.

• Research Organization: California Univ., Berkeley (USA)
• OSTI ID: 6352426
• Country of Publication: United States
• Language: English

Related Subjects

22 GENERAL STUDIES OF NUCLEAR REACTORS
220100* -- Nuclear Reactor Technology-- Theory & Calculation
BARYONS
DELAYED NEUTRONS
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
ELEMENTS
EPITHERMAL REACTORS
EQUATIONS
FAST REACTORS
FERMIONS
FINITE ELEMENT METHOD
FISSION NEUTRONS
FLUIDS
GASES
GROUP THEORY
HADRONS
KINETICS
MATHEMATICAL MODELS
MATHEMATICS
NEUTRON DIFFUSION EQUATION
NEUTRONS
NONMETALS
NUCLEONS
NUMERICAL SOLUTION
ONE-DIMENSIONAL CALCULATIONS
QUANTITY RATIO
RARE GASES
REACTIVITY
REACTOR COMPONENTS
REACTOR CORES
REACTOR KINETICS
REACTORS
SPACE DEPENDENCE
THERMAL REACTORS
TIME DEPENDENCE
TRANSIENTS
TWO-DIMENSIONAL CALCULATIONS
XENON