ANALYTICAL SOLUTION OF FEEDBACK IN NUCLEAR RACTORS BY FINITE-ELEMENT METHOD

The objective is to study the space-time behavior of neutrons in a homogenous nuclear reactor in the presence of feedback effects. Mathematical model for circular region core are formulated with account for one delayed neutron group , fuel and coolant temperature and xenon concentration.The feedback is expressed through linear temperature and xenon concentration coefficients of core parameters.The resulting system are transformed to a system of "stiff" ordinary differential equations by GALERKIN formulation of the equations using the finite element method for space discretization.Thls system is stiff because of the large difference in the time constants.Here we assume that the reactor is initially in a critical condition at t“۰ the reactivity is increased in a step function insertion which cause a departure of the reactor from steady state behavior.Transients in several conditions are analyzed and the results are plotted and discussed.Isoparametric elements are used in the finite element method with element functions, quadratic Lar grange polynomials, expressed in polar coordinates.