New Approximate Analysis of Nonlinear Space-Dependent Reactor Dynamics due to Reactivity Accidents

摘要

The nonlinear space-dependent reactor dynamics related to reactivity accidents have been studied analytically by means of a modified Helmholtz modal expansion method. In this method the neutron fluxes and delayed neutron precursors are expanded in terms of steady state or asymptotic shapes (persisting mode shapes) and of the shapes of higher eigenfunctions of the Helmholtz equation satisfying the boundary conditions that the values of eigenfunctions at the extrapolated boundary of reactor are zero. The expansion coefficients are time-dependent, and are obtained by solving simultaneous nonlinear differential equations. A code (SPEX-1) was developed for the computations related to this analysis, with which a sample calculation was performed on a problem concerning the self-shutdown behavior due to Doppler feedback in a power excursion. The merits of the modified Helmholtz modal expansion method are as follows:(1) Improved convergency of the solution as compared with the conventional modal expansion procedure; (2) Easy comparison with the one-point kinetic model; (3) Simplicity of the procedure of calculations related to power excursion analysis.