State change modal method for numerical simulation of dynamic processes in a nuclear reactor

Abstract

Modeling of dynamic processes in nuclear reactors is carried out, mainly, on the basis of the multigroup diffusion approximation for the neutron flux. The basic model includes a multidimensional set of coupled parabolic equations and ordinary differential equations. Dynamic processes are modeled by a successive change of the reactor states, which are characterized by given coefficients of the equations. In the modal method, the approximate solution is represented as an expansion on the first eigenfunctions of some spectral problem. The numerical-analytical method is based on the use of dominant time-eigenvalues of a multigroup diffusion model taking into account delayed neutrons. Numerical simulations of the dynamic process were performed in the framework of the two-group approximation for the VVER-1000 reactor test model. The last is characterized by the fact that some eigenvalues are complex.

Modal methods for the neutron diffusion equation using different spatial modes

“…The α-modes have been also applied to study reactor instabilities . More recently, the State Change Modal (SCM) method has been proposed (Avvakumov et al, 2018) based also on the calculation of the dominant α-modes. Dulla et al in (Dulla et al, 2018) developed a fully analytical study of the spectrum of the neutron diffusion operator to analyze some general properties of the neutron evolution.…”