دانلود رایگان مقاله خواص طیفی فرآیندهای پویا در راکتور هسته ای

Abstract

As a rule, mathematical modeling of dynamic processes in nuclear reactors is conducted using an approach that treats a neutron flux in the multigroup diffusion approximation. In this approach, the basic model involves a multidimensional system of coupled parabolic-type equations. Similarly to common thermal phenomena, it is possible here to separate a regular mode of nuclear reactor operation that is associated with a selfsimilar development of a neutron field at large times. In this case, the main feature of dynamic processes is a minimal eigenvalue of the corresponding spectral problem. In the present paper, calculations of various eigenvalues are performed via the two-group model and discussed for the VVER-1000 reactor without a reflector and HWR reactor.

5. Conclusions

The spectral problems that may characterize the reactor dynamic behavior are considered. Within the multi-group diffusion approximation, the standard Lambda Modes spectral problem which is related to the definition of k-effective of the reactor core is considered. The Alpha Modes spectral problem is much more informative for considering the dynamic processes. We can relate the dynamics of the reactor at asymptotic stage at large times to fundamental a-eigenvalue and a-eigenfunction. A new spectral problem (Delta Modes spectral problem) is formulated, which is connected to self-adjoint part of operator of neutron absorptiongeneration. Solution of this problem allows making an a priori estimate of neutron flux dynamics. The computational algorithm for approximate solution of the spectral problems is based on a standard finite-element approximation using Lagrange finite elements of p ¼ 1; 2; 3. The matrix spectral problem is solved using a scalable and flexible toolkit for the solution of eigenvalue problems SLEPc. Approximate solution accuracy is checked at a sequence of condensing grid using finite elements of varying degrees. Test calculations are made in two-dimensional approximation for a model of VVER-1000 reactor without reflector and and HWR reactor using two-group diffusion approximation. The first real and complex eigenvalues and eigenfunctions in the Lambda Modes spectral problem are got. A good separability of the eigenvalues in the Alpha Modes spectral problem is identified. The results of the numerical solution of the Delta Modes spectral problem to assess neutron flux dynamics are given.