Том 79, № 8 (2016)

An algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations is presented. The algorithm for systems of first-order differential equations is implemented in the EDELWEISS code with the possibility of parallel computations on supercomputers employing the MPI (Message Passing Interface) standard for the data exchange between parallel processes. The solution is represented by a series of orthogonal polynomials on the interval [0, 1]. The algorithm is characterized by simplicity and the possibility to solve nonlinear problems with a correction of the operator in accordance with the solution obtained in the previous iterative process.

Parallelization is applied to the neutron calculations performed by the heterogeneous method on a graphics processing unit. The parallel algorithm of the modified TREC code is described. The efficiency of the parallel algorithm is evaluated.

Analytical expressions for elements of the triangular matrix of effective conditions at the boundary of the core with a multiregion reflector are derived in the few-group diffusion approximation. The developed technique is verified using the example of fuel assemblies of a light-water reactor with an intermediate neutron spectrum.

The specific features of calculation of the effective multiplication factor using the Monte Carlo method for weakly coupled and non-asymptotic multiplying systems are discussed. Particular examples are considered and practical recommendations on detection and Monte Carlo calculation of systems typical in numerical substantiation of nuclear safety for VVER fuel management problems are given. In particular, the problems of the choice of parameters for the batch mode and the method for normalization of the neutron batch, as well as finding and interpretation of the eigenvalue spectrum for the integral fission matrix, are discussed.

The equilibrium isotopic compositions and the times to equilibrium in the process of thorium–uranium–plutonium oxide fuel recycling in VVER-type reactors using heavy water mixed with light water are estimated. It is demonstrated thEhfat such reactors have a capacity to operate with self-reproduction of active isotopes in the equilibrium mode.

The article covers the uncertainty analysis of the physical calculations of the VVER reactor core for different meshes of the reference values of the feedback parameters (FBP). Various numbers of nodes of the parametric axes of FBPs and different ranges between them are investigated. The uncertainties of the dynamic calculations are analyzed using RTS RCCA ejection as an example within the framework of the model with the boundary conditions at the core inlet and outlet.

The application of experimental information on measured axial distributions of fission reaction rates for development of 3D numerical models of the ASTRA critical facility taking into account azimuthal asymmetry of the assembly simulating a HTGR with annular core is substantiated. Owing to the presence of the bottom reflector and the absence of the top reflector, the application of 2D models based on experimentally determined buckling is impossible for calculation of critical assemblies of the ASTRA facility; therefore, an alternative approach based on the application of the extrapolated assembly height is proposed. This approach is exemplified by the numerical analysis of experiments on measurement of efficiency of control rods mockups and protection system (CPS).

The file-evaluation results of a reactimeter based on the inverse solution to the kinetics equation (ISKE) are presented, which were obtained using an operating hardware-measuring complex with a KNK-4 neutron detector working in the current mode. The processing of power-recording files of the BR-1M, BR-K1, and VIR-2M reactors of the Russian Federal Nuclear Center—All-Russian Research Institute of Experimental Physics, which was performed with the use of Excel simulation of the ISKE formalism, demonstrated the feasibility of implementation of the reactivity monitoring (during the operation of these reactors at stationary power) beginning from the level of ~5 × 10^–4β_eff.

The prompt neutron generation time is measured in the core of the VIR-2M research nuclear reactor. The measurements are performed using the Babala method while the reactor is in the subcritical state. The VIR-2M reactor and the relevant experimental equipment are briefly described, and the experimental procedure and data processing technique are presented. It is shown that the prompt neutron generation time with empty experimental channels is 35 ± 1 μs.