The differential characteristics of control rods of VVER-1000 core simulator at a low number of axial mesh points
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Differential Characteristics of Control Rods of VVER1000 Core Simulator at a Low Number of Axial Mesh Points A. A. Bolsunov* and S. A. Karpov** OAO VNIIAES, ul. Ferganskaya 25, Moscow, 109507 Russia *email: [email protected]; **email: [email protected] Received October 19, 2011
Abstract—An algorithm for refining the differential characteristics of the control rods (CRs) of the control and protection system (CPS) for a neutronics model of the VVER1000 simulator at a low number of axial mesh points of the core is described. The problem of determining the constants for a cell with a partially inserted CR is solved. The cell constants obtained using the proposed approach ensure smoothing of the dif ferential characteristics of an absorbing rod. The algorithm was used in the VVER1000 simulators (Bushehr NPP, unit no. 1; Rostov NPP, unit no. 1; and Balakovo NPP, unit no. 4). Keywords: algorithm, program, computer, simulator, nuclear constants. DOI: 10.1134/S1063778813140032
A threedimensional twogroup diffusion model [1] is used in the neutronics calculation of the VVER1000 simulator model. The active zone (core) contains a total of 163 × 13 calculation points (one point for each fuel assembly (FA) versus 13 height points). The constants for each region of computation are prepared beforehand using the GETERA software program [5] (with the homogenization of properties within each region) in the form of polynomial depen dences on the physical parameters of the core. Thus, the neutron physical constants used in the initial equations for determining the average neutron fluxes at all calculation points are reconstructed at every time instant on the basis of the distribution of physical parameters. Since a control rod (CR) of the control and protection system (CPS) in practice moves discretely with a step of 2 cm, more than ten steps of CR movement fall in a single region of compu tation (if the core is segmented axially into 13 points). In this case, two types of constants (with and with out the absorbing material) are prepared for the con sidered cell beforehand so as to maintain the possibil ity of setting the required cross section on the basis of this information in the online computation. Various algorithms of representation of constants might be used in this connection. If the CPS control rod is inserted in such a way that the depth of its insertion matches one of the height boundaries of the cells, the macroscopic absorption cross section is obtained naturally. In this case, the macroscopic cross sections (without the CR in one
cell and with it in another) prepared beforehand are used. If the CR is partially inserted in the cell, the need for rapid calculation of the average cross sections for this cell as functions of the absorber insertion depth (i.e., the need to switch from a heterogeneous repre sentation of the cell to a homogeneous one) arises. Averaging the (absorption) cross section over the computation cell, we obtain the following: CPS Σ a (z)
=
∫
∫
CPS 0 Σ а (z)Φ(z)dz + Σ а (z)Φ
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