Abstract
The accurate prediction of the neutronic and thermal-hydraulic coupling system transient behavior is important in nuclear reactor safety analysis, where a large-scale nonlinear coupling system with strong stiffness should be solved efficiently. In order to reduce the stiffness and huge computational cost in the coupling system, the high-performance numerical techniques for solving delayed neutron precursor equation are a key issue. In this work, a new precursor integral method with an exponential approximation is proposed and compared with widely used Taylor approximation-based precursor integral methods. The truncation errors of exponential approximation and Taylor approximation are analyzed and compared. Moreover, a time control technique is put forward which is based on flux exponential approximation. The procedure is tested in a 2D neutron kinetic benchmark and a simplified high-temperature gas-cooled reactor-pebble bed module (HTR-PM) multiphysics problem utilizing the efficient Jacobian-free Newton–Krylov method. Results show that selecting appropriate flux approximation in the precursor integral method can improve the efficiency and precision compared with the traditional method. The computation time is reduced to one-ninth in the HTR-PM model under the same accuracy when applying the exponential integral method with the time adaptive technique.
Highlights
Reflective Vacuum0.01 0.00 0.01 0.00 0.01 0.00 were performed for three precursor treatments: independent variable, Taylor expansion approximation, and exponential expansion approximation
E analytical precursor concentrations consist of the integral of neutron flux over time and eliminate precursor variables in the neutron flux equation. erefore, the integral of neutron flux overtime should be accurately calculated
A new exponential form flux is Science and Technology of Nuclear Installations proposed in this work to calculate the integral of neutron flux over time, inspired by the ideas of the stiffness confinement method (SCM) [7] and frequency transform method [8]. e truncation errors of the proposed exponential approximation and Taylor approximation are analyzed and compared
Summary
0.01 0.00 0.01 0.00 0.01 0.00 were performed for three precursor treatments: independent variable, Taylor expansion approximation, and exponential expansion approximation. (1) Compared with the method which treats precursor concentrations as independent variables, the neutron precursor integral method is superior in terms of the accuracy, but an appropriate neutron flux approximation should be employed in analytical precursor concentration expression. (3) Different flux approximations in the precursor integral method introduce truncation errors of different sizes. (4) e exponential approximation gives the most accurate result among precursor integral methods in step reactivity insertion. Considering different time step selections among simulations, a time period of 0 ∼ 50 ms in these two reactivity input cases is chosen. Because of the lack of reference solution, the result of the independent precursor variable method of minimum time step is chosen as base solution. Previous simulations have compared several different precursor integral methods using different flux approximate methods and different length of time steps. 1.00000 1.30922 (−6.8e − 2) 1.31009 (−1.3e − 1) 1.96346 (+2.2e − 1) 1.96712 (+4.1e − 1) 2.07496 (−3.1e − 3) 2.07472 (−1.5e − 2) 2.09242 (+1.6e − 3) 2.09248 (+4.3e − 3) 2.10992 (+1.7e − 3) 2.10998 (+4.4e − 3)
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