Yuanzineng kexue jishu (Oct 2023)
Study on Burnup Calculation Method Based on Proper Orthogonal Decomposition Reduced-order
Abstract
The goal of high-fidelity burnup calculations is to accurately describe the nuclide composition of the reactor over its entire lifetime. As the core physics calculation method evolves to high-fidelity, the number of burnup regions will increase thousands of times from the traditional decimeter level to the centimeter level, and the cost and complexity of the burnup calculation will increase steeply while the accuracy of the burnup calculation increases. In this paper, the fuel consumption calculation method based on the proper orthogonal decomposition (POD) reduced-order method was studied. By establishing a parametric reduced-order model (ROM), a set of complete orthogonal basis functions was used to construct the burnup matrix in each burnup region, and further based on the offline-online calculation strategy to achieve efficient numerical solution. In the offline phase, a high-fidelity burnup calculation was performed to obtain the snapshot matrices of reaction rate and neutron flux. Based on singular value decomposition (SVD), a set of basis functions of the burnup matrix and neutron flux were constructed respectively. In the online phase, the neutron flux was obtained from the real-time transport calculation, the parametric ROM and basis functions in the offline stage were used to quickly construct the burnup matrix and then completed the full-life burnup calculation. Based on the benchmark problem of MOX fuel cell released by JAEA, the numerical results verify the correctness and feasibility of this method. For the calculation of kinf, the relative deviation from the full-order model (FOM) is less than 0.5% with only the first-order ROM. For the calculation of nuclear density of heavy nuclides 235U and 239Pu, the first-, fifth- and tenth-order ROMs were used for calculation. Comparing with the FOM, the relative deviations are within 5%, 0.1% and 0.005%, respectively. However, for the calculation of 155Gd and 149Sm, which have larger neutron absorption cross sections, the calculation accuracy of the first-order ROM is poor, the relative deviation of the fifth-order ROM is within 5%, and the relative deviation of the tenth-order ROM reaches within 0.1%. From the calculation results, it can be seen that a ROM of about fifth-order can be used to construct the burnup matrix for 3 fuel regions at every burnup step, which can obtain good calculation accuracy without repeatedly calculating and storing the burnup matrix. Comparing with the traditional burnup calculation method, the acceleration ratio obtained by different reduced-order models is up to 18-23. Compared with the traditional burnup calculation, the acceleration ratio of the 5-order reduced-order model can reach 17-26, which improves the calculation efficiency. This method can be used as a reference to effectively reduce the cost and improve the efficiency of high-fidelity burnup calculations.
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