k_eff Uncertainty Analysis of Small Prismatic HTGR

Uncertainties on results of reactor physics calculations basically originate from uncertainties of solvers, modeling parameters and nuclear data. The uncertainty quantification (UQ) of import core parameters is critical for the safety and reliability of the innovative nuclear reactor designs. In this paper, the UQ of the k_eff due to the neutron cross section data and the manufacturing tolerance of modeling parameters for a small prismatic high temperature gas-cooled reactor (HTGR) was reported. The stochastic sampling (SS) method, the sensitivity analysis (SA) method and the polynomial chaos expansion (PCE) method have been adopted during the UQ process. Firstly, the sensitivity analysis of k_eff to nuclear data was performed and uncertainties were calculated with sensitivity coefficients and covariance matrix of cross sections. The numerical results show that the k_eff uncertainty due to the neutron cross section data is about 511 pcm, among which 311 pcm are introduced by the neutron cross sections of the graphite and ²⁸Si, the considerable fraction of contribution compared to the conventional ²³⁵U and ²³⁸U. In addition, the SS method and PCE method were used to assess k_eff uncertainties owing to 25 modeling parameters, including important geometry dimensions and material compositions. A large number of input parameters were sampled and physical calculations were repeatedly conducted for each set of sampled parameters. In the PCE analysis, Legendre basis was used to construct polynomials on the assumption that all modeling parameters followed a uniform distribution and the linear regression method was adopted to solve for the coefficients. The analysis results indicate that the control of the uranium loading is the most critical manufacturing requirement. Although the uncertainties of the sizes of TRISO particles are large due to the manufacturing capacity, as long as the total loading of uranium is chosen as an individual control parameter and decoupled from other modeling parameters, k_eff uncertainty introduced by 25 modeling parameters can be reduced from about 1 950 pcm to about 420 pcm, among which the thickness of carbon layers of TRISO particles, the total loading and the enrichment of uranium have the most significant contributions. As far as the UQ analysis methods are concerned, the PCE and the SA methods show better efficiency than the SS method, and they can produce the total uncertainty and the individual uncertainty due to each parameter simultaneously. In addition, the PCE method gives a surrogate model at the same time to predict the k_eff for different modeling parameters without resolving to the time-consuming design calculations.