Generalized Perturbation Theory Based Total Sensitivity and Uncertainty Analysis for High-Fidelity Neutronics Calculation

Neutronics calculation for nuclear reactor with high-fidelity technology can significantly reduce the uncertainties propagated from numerical approximation error and model error. However, the uncertainty of input parameters inevitably exists, especially for nuclear data. On the other hand, resonance self-shielding calculation is essential for multi-group assumption based high-fidelity neutronics calculation, which introduce the implicit effect for calculation responses. In order to fully consider the implicit effects in the process of uncertainty quantification, a generalized perturbation theory (GPT) based implicit sensitivity calculation method is proposed in this paper. Combining the explicit sensitivity coefficient, which can be quantified using classic perturbation theory, the total sensitivity coefficient of calculation responses is obtained. Then the total sensitivity and uncertainty module is established in self-developed neutron transport code with high-fidelity technology-HNET. To verify the accuracy of the sensitivity calculation methods proposed in this paper, a two-dimensional fuel pin problem is chosen to verify the sensitivity results, and the numerical results show good agreement with results calculated by a direct perturbation method. Finally, uncertainty analysis for two-dimensional fuel pin problem is performed and some general conclusions are obtained from the numerical results.

The heuristically-based generalized perturbation theory

The generalized perturbation method is described relevant to ratios of bi-linear functionals of the real and adjoint neutron fluxes of critical multiplying systems. Simple linear analysis for optimization and sensitivity studies are then feasible relative to spectrum and space-dependent quantities, such as Doppler and coolant void reactivity effects in fast reactors.

UNCERTAINTY ANALYSIS OF SUB-EXERCISES IN UAM-SFR BENCHMARK WITH THE MCS CODE

Uncertainty analysis in Modelling (UAM) for Design, Operation and Safety Analysis of Sodium-cooled Fast Reactors (SFRs) has been formed by OECD/NEA to assess the effect of nuclear data uncertainties on parameters of interest in SFR analysis. In this paper, sub-exercises of a medium 1000 MWth metallic core (MET-1000) and a large 3600 MWth oxide core (MOX-3600) are tested by a Monte Carlo code MCS to perform uncertainty analysis. Classical perturbation theory and generalized perturbation theory are used to calculate sensitivity coefficients. Uncertainty is calculated by multiplying the sensitivity coefficients and relative covariance matrix from ENDF/B-VII.1 library.

VOID COEFFICIENT SENSITIVITY ANALYSIS FOR THE TRIGA MARK II REACTOR AT L.E.N.A. (UNIPV)

Sensitivity analysis studies the effect of a change in a given parameter to a response function of the system under investigation. In reactor physics, this usually translates into the study of how cross sections and fission spectrum modifications affect the value of the multiplication factor, the delayed neutron fraction or the void coefficient for example. Generalized Perturbation Theory provides a useful tool for the assessment of adjoint weighed functions such as keff and void coefficient sensitivities. In this work, the capability of SERPENT code to perform sensitivity calculation based on GPT is used to study the TRIGA Mark II research reactor installed at L.E.N.A. of University of Pavia. A general sensitivity analysis to the most important reactor’s cross sections has been performed in order to highlight the biggest reactivity contributions. Two numerically challenging tasks related to GPT calculation have been performed thanks to the relatively quick Monte Carlo approach allowed by this reactor: investigating the linearity of the reactivity injection caused by the flooding of the central channel, and calculating the fuel void coefficient sensitivity to the coolant density.

Uncertainty Analysis of the TRU-Burning Thorium-Fueled RBWR Using Generalized Perturbation Theory

The RBWR-TR is a thorium-based reduced moderation BWR (RBWR) with a high transuranic (TRU) consumption rate. It is charged with LWR TRU and thorium, and it recycles all actinides an unlimited number of times while discharging only fission products and trace amounts of actinides through reprocessing losses. This design is a variant of the Hitachi RBWR-TB2, which arranges its fuel in a hexagonal lattice, axially segregates seed and blanket regions, and fits within an existing ABWR pressure vessel. The RBWR-TR eliminates the internal axial blanket, eliminates absorbers from the upper reflector, and uses thorium rather than depleted uranium as the fertile makeup fuel. This design has been previously shown to perform comparably to the RBWR-TB2 in terms of TRU consumption rate and burnup, while providing significantly larger margin against critical heat flux. This study examines the uncertainty in key neutronics parameters due to nuclear data uncertainty. As most of the fissions are induced by epithermal neutrons and since the reactor uses higher actinides as well as thorium and 233U, the cross sections have significantly more uncertainty than in typical LWRs. The sensitivity of the multiplication factor (keff) to the cross sections of many actinides is quantified using a modified version of Serpent 2.1.19 [1]. Serpent [2] is a Monte Carlo code which uses delta tracking to speed up the simulation of reactors; in this modified version, cross sections are artificially inflated to sample more collision, and collisions are rejected to preserve a “fair game.” The impact of these rejected collisions is then propagated to the multiplication factor using generalized perturbation theory [3]. Covariance matrices are retrieved for the ENDF/B-VII.1 library [4], and used to collapse the sensitivity vectors to an uncertainty on the multiplication factor. The simulation is repeated for several reactor configurations (for example, with a reduced flow rate, and with control rods inserted), and the difference in keff sensitivity is used to assess the uncertainty associated with the change (the uncertainty in the void feedback and the control rod worth). The uncertainty in the RBWR-TR is found to be dominated by the epithermal fission cross section for 233U in reference conditions, although when the spectrum hardens, the uncertainty in fast capture cross sections of 232Th becomes dominant.