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

2021 ◽  
Vol 9 ◽  
Author(s):  
Ji Ma ◽  
Chen Hao ◽  
Guanghao Liu ◽  
Le Kang ◽  
Peijun Li ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Uncertainty Analysis ◽  
Sensitivity Coefficient ◽  
Numerical Results ◽  
High Fidelity ◽  
Two Dimensional ◽  
Sensitivity Calculation ◽  
Generalized Perturbation Theory ◽  
Fuel Pin ◽  
Total Sensitivity

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.

scholarly journals Perturbation Theory-Based Whole-Core Eigenvalue Sensitivity and Uncertainty (SU) Analysis via a 2D/1D Transport Code

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Ji Ma ◽  
Chen Hao ◽  
Lixun Liu ◽  
Yuekai Zhou
Keyword(s):  
Perturbation Theory ◽  
Uncertainty Analysis ◽  
Cross Sections ◽  
Nuclear Reactor ◽  
Neutron Transport ◽  
Group Structure ◽  
Sensitivity Coefficient ◽  
Numerical Results ◽  
Transport Code ◽  
Sensitivity And Uncertainty Analysis

For nuclear reactor physics, uncertainties in the multigroup cross sections inevitably exist, and these uncertainties are considered as the most significant uncertainty source. Based on the home-developed 3D high-fidelity neutron transport code HNET, the perturbation theory was used to directly calculate the sensitivity coefficient of keff to the multigroup cross sections, and a reasonable relative covariance matrix with a specific energy group structure was generated directly from the evaluated covariance data by using the transforming method. Then, the “Sandwich Rule” was applied to quantify the uncertainty of keff. Based on these methods, a new SU module in HNET was developed to directly quantify the keff uncertainty with one-step deterministic transport methods. To verify the accuracy of the sensitivity and uncertainty analysis of HNET, an infinite-medium problem and the 2D pin-cell problem were used to perform SU analysis, and the numerical results demonstrate that acceptable accuracy of sensitivity and uncertainty analysis of the HNET are achievable. Finally, keff SU analysis of a 3D minicore was analyzed by using the HNET, and some important conclusions were also drawn from the numerical results.

scholarly journals Statistical problem of ideal gas in general two-dimensional regions

2014 ◽  
Vol 29 (02) ◽  
pp. 1450243 ◽  
Author(s):  
Ci Song ◽  
Wen-Du Li ◽  
Pardon Mwansa ◽  
Ping Zhang
Keyword(s):  
Perturbation Theory ◽  
Conformal Mapping ◽  
Ideal Gas ◽  
Mapping Method ◽  
Numerical Results ◽  
Statistical Problem ◽  
Thermodynamic Quantities ◽  
Two Dimensional ◽  
Conformal Mapping Method

In this paper, based on the conformal mapping method and the perturbation theory, we develop a method to solve the statistical problem within general two-dimensional regions. We consider some examples and the numerical results and fitting results are given. We also give the thermodynamic quantities of the general two-dimensional regions, and compare the thermodynamic quantities of the different regions.

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

2021 ◽  
Vol 247 ◽  
pp. 15017
Author(s):  
Yunki Jo ◽  
Vutheam Dos ◽  
Nhan Nguyen Trong Mai ◽  
Hyunsuk Lee ◽  
Deokjung Lee
Keyword(s):  
Monte Carlo ◽  
Perturbation Theory ◽  
Uncertainty Analysis ◽  
Covariance Matrix ◽  
Nuclear Data ◽  
Monte Carlo Code ◽  
Sensitivity Coefficients ◽  
Classical Perturbation Theory ◽  
Generalized Perturbation Theory ◽  
Parameters Of Interest

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.

scholarly journals Onset of Convection in Two-Dimensional Porous Cavities with Open and Conducting Boundaries

2021 ◽  
Vol 136 (3) ◽  
pp. 791-812
Author(s):  
Peder A. Tyvand ◽  
Jonas Kristiansen Nøland
Keyword(s):  
Critical Rayleigh Number ◽  
Numerical Results ◽  
Temperature Perturbation ◽  
Two Dimensional ◽  
Onset Of Convection ◽  
Order Problem ◽  
Fourth Order Problem ◽  
Thermally Conducting ◽  
Perturbation Pressure ◽  
Special Case

AbstractThe onset of thermal convection in two-dimensional porous cavities heated from below is studied theoretically. An open (constant-pressure) boundary is assumed, with zero perturbation temperature (thermally conducting). The resulting eigenvalue problem is a full fourth-order problem without degeneracies. Numerical results are presented for rectangular and elliptical cavities, with the circle as a special case. The analytical solution for an upright rectangle confirms the numerical results. Streamlines penetrating the open cavities are plotted, together with the isotherms for the associated closed thermal cells. Isobars forming pressure cells are depicted for the perturbation pressure. The critical Rayleigh number is calculated as a function of geometric parameters, including the tilt angle of the rectangle and ellipse. An improved physical scaling of the Darcy–Bénard problem is suggested. Its significance is indicated by the ratio of maximal vertical velocity to maximal temperature perturbation.

A generalized perturbation theory program for CANDU core analysis

2001 ◽  
Vol 28 (2) ◽  
pp. 169-189 ◽  
Author(s):  
Do Heon Kim ◽  
Jong Kyung Kim ◽  
Hangbok Choi
Keyword(s):  
Perturbation Theory ◽  
Core Analysis ◽  
Generalized Perturbation Theory
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