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Recently, the SCALE6.2 code has implemented the Sampler module for randomly sampling important reactor physics inputs from their parental distributions. The Sampler module uses a stochastic sampling technique based on multivariate (MV) sampling which assumes that the input cross-sections are correlated according to a predefined covariance matrix. Although the methodology used in the Sampler module is relatively straightforward and robust, it can be computationally expensive for applications where a large number of Monte Carlo samples are required. In this paper, the SCALE6.2 capabilities are enhanced by implementing the Unscented Transformation (UT) and Low Rank Approximation (LRA) to decrease computational time. The uncertainties are calculated for k-inf due to perturbations in the multi-group cross-sections for a standard PWR fuel pin but the methodology can be applied to any output parameter of interest (such as few group cross sections). First, the UT is applied to generate a set of sigma points which represent the behavior of the system over the entire space. However, since the input model dimensionality is very high, due to the number of isotopes, reactions, and energy-groups, the generation of the sigma sample points may be computationally burdensome. Therefore, the LRA is applied to reduce the order of sampling space which can significantly reduce the computational cost; this model is called the Truncated Unscented Transformation (TUT). The results show that the input-dimension can be reduced from 896 to 112-subspace and the uncertainties in k-inf calculated by TUT sampling with 225 samples are about 5.62 × 10 - 1 which agrees well with the full MV sampling with N = 1000 runs and results from TSUNAMI. The results also indicate that the uncertainties calculated by the TUT methodology are not sensitive to the scaling parameter λ assumed in the LRA as long as the appropriate weights are applied.

In this work, the reactor kinetics capability is used to compute the design safety parameters in a PWR due to complete loss of coolant flow during protected and unprotected accidents. A thermal-hydraulic code coupled with a point reactor kinetic model are used for these calculations; where kinetics parameters have been developed from the neutronic SRAC code to provide inputs to RELAP5-3D code to calculate parameters related to safety and guarantee that they meet the regulatory requirements. In RELAP5-3D the reactivity feedback is computed by both separable and tabular models. The results show the importance of the reactivity feedback on calculating the power which is the key parameter that controls the clad and fuel temperatures to maintain them below their melting point and therefore prevent core melt. In addition, extending modeling capability from separable to tabular model has nonremarkable influence on calculated safety parameters. Keywords: CLOFA, RELAP5-3D code, Reactor kinetics, PWR

The most important factors in any code used for nuclear reactor modeling are the time and precision of the results. In principle, deterministic codes are used in calculations due to the long computational time required by stochastic codes to achieve reliable results. The accuracy of deterministic codes is related to the method used in treating the resonance self-shielding behavior of the cross-sections; hence it is essential to select the best self-shielding method. Both the equivalence in dilution, and the subgroup approaches are used to represent the self-shielding effect in PWR pin cell. The calculations are performed using three classes of subgroup approaches based on physical and mathematical (Ribon extended model and subgroup projection method) probability tables. In the present paper, various cross-section library formats are considered to assess the performance of three PWR fuel types: UO 2 , PuO 2 –UO 2 , and ThO 2 –UO 2 , using DRAGON4 and WIMS-D5 codes. The accuracy of the calculations is determined by comparison with the stochastic MCNP6 code. The results obtained indicate that the radial sub-divisions and proper resonance treatment are required to treat the rim effect. This is demonstrated in DRAGON code that can accurately calculate the radial distributions for all reaction rates.

The uncertainty of minor actinides transmutation in fast reactors has been estimated for individual nuclides of minor actinides (MA). The burn-up dependent sensitivities of MA number densities are calculated using the generalized perturbation theory, and a method is derived to transform the sensitivities to the sensitivities of minor actinides transmutation. The sensitivities are used to obtain the uncertainties of minor actinides transmutation together with the cross-section covariance data of JENDL-4. The method is applied to the two MA transmutation fast reactor cores with MA content of 6% and 11%. It is seen that the uncertainties of the total MA transmutation amounts are about 3% and 4% for the two cores because the uncertainties of Np-237 and Am-241 transmutations which mainly contribute the total transmutation are small (about 3%). The contribution to the uncertainties is mainly caused by the Np-237 and Am-241 capture cross-sections. The transmutation uncertainties for Np-239, Am-233, Cm-243, and Cm-245 are rather large. However the transmutation amounts of these nuclides are very small, and the large uncertainties are not the problem in practice. However, it is found that the transmutation amount of Cm-244 has large uncertainties of 10% and 13% for the cores with MA content of 6% and 11%, and this large uncertainties have to be considered when MA fuels are fabricated and reprocessed because Cm-244 produces large decay heat and neutron emission.

The purpose of this paper is to apply our improved method for calculating sensitivities and uncertainties of reactivity responses for UO 2 and MOX ( ThO 2 – UO 2 and PuO 2 – UO 2 ) fueled pressurized water reactor cells. The improved method has been used to calculate sensitivity coefficients relative to infinite dilution cross-sections with self-shielding effect taken into account. Two types of reactivities are considered: Doppler reactivity and coolant void reactivity. For each type of reactivity, the sensitivities are calculated for small and large changes of reactivity. The results have demonstrated that the sensitivities are dependent on the changes of reactivity, and the reactivity variation uncertainty is larger than the eigenvalue uncertainty. In addition, the uncertainty of coolant void reactivity is much greater than Doppler reactivity especially for large changes of reactivity because the contribution of U-238 inelastic scattering becomes large. The sensitivity coefficients and uncertainties of both reactivities were verified by comparing with SCALE code results using ENDF/B-VII library and good agreements have been found.

The Low Rank Approximation (LRA) and Unscented Transform (UT) are integrated to produce a new algorithm having the capability to decrease the time required for the uncertainty quantification during Loss of coolant accident (LOCA) in Pressurized Water Reactors (PWR). The LRA is an efficient technique used in reducing computational cost due to its ability to perform dimensionality reduction by revealing the active or important degrees of freedom and calculate the basis of the so-called active subspace basing on the Singular Value Decomposition (SVD). For further reduction in the computational time; the UT algorithm is also implemented to generate a set of sigma points, these sigma points are the representatives of the whole probability distribution (the UT is restricted to Gaussian distribution). The main safety parameter is the maximum cladding temperatures during the accident which are computed by ATHLET thermal-hydraulic code. The reactivity coefficients and the covariance matrix are calculated using the SCALE 6.2 code. The present calculation model has 14-dimensions, therefore the number of sigma points needed for the SVD/UT technique is 29, and can be minimized to 5 sigma points only if the LRA/UT is used where two singular values are sufficient to reproduce/span the space thanks to the strong correlations between the reactivity coefficients.

One task of the regulatory body during the review and assessment process is the quantification of uncertainty and sensitivity (U&S) during normal and accident conditions. Nowadays there are many codes having the capability of estimating U&S, but few of them can estimate uncertainty and sensitivity during severe accident conditions. The IRSN uncertainty propagation and sensitivity analysis tool named SUNSET is considered one of the most important tools used in U&S analysis, where it is coupled with ASTEC software package (Accident Source Term Evaluation Code) for computing U&S during severe accident condition. Unfortunately, the SUNSET tool cannot perform U&S analyses during all the transient time. The SUNSET software can only calculate U&S parameters for maximum, minimum, and last output values, therefore it was necessary to modify the SUNSET tool to calculate U&S during the whole transient time. The main objective of this study is to develop a Python script to replace the SUNSET post-processing step, extract the results, and perform U&S analysis. ASTEC code has been used for the simulation of a loss of coolant accident in the cold leg of the primary circuit of the FPT-1 test. The obtained results indicate the efficiency of the modified SUNSET tools to calculate the uncertainty during severe accidents. In general, it was found that the code is capable to model the main severe accident phenomena. SUNSET package shows good agreement with the experimental data, for the whole calculation period, until thermocouples failure moment. The obtained results show that the main safety parameters are very sensitive to the power multiplier.

The present studies focus on the quantification of uncertainty during the main steam line break accident scenario (MSLB) in PWR, assuming that there is a failure on the feed-water regulating valve of the broken steam generator. The scenario is characterized by the associated positive Doppler and coolant density reactivities which bring the core back to critical (return-to-power). Accordingly, the input uncertainty parameters are the Doppler and coolant density reactivities taking into account the correlation matrix among the input parameters, which is calculated by SCALE 6.2 code. The main safety parameters are the maximum cladding surface temperatures and average core power during the accident which are computed by ATHLET thermal-hydraulic code. The sampling-based uncertainty technique is considered to be the most dependable technique which can be applicable to any code, however it is computationally expensive. Therefore, it is important to develop efficient techniques which are capable of reducing the calculation time. The first approach is the SVD-UT where the Unscented Transform (UT) algorithm and singular value decomposition (SVD) are combined to generate a minimal sample points. In addition, due to the strong correlation between the input reactivities, the computational time can be further reduced by implementing the Low Rank Approximation (LRA) and revealing the active subspace.

This paper discusses one of the most important issues facing the regulatory body while performing the uncertainty analysis of the nuclear reactor parameter during accident conditions. This problem is the long computational time required by the statistical sampling methods to compute the uncertainty. We overcome this problem by introducing the Unscented Transform (UT) algorithm and singular value decomposition (SVD). Where both algorithms are combined (SVD/UT) to generate a set of sigma points, these sigma points are the representatives of whole probability distribution. The uncertainty quantification is performed during Loss of coolant accident in Pressurized Water Reactor (PWR), where the input variable of uncertainty is the coolant density reactivity. The SCALE 6.2 code is used for calculating the reactivity coefficients and the covariance matrix. The response variables are the peak cladding temperatures during the accident which are computed by ATHLET thermal-hydraulic code. The results obviously confirm the efficiency of the SVD/UT sampling in predicting the new mean values, and assure its ability to reduce the sampling size leading to a dramatic reduction of computational cost.

This paper discusses the improvement of a method for calculating sensitivity coefficients of neutronics parameters relative to infinite dilution cross-sections because the conventional method neglects resonance self-shielding effect. In this study, the self-shielding effect is taken into account by using the intermediate resonance approximation in order to get accurate results in both high and low energy groups. The improved method is applied to calculate sensitivity coefficients and uncertainties of eigenvalue responses for UO 2 and MOX ( ThO 2 – UO 2 and PuO 2 – UO 2 ) fueled pressurized water reactor cells. The verification of the improved method was performed by comparing the sensitivities with MCNP6 and TSUNAMI-1D. For uncertainty, calculation comparisons were done with TSUNAMI-1D, and we demonstrate that the differences are caused by the use of different covariance matrices.

In order to perform sensitivity analyzes in light water reactors where self-shielding effect becomes important, a new method has been developed for calculating sensitivity coefficient of core characteristics relative to the infinite dilution cross-sections instead of the effective cross-sections. This method considers the change of the self-shielding factor due to cross-section perturbation for different nuclides and reactions. SRAC and SAINT codes are used to calculate the improved sensitivity; while the accuracy of the present method has been verified by MCNP code and good agreement has been found.

A new method of calculating sensitivity coefficients of core characteristics relative to infinite-dilution cross sections has been developed. Conventional sensitivity coefficients are evaluated for the changes of effective cross sections which are dependent on individual models of core and cell. Therefore a correction has been derived to the conventional sensitivity coefficients based on the perturbation theory. The accuracy of the present method has been verified by comparing numerical results of sensitivity coefficients with a reference Monte-Carlo method.

The purpose of this paper is to apply our improved method for calculating sensitivities and uncertainties of reactivity responses for UO2 and MOX fueled pressurized water reactor cells. The improved method has been used to calculate sensitivity coefficients relative to infinite dilution cross-sections, where the self-shielding effect is taken into account. Two types of reactivities are considered: Doppler reactivity and coolant void reactivity, for each type of reactivity, the sensitivities are calculated for small and large perturbations. The results have demonstrated that the reactivity responses have larger relative uncertainty than eigenvalue responses. In addition, the uncertainty of coolant void reactivity is much greater than Doppler reactivity especially for large perturbations. The sensitivity coefficients and uncertainties of both reactivities were verified by comparing with SCALE code results using ENDF/B-VII library and good agreements have been found.