Resonance Self-shielding Calculation Research Articles

Resonance Calculation of FCM Fuel Based on the Global-Local Method

Fully ceramic microencapsulated fuels is a promising potential fuel for pressurized water reactors because of its inherent safety, but double heterogeneity (DH) brings challenges to the neutronic calculation. In this paper, the Hébert model is applied to the global-local resonance method to solve DH, in which the Dancoff factor obtained by the neutron current method is used to transform the coupled fuel pins in the reactor into multiple independent one-dimensional equivalent cylindrical fuel pins. Then, the Hébert model and the hyperfine group method are used to perform the resonance self-shielding calculation in these independent pins. The Sanchez-Pomraning method coupled with the Method of Characteristics (Sanchez-MOC) method is introduced to the two-dimensional/one-dimensional transport module to realize the subsequent whole-core DH transport calculations. The proposed method has been implemented in the high-fidelity neutronics code NECP-X and tested with a set of cases. The results show good agreement with the Monte Carlo reference values for the reactivity and self-shielding cross sections.

Impact of the resonance elastic scattering on reactor-core physics calculation results based on the deterministic method

NECP-Atlas and similar nuclear data processing codes have developed the function of incorporating the resonance elastic scattering effect into the multi-group cross sections and scattering matrices. However, the hyper-fine group method is commonly used in deterministic-based lattice physics codes and whole-core neutronics codes for resonance self-shielding calculations. In this method, the neutron slowing-down equation is established based on the conventional asymptotic scattering model where the neutron up-scattering caused by the resonance elastic scattering is ignored. Consequently, the deterministic codes cannot directly use the multi-group data produced by the nuclear data processing codes. In this paper, a correction factor method is proposed to correct the multi-group cross sections and scattering matrices obtained by the hyper-fine group calculations to consider the resonance elastic scattering. The proposed method has been implemented in the lattice physics code LOCUST. The few-group constants produced by the LOCUST code are provided to reactor-core analysis code SPARK to simulate a CNP-1000 type PWR reactor operated in China. Some core parameters measured during zero-power physics tests at 600 K and operations are analyzed to show the effect of the resonance elastic scattering on the core parameters. The numerical results show that the boron concentration reduces by 10 ∼ 14 ppm at 900 K during operations, which is closer to the measured value and improves the accuracy of reactor-core physics calculation.

Annular fuel neutronic analysis

The annular fuel was proposed to increase the power density while keeping or improving the safety margins, given the considerably lower surface heat flux and lower fuel temperature than conventional solid fuel. In this paper, neutronic characteristics of this new fuel design were analysed using the new transport code of the Westinghouse, called PARAGON2, using Ultra-Fine Energy Mesh Library for multi-group cross section calculations. The bibliographical review showed there is a lack of deterministic transport codes capable to model such fuel with acceptable accuracy, because the equivalence relations for heterogeneous resonance integrals adopted in the standard codes were formulated only for solid cylindrical rods. Therefore, the main objective of this paper is to perform neutronic analysis for annular fuel using PARAGON2, evaluating the use of Ultra-Fine Energy Mesh Library to eliminate resonance self-shielding calculation. The results of this paper analysed the power distributions, the ratio of U-238 capture rate to U-235 fission rate and behaviour of the infinite multiplication factor for annular fuel and compared with the Monte Carlo code MCNP.

Development of the capability for multi-group shielding library generation in the nuclear data processing code NECP-Atlas

The capability to generate multi-group shielding library is developed in the nuclear data processing code NECP-Atlas. To make the code suitable for the applications in different types of reactors, several improvements are made in the code, such as the resonance self-shielding method and energy-group structure optimization. The hyperfine group method is applied to perform resonance self-shielding calculations for different configurations. The energy-group structure optimization method is developed based on the contributon theory to enhance the calculation accuracy of the thermal neutron flux and photon flux. The accuracy of the newly developed capability is verified with the reference results calculated using BUGLE-B7 libraries. Two libraries with optimized neutron energy-group structures of 47 groups and 60 groups are obtained based on the contributon theory. Numerical results show that the thermal neutron flux and photon flux calculated based on the two libraries are greatly improved.

Refinements of the Pin-Based Pointwise Energy Slowing-Down Method for Resonance Self-Shielding Calculation—I: Theory

The pin-based pointwise energy slowing-down method (PSM), which is a resonance self-shielding method, has been refined to treat the nonuniformity of material compositions and temperature profile in the fuel pellet by calculating the exact collision probability in the radially subdivided fuel pellet under the isolated system. The PSM has generated the collision probability table before solving the pointwise energy slowing-down equation. It is not exact if the fuel pellet has nonuniform material compositions or temperature profile in all the subdivided regions. In the refined PSM-CPM, the pre-generated table is not required for directly calculating the collision probability in all the subdivided regions of the fuel pellet while solving the slowing-down equation. There are an advantage and a disadvantage to the method. The advantage is to exactly consider the nonuniformity of the material compositions and temperature profile in the fuel pellet. The disadvantage is the longer computing time than that of the PSM when the fuel pellet has more than five subdivided regions. However, in the practical use for UO2 pin-cells, it is still comparable for the computation time with the PSM and the conventional equivalence theory methods. In this article, using simple light water reactor 17 × 17 F A problems with a uniform material composition and temperature profile, it is demonstrated that PSMs (PSM and PSM-CPM) exhibit consistent accuracy in calculating the multiplication factor and the pin power distribution with no compromise in the computation time. More detailed accuracy assessments with various test cases, including problems representing the nonuniformity, are presented in the accompanying article.

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.

Recent developments in PSI BEPU analysis for SPERT-III RIA transient: ND uncertainty breakdown and kinetic parameters uncertainty assessment

The current research summarizes recent developments performed within the PSI BEPU methodology and the corresponding results on the SPERT-III RIA experiments. In this regard, three main studies have been carried out. First, an uncertainty breakdown study has been performed in order to identify the dominant nuclear data and to quantify their respective contributions to the overall uncertainties of the parameters of interest. On the other hand, the second study was devoted to assess the impact of considering the effect of cross section perturbation (limited for the time being to U-238 capture) in the resonance self-shielding calculation, known as the implicit effect, on different parameters’ uncertainties in SPERT-III RIA transient. Finally, the third study was conducted with the main goal to assess the impact of kinetic parameter uncertainties, such as delayed neutron yields and associated decay constants, on the overall uncertainties.The uncertainty quantification results of the first study, based on the ENDF/B-VII.1 library, showed that, for steady-state, the first dominant contributor to the overall uncertainties of the static reactivity worth and k-eff is U-235 nubar, followed by U-238 then U-235 capture cross sections. However, for the transient, the first dominant contributor to the overall uncertainties, in e.g. total power and reactivity, is the U-238 inelastic scattering. More interestingly, it was found that, the second dominant contribution to the overall power uncertainty, during the initial excursion phase, is due to the U-235 nubar, while during the power reversal phase, the U-238 capture becomes the second dominant contribution, and even the first one by the end of the transient. Moreover, results of the second study demonstrated a clear systematic decrease of the uncertainty of all parameters due to the inclusion of the implicit effect. In steady state, due to the impact of the implicit effect, the Doppler coefficient relative uncertainty could be reduced up to 30%, which is reflected in the transient, especially in the reversal phase of the power excursion where Doppler effect plays a key role, by a systematic decrease of the relative uncertainty of total power and other parameters. Finally, in the third study, the estimated uncertainties, regarding both steady-state and transient parameters, have shown systematic larger values due to kinetic parameter uncertainties compared to those due to the other nuclear data.

IMPROVEMENT OF SCALE-XSProc MULTIGROUP CROSS SECTION PROCESSING BASED ON THE CENTRM POINTWISE SLOWING DOWN CALCULATION

The SCALE-XSProc multigroup (MG) cross section processing procedure based on the CENTRM pointwise slowing down calculation is the primary procedure to process problem-dependent self-shielded MG cross sections and scattering matrices for neutron transport calculations. This procedure supports various cell-based geometries including slab, 1-D cylindrical, 1-D spherical and 2-D rectangular configurations and doubly heterogeneous particulate fuels. Recently, this procedure has been significantly improved to be applied to any advanced reactor analysis covering thermal and fast reactor systems, and to be comparable to continuous energy (CE) Monte Carlo calculations. Some reactivity bias and reaction rate differences have been observed compared with CE Monte Carlo calculations, and several areas for improvement have been identified in the SCALE-XSProc MG cross section processing: (1) resonance self-shielding calculations within the unresolved resonance range, (2) 10 eV thermal cut-off energy for the free gas model, (3) on-the-fly adjustments to the thermal scattering matrix, (4) normalization of the pointwise neutron flux, and (5) fine MG energy structure. This procedure ensures very accurate MG cross section processing for high-fidelity deterministic reactor physics analysis for various advanced reactor systems.

THE TWO-STEP APPROACH FOR WHOLE-CORE RESONANCE SELF-SHIELDING CALCULATION

A two-step approach is proposed to accomplish high-fidelity whole-core resonance self-shielding calculation. Direct slowing-down equation solving based on the pin-cell scale is performed as the first step to simulate different operating conditions of the reactor. Resonance database is fitted using the results from the pin-cell calculation. Several techniques are used in the generation of the resonance database to estimate multiple types of resonance effects. The second step is the calculation of practical whole-core problem using the resonance database obtained from the first step. The transport solver is embedded both at the first step and the second step to establish the equivalence relationship between the fuel rod in the practical problem and the pin-cell at the first step. The numerical results show that the new approach have capability to perform high-fidelity resonance calculations for practical problem.

Evaluation of improved subgroup resonance treatment based on Sanchez-Pomraning method for double heterogeneity in PWR

The feasibility of the improved subgroup method coupled with the Sanchez-Pomraning Method (ISSP) is analyzed for the resonance self-shielding calculation of double heterogeneity (DH) problems in PWR. The Sanchez-Pomraning method is developed for both fixed source and the eigenvalue problems. The improved subgroup method adopts a fine-mesh energy structure to handle the resonance interference effect. In this process, the subgroup fixed source equations are solved to get the fine-mesh cross section and the slowing-down equations are solved for group condensation. To extend the improved subgroup method to DH condition, the Sanchez-Pomraning method is applied twice to the subgroup fixed source equation and slowing-down equation respectively. Afterward, the Sanchez-Pomraning method is used the third time for multi-group transport problems. The ultra-fine group method coupled with the Sanchez-Pomraning method (UFGSP) is also established for comparison with ISSP. Numerical validation shows that both ISSP and UFGSP could treat the DH resonance effect precisely.

Fitting-based resonance database method for resonance self-shielding calculations of large-scale task considering depletion and intra-pin distribution

A fitting-based resonance database method is proposed to perform self-shielding calculation for large-scale problems. The intra-pin radial effects are also treated by this method. The new method is mainly divided into two steps. First, the operating conditions of different pin-cells existing in the target problem are simulated by the adjustments of the parameters of single pin-cell cases. The ultra-fine-group slowing-down solving process is performed for these pin-cells and the resonance database for the target problem is fitted using the obtained results. Second, the target problem is calculated using the resonance database generated. Transport calculations are performed at both steps to establish the equivalence relationship between the target problems and the single pin-cell cases. Several techniques are adopted to evaluate the resonance interference and radial effects. Numerical tests prove that the method is capable to give the accurate prediction for the spatial-dependent resonance self-shielded cross-sections in an efficient way.

A Comparison Between the Embedded Self-Shielding Method and the Enhanced Neutron Current Method Based on the Equivalent Pin Cell Model on the Irregular Fuel Lattice Problem

The Embedded Self-Shielding Method (ESSM) coupled with the heterogeneous Resonance Integral tables and the Enhanced Neutron Current Method (ENCM) with equivalent Dancoff factor are reviewed and reformulated to a unified framework by incorporating the ultra-fine-group slowing-down calculation on two-dimensional square pin cell problems. The comparison between the two approaches on the resonance self-shielding calculation of irregular fuel lattices shows that the reformulated ESSM approach will bring errors to the cross-section prediction of fuel pins in the irregular lattice, especially when the moderator density is low. Also, the reformulated ENCM approach is more stable for different configurations. Further numerical tests show that the scalar flux calculated by the ESSM approach is affected by the global neutron balance across the fuel lattice and ESSM is more sensitive to the error brought by the enforced equivalence.

Development of methodology for efficient fuel design evaluation of the Advanced High Temperature Reactor (AHTR)

This paper presents a methodology for developing a neutronics model to be used for a fluoride-salt high temperature reactor (FHR) fuel design optimization study. The reactor design is based on the Advanced High-Temperature Reactor (AHTR) with hexagonal fuel element with fuel “planks” (plates) developed at the Oak Ridge National Laboratory. The overall objective of this research was to develop a methodology accurate enough, yet practical and fast enough for a fuel plank design optimum search that minimizes the fuel cycle cost (FCC) of FHR. Resonance self-shielding calculations for double heterogeneous fuel planks of AHTR design is currently unavailable in most codes. Therefore, automated modeling of the double heterogeneity was implemented to allow accurate use of multi-group simulations. The methodology generates MCDancoff Factors using SCALE6.2; its adequate accuracy was verified. A MCDancoff Factor surrogate model was created so on-the-fly MCDancoff Factors could be provided for depletion calculations over the design space for parametric studies. A simple non-linear reactivity model with assembly-to-whole-core reactivity correction was applied to analyze performance of multi-batch refueling. Results indicate that cycle length is maximized at 40% packing fraction with a carbon-to-heavy metal ratio (CHM) of approximately 250, which minimizes the cost of outages. In contrast, discharge burnup and fuel utilization is maximized at around 20% packing fraction and a CHM of approximately 600, which minimizes fuel cost, but not necessarily the FCC cost, which also accounts for outage penalty. Void and power reactivity coefficients were determined over the design phase space to establish the envelope for stable design. The minimum FCC is the optimum trade-off between the two, within the limits of the stability envelope. In combination with the cost model the objective function is non-linear and requires global optimization methods. This paper presents the methodology needed for global optimization, while the optimization itself will be presented in a follow up companion paper.

Modeling of Resonance-Interference Effect in Depleted Fuel Compositions by Pseudo Resonant Isotopes

In order to develop an efficient resonance self-shielding method that can model the complex resonance-interference effects in depleted fuel compositions, an improved Pseudo Resonant Isotope Model (PRIM) has been developed by incorporating a number density–perturbation technique in the resonance cross-section tables for pseudo isotopes. Numerical results for homogeneous mixtures, pin cells, and pressurized water reactor lattice problems show that the new model is able to produce accurate group cross sections for a wide range of depletion states of different types of fuels, comparable to those obtained from online ultra-fine-group slowing-down calculations. Computational cost analysis shows that the improved PRIM is a promising method applicable to the resonance self-shielding calculations for large-scale reactor core analysis with depletion.

Improvement and optimization of the pseudo-resonant-nuclide subgroup method in NECP-X

The pseudo-resonant-nuclide subgroup method is a newly emerged self-shielding calculation method to treat resonance interference effect. It has been implemented in the NECP-X code which is developed for the high-fidelity neutronics calculation. Though this method has high accuracy, its computation time occupies more than half of the total computation time (mainly including resonance self-shielding calculation, multi-group transport calculation and depletion calculation). To improve the efficiency of the resonance self-shielding calculation, some analysis and optimization are performed in several aspects: firstly, the maximum number of subgroups is reduced from 7 to 5; secondly, the number of dilution cross section points is reduced from 21 to 9; thirdly, the number of fuel meshes in solving SFSE is reduced from 15 to 5; finally, number of fuel meshes in solving one-group fixed-source equation for the SPH factor is reduced from 15 to 1. The acceleration ratio of the self-shielding calculation is 3.45 for assembly without poison and 3.49 for assembly with poison. The time proportion of self-shielding calculation is reduced to less than 30%. The accuracy loss is negligible in the accelerations. Besides, it is found that the subgroup condensation scheme can obtain better self-shielded cross sections of component resonant nuclides than the dilution interpolation scheme.

Resonance self-shielding treatment and analysis of resonance integral tables for Fully Ceramic Micro-encapsulated fuels with the Embedded Self-Shielding Method

A resonance calculation method for Fully Ceramic Micro-encapsulated (FCM) fuels containing stochastically dispersed tri-structural isotropic (TRISO) coated fuel particles has been proposed in this research. The purpose is to obtain effective homogenized resonance cross sections representing the effect of double heterogeneity (DH). The Monte Carlo code MVP is used to solve the heterogeneity in the isolated FCM fuels pin, and to couple with the method of characteristic (MOC) to generate heterogeneous resonance integral (RI) tables for the following Embedded Self-Shielding Method (ESSM) based resonance calculation. The ESSM method is employed to treat the heterogeneity in the lattice (Dancoff effect). Heterogeneous RI tables based on different packing fraction may differ in relationship between background and self-shielded cross sections. Analysis of this distinction’s impact on ESSM calculation has been conducted. Furthermore, resonance interference effect is neglected in ESSM because heterogeneous RI tables are developed for isolated resonant nuclide system. Therefore, Resonance Interference Factor (RIF) Method was applied to correct cross sections from ESSM. To obtain RIF, slowing-down equation need be solved twice for different homogeneous systems. Whereas, the cross section neglecting interference effect could be received by interpolating in homogeneous RI tables to improve efficiency. Evaluation of errors caused by interpolation in RIF method was performed with reference solutions from MVP. Numerical results show that the new method is proved effective in DH capability for resonance self-shielding calculation.

A lumped parameter method of characteristics approach and multigroup kernels applied to the subgroup self-shielding calculation in MPACT

Abstract An essential component of the neutron transport solver is the resonance self-shielding calculation used to determine equivalence cross sections. The neutron transport code, MPACT, is currently using the subgroup self-shielding method, in which the method of characteristics (MOC) is used to solve purely absorbing fixed-source problems. Recent efforts incorporating multigroup kernels to the MOC solvers in MPACT have reduced runtime by roughly 2×. Applying the same concepts for self-shielding and developing a novel lumped parameter approach to MOC, substantial improvements have also been made to the self-shielding computational efficiency without sacrificing any accuracy. These new multigroup and lumped parameter capabilities have been demonstrated on two test cases: (1) a single lattice with quarter symmetry known as VERA (Virtual Environment for Reactor Applications) Progression Problem 2a and (2) a two-dimensional quarter-core slice known as Problem 5a-2D. From these cases, self-shielding computational time was reduced by roughly 3–4×, with a corresponding 15–20% increase in overall memory burden. An azimuthal angle sensitivity study also shows that only half as many angles are needed, yielding an additional speedup of 2×. In total, the improvements yield roughly a 7–8× speedup. Given these performance benefits, these approaches have been adopted as the default in MPACT.

Heterogeneous Pseudo-Resonant Isotope Method for Resolved Resonance Interference Treatment in Resonance Self-Shielding Calculation

The theory of resonance interference factor (RIF) method is examined for thermal reactor problems, and the approximations and limitations are identified. To evaluate the interference effect between resonance isotopes, the RIF method establishes an approximate equivalent relationship between a heterogeneous system and a homogeneous system by introducing background cross sections, and the approximation is a source of deviation in self-shielding calculations. Furthermore, each resonance isotope is treated individually in the self-shielding procedure, which requires unnecessary calculation effort, especially for whole-core and burnup cases. Based on the analysis, a heterogeneous pseudo-resonant isotope method (HPRIM) is proposed to overcome these problems. The mixture of resonant nuclides is considered as a pseudo-resonant isotope, and the resonance integral is generated in a one-dimensional heterogeneous system. The numerical results show that HPRIM improves the accuracy of evaluating the resonance interference effect and improves the efficiency of the self-shielding procedure.

Nuclear-data uncertainty propagations in burnup calculation for the PWR assembly

In this paper, our home-developed lattice code NECP-CACTI has been implemented into our UNICORN code to perform sensitivity and uncertainty analysis for the lattice calculations. The verified multigroup cross-section perturbation model and methods of the sensitivity and uncertainty analysis are established and applied to different lattice codes in UNICORN. As DRAGON5.0 and NECP-CACTI are available for the lattice calculations in UNICORN now, the effects of different neutronics methods (including methods for the neutron-transport and resonance self-shielding calculations) on the results of sensitivity and uncertainty analysis were studied in this paper. Based on NECP-CACTI, uncertainty analysis using the statistical sampling method has been performed to the burnup calculation for the fresh-fueled TMI-1 assembly, propagating the nuclear-data uncertainties to k∞ and two-group constants of the lattice calculation with depletions. As results shown, for different neutronics methods, it can be observed that different methods of the neutron-transport calculation introduce no differences to the results of sensitivity and uncertainty analysis, while different methods of the resonance self-shielding calculation would impact the results. With depletions of the TMI-1 assembly, for k∞, the relative uncertainty varies between 0.45% and 0.60%; for two-group constants, the largest variation is between 0.35% and 2.56% for vΣf,2. Moreover, the most significant contributors to the uncertainty of k∞ and two-group constants varied with depletions are determined.

Advanced Bondarenko method for resonance self-shielding calculations in deterministic reactor physics code system CBZ

The advanced Bondarenko method for resonance self-shielding calculations is devised and proposed. This method is based on three numerical methods; the Bell factor optimization for accurate fuel escape probability representation, extension of resonance interference factors and correction factors for current-weighted total cross sections. A 107-group library for light water reactor applications based on the advanced Bondarenko method is generated for a reactor physics code system CBZ. Performance of the CBZ code with this 107-group library is examined against a suit of light water reactor cell problems. The infinite neutron multiplication factors calculated with CBZ agree with reference continuous-energy Monte Carlo solutions within 0.15%Δk/kk′ differences, and no significant biases on fuel compositions and geometrical specifications are observed. Energy-averaged cross sections are also examined. Numerical tests reveal that significant accuracy improvements in resonance self-shielding calculations are realized by adopting the advanced Bondarenko method without any significant increase of computational burden.