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Wu, Hongchun

Publications and source records attributed to Wu, Hongchun.

14 records
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DOE OSTI2022

Data assimilation for burnup distribution of PWR with three-dimensional variational algorithm and artificial neutral network

In this paper, a data-assimilation method has been proposed and applied for the burnup distribution of PWR. The burnup distribution is significant to the safety and economy of the reactor, as it is essential for the fuel-reloading design and optimization. Due to the burnup distribution cannot be measured directly during the reactor operation, the numerical simulation is widely applied to determine the burnup distribution. However, there is a deviation between the numerical simulation and the actual core due to some unavoidable factors, such as component manufacturing deviation, uneven flow distribution and so on. These differences would induce the errors to the simulation values of power distributions and hence to the burnup distribution. To address this problem, a data-assimilation method for the burnup distribution has been proposed with the application of power-distribution measurements. In our research, the three-dimensional variational (3DVAR) algorithm was applied for burnup-distribution calibration and the artificial neutral network (ANN) was applied to establish the relation between power distribution and corresponding burnup distribution. As engineering verification, the proposed data-assimilation method has been applied to the CNP1000 PWR operated in China. The numerical results indicated that the burnup-distribution errors can be reduced notably, as the maximum value of relative errors for power distribution can be reduced from 5.35% to 3.96%. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2017

Heterogeneous Neutron Leakage Model for PWR Pin-by-pin Calculation

In the last few decades, the nodal diffusion calculation accompanied with the assembly homogenization has been widely employed. The single assembly calculation with the reflective boundary condition (BC) would be carried out to determine the assembly-homogenized parameters. Because of the reflective BC, no axial and/or radial leakage rates have been taken into accounted for the lattice calculation. To represent the global influence of the reactor core on an assembly calculation, one mostly frequently uses a procedure called leakage model to approximately take into account the absorption due to the macroscopic structure of the physical flux in a heterogeneous situation. For the assembly homogenization, this absorption is introduced as the product of the leakage coefficient and the buckling obtained for an equivalent homogeneous medium using the well-known homogeneous B1 theory. Clearly, this is an imperfect representation of leakages in a heterogeneous medium. However, the errors introduced by the foregoing procedure are small for the whole? -assembly homogenization in a PWR. When it comes to the pin-by-pin calculation, it is not the case. The leakage rate? will be affected by the neutron streaming effect caused by the heterogeneity of the assembly. Especially when poison pins or empty channels are present, the streaming effect becomes important. The errors introduced appear particularly visible. The heterogeneous leakage model? which assumes that the neutron flux is variational and the leakage rate is not uniform over the lattice pitch is a more appropriate choice. When the heterogeneous leakage model is applied in the lattice calculation for the pin-cell homogenization, the pin-homogenized problem would be changed compared with the original assembly problem without any homogenization technique. So, the Cooperation of the heterogeneous leakage model with the pin-cell homogenization theory is unsettled. In this paper, both homogenous and heterogeneous leakage models are evaluated in pin-by-pin calculation. Their implements used in pin-cell homogenization of the lattice calculation are studied. The diffusion coefficient obtained from transport cross-section and the space-dependent leakage coefficient together with the two leakage models are analyzed for the practical reactor-core applications.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2017

Treatment of Nonuniform Temperature Distribution by Subgroup Method

The subgroup method divides an energy group into several subgroups according to the magnitude of the cross section. The subgroup fixed source equation is formulated on the energy range of a subgroup, the ratio of which to the energy range of an energy group is defined as subgroup probability. Typically the physical probability table or the mathematical probability table is applied. However, both of the tables are not guaranteed to share the same set of subgroup probabilities for a resonant nuclide at different temperatures. This means that the subgroup fixed source equation cannot be formulated and the subgroup method will not work when the temperature distribution is nonuniform. To overcome this defect, the subgroup method based on partial cross section fit scheme (PXSFS) and the simplified partial cross section fit scheme (SPXSFS) are proposed. These methods fit the cross sections at different temperatures as partial cross sections to share a same set of subgroup probabilities. The new methods is compared to the conventional subgroup method (CSM) based on physical probability table and the preexisting methods: the correlation model (CM), the subgroup level adjustment scheme (SLAS) and the number density adjustment scheme (NDAS). The numerical results show that the new methods can better predict the spatial dependent reaction rate than preexisting methods. Within these two methods, the simplified scheme consumes less time.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2017

Verification of the Coupled Neutronics/Thermal-Hydraulics Code TANSY against the MSFR Benchmark

The MSRs is a liquid-fuel reactor in which uranium, fission products and actinides are dissolved in the molten salt. The molten salt reactors are featured by circulating fuel, low pressure and high temperature. The MSRs meets many of the future goals of nuclear technology, in particular for what concerns as improved sustainability and unique characteristics in terms of actinide burning. The fluid nature of fuel in MSRs gives extra flexibility in reactor design, fuel fabrication and recycling. But because of the application of fluid fuel, MSRs have several special characteristics compared with the traditional solid-fuel reactors. Firstly, the transport of the delayed neutron precursors by the fluid flow reduces the contribution of delayed neutrons to the chain reaction.. Secondly, the fact that the fuel is dissolved in the coolant rather than separated from the coolant by the claddings results in a much stronger coupling phenomenon between the neutronics and thermal-hydraulics. Thirdly, the shape of the fuel is determined by the container because of the characteristics of fluid, the unstructured meshes are required to model the complex geometry accurately. However most of the conventional reactor codes were developed for solid-fuel reactor and therefore not capable of taking liquid fuel flow into account. To address all these particular modeling issues of MSRs, a multi-physics code named TANSY has been developed in our laboratory. In this paper, the benchmark problem based on the MSFR design was calculated to verify the code.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2017

A Variational Nodal Approach to 2D/1D Pin Resolved Neutron Transport for Pressurized Water Reactors

A two-dimensional/one-dimensional (2D/1D) variational nodal approach is presented for pressurized water reactor core calculations without fuel-moderator homogenization. A 2D/1D approximation to the within-group neutron transport equation is derived and converted to an even-parity form. The corresponding nodal functional is presented and discretized to obtain response matrix equations. Within the nodes, finite elements in the x-y plane and orthogonal functions in z are used to approximate the spatial flux distribution. On the radial interfaces, orthogonal polynomials are employed; on the axial interfaces, piecewise constants corresponding to the finite elements eliminate the interface homogenization that has been a challenge for method of characteristics (MOC)-based 2D/1D approximations. The angular discretization utilizes an even-parity integral method within the nodes, and low-order spherical harmonics (P N ) on the axial interfaces. The x-y surfaces are treated with high-order P N combined with quasi-reflected interface conditions. Furthermore, the method is applied to the C5G7 benchmark problems and compared to Monte Carlo reference calculations.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

Pn-FEM Method for Solving the First-Order Neutron Transport Equation

A deterministic method was investigated and developed for the photon-neutron transport calculation for fusion reactor blanket. Firstly, considering the fact that the second order transport equation cannot describe void region accurately due to the appearance of zero total cross section in the denominator, the first order equation was selected as the starting point of the solution. The angular discretization uses the spherical harmonics (Pn) method. Although discrete ordinates (Sn) method has been most commonly applied due to its efficiency, it suffers from the ray effect. To describe unstructured geometry, the finite element method was used to discrete spatial variable. It is well known that Bubnov-Galerkin discretization of the first-order equation is inappropriate which will create oscillations. To obtain robust solutions, Petrov- Galerkin methods have been developed such as the Streamline-Upwind Petrov-Galerkin (SUPG) method and the Generalized Least-Squares (GLS) method. These methods require a stabilization term added to its test functions, which will incur additional computational cost. Another finite element formulation that usually used for first order equation is the Discontinuous-Galerkin (DG) method. In this method, each element has a unique and separate set of basis function. Then the adjacent elements can be connected by using the in-coming flux. Its main drawback is the number of unknowns, much larger than Continuous-Galerkin (CG) method. The Sub-Grid Scale (SGS) finite element method combines the advantages of CG and DG methods together. It inserts the DG method in each element to correct the CG solution, and provides numerically stable solution of first-order equation without increasing the number of unknowns. The boundary conditions and interface conditions for Pn method is a hard nut to crack. We use Riemann method to deal with this problem. It decomposes the neutron angular flux into in-coming and out-going information through an interface, and applies boundary condition to the in-coming one. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Improved Variable-Transformation Algorithm for the Hexagonal Variational Nodal Method

Hexagonal Variational Nodal Method (VNM) has been widely employed in fast reactor core calculation codes. It provides the weak form solution of the second order transport equation. It employs a direct three-dimensional expansion instead of the transverse integration technique, with the singular term caused by transverse integration over the hexagonal nodal avoided. However, as the increasing Pn expansion order in angle, the number of moments increases dramatically, which significantly increases the requirements in both memory and computational time. As a consequence, Yang proposed the Variable-Transformation Algorithm. It firstly used the reverse Cuthill-McKee (RCMK) reordering method to transform the response matrices into block-diagonal. Then, for the unreducible matrices, orthogonal transformation was applied, after which the matrices were sparse enough to be reduced by using the RCMK reordering once more. In this summary, based on a newly developed hexagonal VNM code NECP-VioletHex, the Variable Transformation Algorithm was investigated and improved by adopting more constraints to the basis functions to further take advantage of the symmetric properties of the hexagonal-z nodes. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2016

Variational Nodal 2D/1D Transport/Diffusion Solutions of the C5G7 Benchmark Problems

This work is the continuation of our effort to generalize the variational nodal method (VNM) for application to pin-resolved whole-core PWR problems. To this end, a 2D/1D VNM method without spatial homogenization is formulated and implemented in the PANX code. We employ diffusion theory in the axial direction combined with two-dimensional transport in the x-y plane. In our initial work, we employed the standard spherical harmonics method. To increase accuracy and reduce computational effort, we present two refinements: First, the even-parity integral method within the nodes reduces the computational effort required to form the response matrices. Second, the use of quasi-reflected interface conditions reduces the dimension of the resulting response matrices and therefore the CPU time required to solve the equations. We apply the method to the three-dimensional, un-rodded C5G7 benchmark problem. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

Improved Few-group Homogenized Cross-section Sensitivity Analysis for Lattice Physics Calculation

In the conventional reactor physics 'two-step' calculation scheme, lattice-physics calculation is followed by core calculation using neutron diffusion theory. The few-group spatially homogenized cross-sections are the outputs of the lattice-physics calculation as well as the inputs of the core calculation. The uncertainties of fundamental nuclear data will be propagated to the core calculation results through few-group spatially homogenized cross-sections. Consequently, assessing the sensitivity and uncertainty of few-group homogenized cross-sections is necessary for the core-calculation sensitivity and uncertainty analysis. Conventional method for sensitivity analysis is usually performed with respect to effective self-shielding cross sections but not continuous-energy cross sections by neglecting resonance self-shielding effects. The purpose of this work is to improve the sensitivity analysis of few-group cross sections and assess the effects introduced by resonance calculation with the subgroup method being used for resonance calculation. This paper is organized as follows: Firstly, theoretical models of this work are described. Secondly, validation and analysis are performed based on a boiling-water reactor (BWR) fuel-pin cell under hot zero power (HZP) condition. Finally, summaries and conclusions are given. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

The Effects of Different Lattice Codes on Results of Sensitivity and Uncertainty Analysis

According to the UAM ('Uncertainty Analysis in Modeling') benchmark, uncertainties in the LWR system calculations at all stages should be determined and quantified. As the neutronics calculations are prerequisite for the predictions of the reactor system, and the uncertainties introduced by the neutronics calculations would be propagated to the subsequent calculations, hence uncertainty analysis has been firstly focused on the neutronics phase to quantify the uncertainties of the reactor-physics predictions in UAM. For the lattice physics, the objective of uncertainty analysis is focused on uncertainty quantifications of the few-group constants; for the core physics, uncertainties of the core steady-state stand-alone neutronics calculations are focused on. Based on the previous researches, the nuclear-data uncertainty has been treated as one of the most significant source of uncertainty and received the most focus. In the previous works, the domestic code UNICORN has the capability of performing sensitivity analysis and uncertainty analysis using the direct numerical perturbation (DNP) method and statistical sampling (SS) method. In this paper, the capability of the UNICORN code has been improved. The domestic lattice code NECP-CACTI has been added in UNICORN to perform the lattice calculations, with DRAGON5.0 and NECP-CACTI available for lattice calculations. For DRAGON5.0 and NECP-CACTI, all the methods and technologies are shared in UNICORN. Therefore, the effects of different lattice codes on the results of sensitivity and uncertainty analysis have been researched and determined in this paper. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

NECP-Cypress: Development and Benchmarking of a 3D PWR Core-Analysis Code

As one of the key components of nuclear reactor design and safety analysis software for Pressurized Water Reactor (PWR), the advance of the core-analysis code indicates the nuclear power development of the corresponding country. Hence, Nuclear Engineering Computational Physics Lab. (NECP) developed a PWR core-analysis code NECP-Cypress. Currently, it contains several modules including a generalized cross section module, a diffusion module using the Variational Nodal Method (VNM), a depletion-calculation using the traditional macroscopic module, a thermal-hydraulics module solving the single channel heat transfer equation and 1D heat conduction equation. With the VNM employed, NECP-Cypress can eliminate the control rod cusping effect and provide a better pin power reconstruction. In this paper, we firstly introduce the modules of the code NECP-Cypress. Secondly, two large-scale PWR core benchmarks were employed to demonstrate the ability of the code by comparing with SIMULATE-3, including the BEAVRS problem and a pseudo CAP1400 reactor core problem. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

Finite Volume Method Based Neutronic Solvers for Steady and Transient Analysis of Molten Salt Reactors

In recent years, the coupled neutronics and thermal hydraulics analysis becomes more and more important, because it helps to identify the most relevant safety issues without conservative assumptions. In addition, such coupled simulations are essential for the generation IV advanced nuclear power systems such as molten salt reactor (MSR), because the presence of strong coupling between different phenomena, like the transport of delayed neutron precursors by the fluid flow?. Due to the different discretization methods used in reactor physics analysis and thermal-hydraulics analysis, it is hard to couple different kinds of codes. This work presents an attempt to solve the multigroup neutron diffusion equation with the finite volume method which is quite widely used for the numerical simulation of a variety of applications involving fluid flow and heat and mass transfer. The unstructured finite volume method (FVM) based on open source C++ library OpenFOAM was chosen as the development platform?. The objective of this paper is to concisely present the main features of the developed codes in terms of the theoretical background and numerical approach and as can be seen in the following sections, the calculation results obtained by the NDSFoam which solves the steady-state neutron diffusion equation and NDTFoam which solves the transient-state neutron diffusion equation are discussed and compared to the benchmark problems. In this paper, two new neutronic solvers using finite volume method have been developed to perform the neutron physics analysis. The solvers are based on OpenFOAM, and have been tested with several steady state and transient-state benchmark problems. By verifications of the codes, it is proved that the development of NDSFoam and NDTFoam are correct. In our future work, both of these two solvers will be coupled with the precompiled CFD solvers in OpenFOAM to analyze the molten salt fast reactors. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2016

Variational Nodal 2D/1D Transport/Diffusion Solutions of the C5G7 Benchmark Problems

This work is the continuation of our effort to generalize the variational nodal method (VNM) for application to pin resolved whole-core PWR problems. To this end, a 2D/1D VNM method without spatial homogenization is formulated and implemented in the PANX code. We employ diffusion theory in the axial direction combined with two-dimensional transport in the x-y plane. In our initial work, we employed the standard spherical harmonics method. To increase accuracy and reduce computational effort, we present two refinements: First, the even-parity integral method within the nodes reduces the computational effort required to form the response matrices. Second, the use of quasi-reflected interface conditions reduces the dimension of the resulting response matrices and therefore the CPU time required to solve the equations. We apply the method to the three-dimensional, unrodded C5G7 benchmark problem.

97 MATHEMATICS AND COMPUTING↗