Development of Three-Dimensional Neutron Kinetics Code Based on High Order Nodal Expansion Method in Hexagonal-Z Geometry

2018 ◽  
Author(s):  
Guo Chao ◽  
Liu Yu ◽  
He Hangxing ◽  
Liu Luguo ◽  
Wang Xiaoyu ◽  
...  
Keyword(s):  
Cross Sections ◽  
Three Dimensional ◽  
Expansion Method ◽  
High Order ◽  
Benchmark Problems ◽  
Weighting Method ◽  
Control Rod ◽  
Order Polynomial ◽  
Runge Kutta ◽  
Nodal Expansion Method

To solve three-dimensional kinetics problems, a high order nodal expansion method for hexagonal-z geometry (HONEM) and a Runge-Kutta (RK) method are respectively adopted to deal with the spatial and temporal problem. In the HONEM, 1D partially-integrated flux are approximated by using four order polynomial. The two order polynomial is adopted to the approximation of partially-integrated leakages. The Runge-Kutta method is adopted as a tool for dispersing the time term of 3D kinetics equation. A flux weighting method (FWM) is used for obtaining homogenized cross sections of mix node. The three-dimensional hexagonal kinetics code has been developed based on this method and tested with two benchmark problems of VVER which are the control rod ejection without any feedback and with simple adiabatic Doppler feedback. The results calculated by this code agree well with the reference results and the code is validated.

scholarly journals Development and Validation of a Three-Dimensional Diffusion Code Based on a High Order Nodal Expansion Method for Hexagonal-zGeometry

2016 ◽  
Vol 2016 ◽  
pp. 1-21 ◽  
Author(s):  
Daogang Lu ◽  
Chao Guo
Keyword(s):  
Order Approximation ◽  
Three Dimensional ◽  
Expansion Method ◽  
High Order ◽  
Quadratic Polynomial ◽  
Quadratic Approximation ◽  
Polynomial Expansion ◽  
Benchmark Problems ◽  
One Dimensional ◽  
Nodal Expansion Method

A three-dimensional, multigroup, diffusion code based on a high order nodal expansion method for hexagonal-zgeometry (HNHEX) was developed to perform the neutronic analysis of hexagonal-zgeometry. In this method, one-dimensional radial and axial spatially flux of each node and energy group are defined as quadratic polynomial expansion and four-order polynomial expansion, respectively. The approximations for one-dimensional radial and axial spatially flux both have second-order accuracy. Moment weighting is used to obtain high order expansion coefficients of the polynomials of one-dimensional radial and axial spatially flux. The partially integrated radial and axial leakages are both approximated by the quadratic polynomial. The coarse-mesh rebalance method with the asymptotic source extrapolation is applied to accelerate the calculation. This code is used for calculation of effective multiplication factor, neutron flux distribution, and power distribution. The numerical calculation in this paper for three-dimensional SNR and VVER 440 benchmark problems demonstrates the accuracy of the code. In addition, the results show that the accuracy of the code is improved by applying quadratic approximation for partially integrated axial leakage and four-order approximation for one-dimensional axial spatially flux in comparison to flat approximation for partially integrated axial leakage and quadratic approximation for one-dimensional axial spatially flux.

Optimization of the Navy’s three-dimensional mine impact burial prediction simulation model, Impact35, using high-order numerical methods

2021 ◽  
pp. 154851292110286
Author(s):  
Athanasios Donas ◽  
Ioannis Famelis ◽  
Peter C Chu ◽  
George Galanis
Keyword(s):  
Numerical Analysis ◽  
Numerical Methods ◽  
Prediction Model ◽  
Simulation Model ◽  
Three Dimensional ◽  
Simulation System ◽  
High Order ◽  
Alternative Methodology ◽  
Runge Kutta ◽  
Fifth Order

The aim of this paper is to present an application of high-order numerical analysis methods to a simulation system that models the movement of a cylindrical-shaped object (mine, projectile, etc.) in a marine environment and in general in fluids with important applications in Naval operations. More specifically, an alternative methodology is proposed for the dynamics of the Navy’s three-dimensional mine impact burial prediction model, Impact35/vortex, based on the Dormand–Prince Runge–Kutta fifth-order and the singly diagonally implicit Runge–Kutta fifth-order methods. The main aim is to improve the time efficiency of the system, while keeping the deviation levels of the final results, derived from the standard and the proposed methodology, low.

scholarly journals Three-dimensional time-dependent neutron diffusion simulation using average current nodal expansion method

2020 ◽  
Vol 35 (3) ◽  
pp. 189-200
Author(s):  
Kambiz Valavi ◽  
Ali Pazirandeh ◽  
Gholamreza Jahanfarnia
Keyword(s):  
Three Dimensional ◽  
Reactor Core ◽  
Expansion Method ◽  
Steady State Solution ◽  
Time Dependent ◽  
Test Case ◽  
Neutron Diffusion ◽  
Average Current ◽  
Coarse Meshes ◽  
Nodal Expansion Method

In this work, the average current nodal expansion method was developed for the time-dependent neutronic simulation of transients in a nuclear reactor's core. For this purpose, an adopted iterative algorithm was proposed for solving the 3-D time-dependent neutron diffusion equation. In the average current nodal expansion method, the domain of the reactor core can be modeled by coarse meshes for neutronic calculation associated with reasonable precision of results. The discretization of time differential terms in the time-dependent equations was fulfilled, according to the implicit scheme. The proposed strategy was implemented in some kinetic problems including an infinite slab reactor, TWIGL 2-D seed-blanket reactor, and 3-D LMW LWR. At first, the steady-state solution was carried out for each test case, and then, the dynamic neutronic calculation was performed during the time for a specified transient scenario. Obtained results of static and dynamic solutions were verified in comparison with well-known references. Results can indicate the ability of the developed calculator to simulate transients in a nuclear reactor's core.

scholarly journals Development and Application of MCNP5 and KENO-VI Monte Carlo Models for the Atucha-2 PHWR Analysis

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
M. Pecchia ◽  
C. Parisi ◽  
F. D'Auria ◽  
O. Mazzantini
Keyword(s):  
Monte Carlo ◽  
Cross Sections ◽  
3D Model ◽  
Three Dimensional ◽  
Control Rod ◽  
Geometrical Complexity ◽  
Reactor Criticality ◽  
Reactor Cell ◽  
And Control ◽  
Control Rods

The geometrical complexity and the peculiarities of Atucha-2 PHWR require the adoption of advanced Monte Carlo codes for performing realistic neutronic simulations. Core models of Atucha-2 PHWR were developed using both MCNP5 and KENO-VI codes. The developed models were applied for calculating reactor criticality states at beginning of life, reactor cell constants, and control rods volumes. The last two applications were relevant for performing successive three dimensional neutron kinetic analyses since it was necessary to correctly evaluate the effect of each oblique control rod in each cell discretizing the reactor. These corrective factors were then applied to the cell cross sections calculated by the two-dimensional deterministic lattice physics code HELIOS. These results were implemented in the RELAP-3D model to perform safety analyses for the licensing process.

Runge-Kutta Discontinuous Galerkin Method Using Weno-Type Limiters: Three-Dimensional Unstructured Meshes

2012 ◽  
Vol 11 (3) ◽  
pp. 985-1005 ◽  
Author(s):  
Jun Zhu ◽  
Jianxian Qiu
Keyword(s):  
Discontinuous Galerkin ◽  
Hyperbolic Conservation Laws ◽  
Three Dimensional ◽  
Unstructured Meshes ◽  
Finite Volume Methods ◽  
High Order ◽  
High Order Accuracy ◽  
Hyperbolic Conservation ◽  
Runge Kutta ◽  
Nonlinear Hyperbolic Conservation Laws

AbstractThis paper further considers weighted essentially non-oscillatory (WENO) and Hermite weighted essentially non-oscillatory (HWENO) finite volume methods as limiters for Runge-Kutta discontinuous Galerkin (RKDG) methods to solve problems involving nonlinear hyperbolic conservation laws. The application discussed here is the solution of 3-D problems on unstructured meshes. Our numerical tests again demonstrate this is a robust and high order limiting procedure, which simultaneously achieves high order accuracy and sharp non-oscillatory shock transitions.

Structural Finite Elements With High-Order Basis Functions

1991 ◽  
Author(s):  
Chad D. Balch
Keyword(s):  
Finite Element ◽  
Dimensional Space ◽  
Three Dimensional ◽  
General Purpose ◽  
High Order ◽  
Benchmark Problems ◽  
Shell Elements ◽  
Space Curves ◽  
Doubly Curved ◽  
Deformation Modes

Abstract In the p-version of the finite element method, convergence is achieved by increasing the polynomial order of the elements. This paper discusses high-order three-dimensional carved beam and shell elements which have been implemented in a general purpose p-version linear finite element code. The displacement and rotation fields are represented by polynomials up to ninth order. Beam axes are three-dimensional space curves, and shell midsurfaces are general doubly-curved surfaces. Results for linear static and modal analyses are presented. In particular, it is demonstrated that a relatively small number of elements provide highly accurate results for typical benchmark problems. The elements perform robustly, with no locking or spurious deformation modes.

scholarly journals IMPROVEMENT TO NEM SP3 MODELLING AND SIMULATION

2021 ◽  
Vol 247 ◽  
pp. 03008
Author(s):  
Yuchao Xu ◽  
Jason Hou ◽  
Kostadin N. Ivanov
Keyword(s):  
Cross Sections ◽  
Mixed Type ◽  
Three Dimensional ◽  
Reactor Core ◽  
Expansion Method ◽  
Second Order ◽  
Global Trends ◽  
North Carolina State University ◽  
Multiphysics Coupling ◽  
Equivalence Theory

Accurate reactor core steady state safety analysis requires coupling between thermal-hydraulics and three dimensional multigroup pin by pin neutronics. Concerning the neutronics modeling, the Nodal Expansion Method (NEM) code is developed at North Carolina State University in the framework of high fidelity multiphysics coupling with CTF. NEM includes a simplified third-order Spherical Harmonic (SP3) solver. In this work, the solver has been improved by incorporating higher order scattering matrix library. The boundary conditions were corrected with one dimensional P3 theory and a consistent coupling coupling between zeroth- and second-order flux moments was established. Two methods for generating second order discontinuity factors (DFs) has ben developed, one based on the Generalized Equivalence Theory (GET) and one based on Parial Current Equivalence Theory (PCET). DFs were generated with three lattice sizes: single pin, 2 pins and assembly level. These developments were tested using the C5G7 benchmark. The results of the SP3 solver improvement, by using P2 and P3 scattering cross sections, show a 50% decrease in the eigenvalue (keff) prediction error compared to the reference transport solution. The GET DFs are applied in the C5G7 core pin by pin calculation and are compared with PCET DFs. The results show that PCET have a better performance in global results (eigenvalue). Concerning the different lattice sizes studies, the results show that DFs generated in smalll colorsets can improve local solutions. However, in order to reveal strong global trends, DFs should be generated in a larger corloset representative of the whole core. For the core calculations, DFs generated with the three colorsets together with an additional mixed type DFs were tested. For the mixed type, DFs generated from assembly size lattice were used for the internal interfaces and DFs generated from 2 pins size lattice were used for the assemblies boundary interfaces. These mixed DFs outperformed all the other configurations indicating that they manage to accomplish a satisfying compromise between global and local trends.

Validation of TRACG05 for Application to BWR AOO

2012 ◽  
Author(s):  
Asuka Matsui ◽  
Masashi Tamitani ◽  
Yoshiro Kudo ◽  
Sho Takano ◽  
Tatsuya Iwamoto ◽  
...  
Keyword(s):  
Experimental Data ◽  
Three Dimensional ◽  
Reactor Core ◽  
Expansion Method ◽  
Thermal Hydraulics ◽  
Control Rod ◽  
Neutron Kinetics ◽  
Safety Issues ◽  
Best Estimate ◽  
Assessment Matrix

TRACG code, coupling a three-dimensional neutron kinetics model for the reactor core with thermal-hydraulics based on two-fluid conservation equations, is a best-estimate (BE) code for BWRs to realistically simulate their transient and accidental behaviors. TRACG05 is the latest version and was originally developed to analyze Reactivity Initiated Accident (RIA). TRACG05 incorporates the same neutronics model of the latest core simulator with a three-group analytic-polynomial nodal expansion method. In addition to application to RIA safety analyses, TRACG05 has been planned to apply to safety analyses for Anticipated Operational Occurrences (AOOs) in BWRs by using a Best Estimate Plus Uncertainty (BEPU) methodology. To apply BEPU with TRACG05 to BWR AOOs, validations must be performed to evaluate the uncertainties of models relevant to important phenomena by comparing with appropriate test results for BWR AOOs. At first, a PIRT (Phenomena Identification and Ranking Table) was developed for each event scenario in AOOs to identify relevant physical processes and to determine their relative importance. According to the PIRT, an assessment matrix was established for separate effects tests (SETs), component effects tests (CETs), integral effects tests (IETs), and integral BWR plant start-up tests. The assessment matrix related the important phenomena to the test database, which was confirmed that all the important phenomena were covered by all tests specified in the matrix. According to the assessment matrix, comparison analyses have been specified to perform systematic and comprehensive validations of TRACG05 applicability to AOOs. The comparison analyses were done as the integrated code system with the up-stream reactor core design codes, therefore higher quality was enabled to evaluate the safety parameters. As the result, the uncertainties of important models in TRACG05 were determined so as to enable BEPU approaches for AOO safety issues. Here, as a SET, comparisons between TRACG05 and experimental data of void fraction in a bundle simulating an actual fuel bundle, which is one of the most important models in the application of TRACG05 to AOO analyses are shown. In addition, as pressurization event in AOOs, comparisons between TRACG05 and experimental data of Peach Bottom 2 Turbine Trip Test, which is one of integral tests for a BWR plant, are shown. This is the only test showing large neutron flux increase and strong coupling of neutron kinetics and thermal-hydraulics in the core due to void and Doppler feedbacks. Furthermore, a sensitivity analysis regarding a delay time of control rod (CR) insertion initiation which was the most sensitive uncertainty to the results is also shown.

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