scholarly journals Methodology for Discontinuity Factors Generation for Simplified P3 Solver Based on Nodal Expansion Formulation

Energies ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6478
Author(s):  
Yuchao Xu ◽  
Jason Hou ◽  
Kostadin Ivanov
Keyword(s):  
Power Distribution ◽  
Spherical Harmonic ◽  
Three Dimensional ◽  
Reactor Core ◽  
Expansion Method ◽  
Order Moment ◽  
Third Order ◽  
New Developments ◽  
Equivalence Theory ◽  
Homogeneous Regions

The Simplified Spherical Harmonic (SPN) approximation was first introduced as a three-dimensional (3D) extension of the plane-geometry Spherical Harmonic (PN) equations. A third order SPN (SP3) solver, recently implemented in the Nodal Expansion Method (NEM), has shown promising performance in the reactor core neutronics simulations. This work is focused on the development and implementation of the transport-corrected interface and boundary conditions in an NEM SP3 solver, following recent published work on the rigorous SPN theory for piecewise homogeneous regions. A streamlined procedure has been developed to generate the flux zero and second order/moment discontinuity factors (DFs) of the generalized equivalence theory to minimize the error introduced by pin-wise homogenization. Moreover, several colorset models with varying sizes and configurations are later explored for their capability of generating DFs that can produce results equivalent to that using the whole-core homogenization model for more practical implementations. The new developments are tested and demonstrated on the C5G7 benchmark. The results show that the transport-corrected SP3 solver shows general improvements to power distribution prediction compared to the basic SP3 solver with no DFs or with only the zeroth moment DF. The complete equivalent calculations using the DFs can almost reproduce transport solutions with high accuracy. The use of equivalent parameters from larger size colorset models show a slightly reduced prediction error than that using smaller colorset models in the whole-core calculations.

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.

CFD Investigation of Thermal-Hydraulic Behaviors in Full Reactor Core for Sodium-Cooled Fast Reactor

2018 ◽  
Author(s):  
Jing Chen ◽  
Dalin Zhang ◽  
Suizheng Qiu ◽  
Kui Zhang ◽  
Mingjun Wang ◽  
...  
Keyword(s):  
Fast Reactor ◽  
Power Distribution ◽  
Three Dimensional ◽  
Reactor Core ◽  
Heat Removal ◽  
The Core ◽  
Computational Fluid Dynamics Cfd ◽  
Heat Removal System ◽  
China Experimental Fast Reactor ◽  
Full Core

As the first developmental step of the sodium-cooled fast reactor (SFR) in China, the pool-type China Experimental Fast Reactor (CEFR) is equipped with the openings and inter-wrapper space in the core, which act as an important part of the decay heat removal system. The accurate prediction of coolant flow in the reactor core calls for complete three-dimensional calculations. In the present study, an investigation of thermal-hydraulic behaviors in a 180° full core model similar to that of CEFR was carried out using commercial Computational Fluid Dynamics (CFD) software. The actual geometries of the peripheral core baffle, fluid channels and narrow inter-wrapper gap were built up, and numerous subassemblies (SAs) were modeled as the porous medium with appropriate resistance and radial power distribution. First, the three-dimensional flow and temperature distributions in the full core under normal operating condition are obtained and quantitatively analyzed. And then the effect of inter-wrapper flow (IWF) on heat transfer performance is evaluated. In addition, the detailed flow path and direction in local inter-wrapper space including the internal and outlet regions are captured. This work can provide some valuable understanding of the core thermal-hydraulic phenomena for the research and design of SFRs.

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 Kolmogorov laws for stratified turbulence

2012 ◽  
Vol 709 ◽  
pp. 659-670 ◽  
Author(s):  
Pierre Augier ◽  
Sébastien Galtier ◽  
Paul Billant
Keyword(s):  
Scaling Law ◽  
Three Dimensional ◽  
Boussinesq Approximation ◽  
Order Moment ◽  
Stratified Turbulence ◽  
Scaling Relation ◽  
Third Order ◽  
Exact Relation ◽  
Length Scales

AbstractFollowing the Kolmogorov technique, an exact relation for a vector third-order moment $\mathbi{J}$ is derived for three-dimensional incompressible stably stratified turbulence under the Boussinesq approximation. In the limit of a small Brunt–Väisälä frequency, isotropy may be assumed which allows us to find a generalized $4/ 3$-law. For strong stratification, we make the ansatz that $\mathbi{J}$ is directed along axisymmetric surfaces parameterized by a scaling law relating horizontal and vertical coordinates. An integration of the exact relation under this hypothesis leads to a generalized Kolmogorov law which depends on the intensity of anisotropy parameterized by a single coefficient. By using a scaling relation between large horizontal and vertical length scales we fix this coefficient and propose a unique law.

MTC 3D: A Fully Coupled Methodology for MSLB Safety Analysis

2014 ◽  
Author(s):  
Christian Royère ◽  
Michel Gonnet ◽  
Brahim Manchid
Keyword(s):  
Power Distribution ◽  
Three Dimensional ◽  
Reactor Core ◽  
Nucleate Boiling ◽  
Steam Line ◽  
Second Step ◽  
Inlet Temperature ◽  
Original Design ◽  
The Core ◽  
Strong Asymmetry

The main steam line break (MSLB) is an overcooling accident that may lead to an over criticality, and so to a power increase, after the reactor trip. The most penalizing single failure is a RCCA bank stuck out of the core when the reactor trip occurs. This configuration leads to a strong asymmetry of the radial power shape combined with a strong asymmetry of the core inlet temperature that results in a strongly distorted 3D power distribution. In the original design, the MSLB accident was studied with a simplified and conservative 0D method. The point kinetics approach requires the use of extremely conservative assumptions in order to account for the asymmetry in the core region that takes place during the transient. The use of the coupling between a three-dimensional neutronic code (SMART), a 3D core thermal-hydraulic code (FLICA cf. ref [4]) and a reactor coolant system code (MANTA cf. ref [3]) allows representing the 3D heterogeneity of the power shape and also of the resulting cross flows. In addition, this coupling allows determining moderator and Doppler feedback effects in a much more realistic way thus limiting accident consequences estimated. A methodology, called MTC3D (for Méthode Totalement Couplée 3D in French), has been developed using the coupling between the three codes to perform the MSLB analysis. The physical dominant parameters of the transient are identified through a comprehensive sensitivity analysis. Then, a deterministic approach is used in the entire transient simulation considering dominant parameters in a penalizing way. In a first step, neutronic data are determined with SMART calculations. In a second step, MANTA/SMART/FLICA transients are performed with penalized neutronic and thermal-hydraulic data. In a third step, as the steam line break transient is a relatively slow transient, the core power distribution is evaluated with a steady state SMART/FLICA calculation without penalization. In a last step, safety criteria, such as minimum DNBR (Departure from Nucleate Boiling Ratio) are calculated with FLICA calculations based on core power distribution calculated at the third step and boundary conditions calculated at the second step. The use of 3D neutronic and detailed thermal-hydraulic codes to model the reactor core allows considering a more physical representation of the core configuration for transient analysis. The coupling between 3D neutronic and core thermal-hydraulic codes allows exhibiting intrinsic margins without over penalizations related to a simplified 0D method.

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.

Tire Modeling by Finite Elements

1992 ◽  
Vol 20 (1) ◽  
pp. 33-56 ◽  
Author(s):  
L. O. Faria ◽  
J. T. Oden ◽  
B. Yavari ◽  
W. W. Tworzydlo ◽  
J. M. Bass ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Rolling Contact ◽  
Test Problems ◽  
State Behavior ◽  
Normal Contact ◽  
New Developments ◽  
Applied Torque ◽  
Dimensional Finite Element ◽  
Tire Modeling ◽  
Three Dimensional Finite Element

Abstract Recent advances in the development of a general three-dimensional finite element methodology for modeling large deformation steady state behavior of tire structures is presented. The new developments outlined here include the extension of the material modeling capabilities to include viscoelastic materials and a generalization of the formulation of the rolling contact problem to include special nonlinear constraints. These constraints include normal contact load, applied torque, and constant pressure-volume. Several new test problems and examples of tire analysis are presented.

scholarly journals Three-dimensional Maxwellian extended Newtonian gravity and flat limit

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Patrick Concha ◽  
Lucrezia Ravera ◽  
Evelyn Rodríguez ◽  
Gustavo Rubio
Keyword(s):  
Cosmological Constant ◽  
Three Dimensional ◽  
Expansion Method ◽  
Gravity Models ◽  
Newtonian Gravity ◽  
Newtonian Theory ◽  
Relativistic Limit ◽  
Expansion Procedure ◽  
Three Space ◽  
Chern Simons

Abstract In the present work we find novel Newtonian gravity models in three space-time dimensions. We first present a Maxwellian version of the extended Newtonian gravity, which is obtained as the non-relativistic limit of a particular U(1)-enlargement of an enhanced Maxwell Chern-Simons gravity. We show that the extended Newtonian gravity appears as a particular sub-case. Then, the introduction of a cosmological constant to the Maxwellian extended Newtonian theory is also explored. To this purpose, we consider the non-relativistic limit of an enlarged symmetry. An alternative method to obtain our results is presented by applying the semigroup expansion method to the enhanced Nappi-Witten algebra. The advantages of considering the Lie algebra expansion procedure is also discussed.

Packing Optimization by Enhanced Rubber Band Analogy

2005 ◽  
Author(s):  
Hong Dong ◽  
Georges M. Fadel ◽  
Vincent Y. Blouin
Keyword(s):  
Three Dimensional ◽  
Optimization Method ◽  
Rubber Band ◽  
Volume Relaxation ◽  
New Developments ◽  
Packing Problems ◽  
Rubber Balloon ◽  
Elastic Forces ◽  
Reaction Forces ◽  
Packing Optimization

In this paper, some new developments to the packing optimization method based on the rubber band analogy are presented. This method solves packing problems by simulating the physical movements of a set of objects wrapped by a rubber band in the case of two-dimensional problems or by a rubber balloon in the case of three-dimensional problems. The objects are subjected to elastic forces applied by the rubber band to their vertices as well as reaction forces when contacts between objects occur. Based on these forces, objects translate or rotate until maximum compactness is reached. To improve the compactness further, the method is enhanced by adding two new operators: volume relaxation and temporary retraction. These two operators allow temporary volume (elastic energy) increase to get potentially better packing results. The method is implemented and applied for three-dimensional arbitrary shape objects.

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