A New Method on Flux Mapping by Function Expansion

2010 ◽  
Author(s):  
Bin Zhong ◽  
Kan Wang ◽  
Ganglin Yu
Keyword(s):  
Power Distribution ◽  
Synthesis Method ◽  
Expansion Method ◽  
Mapping Method ◽  
Least Square ◽  
New Method ◽  
Coolant Temperature ◽  
Fuel Temperature ◽  
Function Expansion ◽  
Flux Mapping

The core flux (power) distribution is very important to safe and economical operation of nuclear reactor. It can be obtained by many methods depending on the desired accuracy and execution time. For on-line core surveillance and regulation, we need to get the real-time flux distribution. If the true local parameters such as fuel temperature, coolant temperature and material density were known, the solution of the diffusion equation with instantaneous parameters could, in principle, provide the necessary spatial details. However, in reality, it is impossible to obtain the operational “readings” of these parameters for each fuel cell. The detector results at certain locations can be applied to improve the results of the only diffusion calculations by Flux Mapping methods. Function expansion method is employed to express the approximate real distribution by the combination of several Flux Mapping method results as the expansion basis functions. The Harmonics Synthesis Method (HSM) and Least-Square method are combined to get a new Flux Mapping method in this paper. The simulation results show that the new method can be used for Flux Mapping and get better results.

A Small PWR-Core Physical Calculation Based on PWR-Core Analysis Code CORAL

2021 ◽  
Author(s):  
Wen Yang ◽  
Lun Zhou ◽  
Junrong Qiu ◽  
Yun Tai
Keyword(s):  
Density Distribution ◽  
Power Distribution ◽  
Channel Model ◽  
Three Dimensional ◽  
Least Square ◽  
Object Oriented Programming ◽  
Core Analysis ◽  
Fuel Temperature ◽  
Fuel Assemblies ◽  
Calculation Results

Abstract Three dimensional PWR-core analysis code CORAL is developed by Wuhan Second Ship Design and Research Institute. This code provides basic functions including three-dimensional power distribution, fine power reconstruction, fuel temperature distribution, critical search, control rod worth, reactivity coefficients, burnup and nuclide density distribution, etc. CORAL employ nodal expansion method to solve neutron diffusion equation, and the least square method is used to achieve few group constants, and sub-channel model and one-dimensional heat transfer is used to calculate fuel temperature and coolant density distribution, and burnup distribution and nuclide nuclear density could be obtained by solving macro-depletion and micro-depletion equation. The CORAL code is convenient to update and maintain in consider of modular, object-oriented programming technology. In order to analyze the computational accuracy of the CORAL code in small PWR-core and its capability to deal with heterogeneous, calculation analysis are carried out based on the material and geometry parameters of the SMART core. The core has 57 fuel assemblies, with 8, 20 or 24 gadolinium rods arranged in the fuel assemblies. In this paper, a quantitative comparison and analysis of the small PWR problem calculation results are carried out. Numerical results, including effective multiplication factor, assembly power distribution and pin power distribution, all agree well with the calculation results of OpenMC or Bamboo at both hot zero-power (HZP) and hot full-power (HFP) conditions.

To Improve the Accuaracy of Harmonic Synthesis Method by Using More Detectors in Azimuthal Direction in HTR

2014 ◽  
Author(s):  
Kai Fan ◽  
Fu Li ◽  
Xuhua Zhou
Keyword(s):  
Power Distribution ◽  
Synthesis Method ◽  
Expansion Method ◽  
Azimuthal Direction ◽  
Neutron Detectors ◽  
Tsinghua University ◽  
The Core ◽  
Demonstration Plant ◽  
Polynomial Expansion Method ◽  
High Temperature Gas

Modular high temperature gas cooled reactor HTR-PM demonstration plant, designed by INET, Tsinghua University, is being built in Shidaowan, Shandong province, China. HTR-PM adopts pebble bed concept. Like other HTR, monitoring the core power distribution of HTR-PM is very important but challenging, as there is no in-core neutron detectors. There are some proposals to reconstruct the power distribution using the readings of ex-core neutron detectors. One method is harmonic synthesis method. In HTR, the neutron detectors are arranging symmetrically; and the power distribution of the core is also symmetrical. So in the before, only one set of detectors were used to reconstruct the power distribution, for considering the readings of different sets were almost same. In this paper, all readings of the neutron detectors were used, and new results were calculated and evaluated. It is showed that using more detector readings has no help to the accuracy of the harmonic synthesis method but improve the robustness of the method obvious. Using more detectors could improve both the robustness and the accuracy to the harmonics’ coefficients polynomial expansion method.

Axial Power and Coolant-Temperature Profiles for a Non-Re-Entrant Pressure-Tube Supercritical Water-Cooled Reactor Fuel Channel

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Vitali Kovaltchouk ◽  
Eleodor Nichita ◽  
Eugene Saltanov
Keyword(s):  
Cross Sections ◽  
Power Distribution ◽  
Pressure Tube ◽  
Coolant Temperature ◽  
Outlet Temperature ◽  
Thermal Hydraulics ◽  
Fuel Temperature ◽  
Fuel Channel ◽  
Technical Specifications ◽  
Institute Of Technology

The axial power and coolant-temperature distributions in a fuel channel of the Generation IV pressure-tube super-critical water-cooled reactor (PT-SCWR) are found using coupled neutronics-thermal-hydraulics calculations. The simulations are performed for a channel loaded with a fresh, 78-element Th-Pu fuel assembly. Neutronics calculations are performed using the DONJON diffusion code using two-group homogenized cross sections produced using the lattice code DRAGON. The axial coolant temperature profile corresponding to a certain axial linear heat generation rate is found using a code developed in-house at University of Ontario Institute of Technology (UOIT). The effect of coolant density, coolant temperature, and fuel temperature variation along the channel is accounted for by generating macroscopic cross sections at several axial positions. Fixed-point iterations are performed between neutronics and thermal-hydraulics calculations. Neutronics calculations include the generation of two-group macroscopic cross sections at several axial positions, taking into account local parameters such as coolant temperature and density and average fuel temperature. The coolant flow rate is adjusted so that the outlet temperature of the coolant corresponds to the SCWR technical specifications. The converged axial power distribution is found to be asymmetric, resembling a cosine shape skewed toward the inlet (reactor top).

Traveling wave solutions for the Couple Boiti-Leon-Pempinelli System by using extended Jacobian elliptic function expansion method

2015 ◽  
Vol 11 (3) ◽  
pp. 3134-3138 ◽  
Author(s):  
Mostafa Khater ◽  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Elliptic Function ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Nonlinear Evolution Equations ◽  
Jacobian Elliptic Function ◽  
Function Expansion

In this work, an extended Jacobian elliptic function expansion method is pro-posed for constructing the exact solutions of nonlinear evolution equations. The validity and reliability of the method are tested by its applications to the Couple Boiti-Leon-Pempinelli System which plays an important role in mathematical physics.

scholarly journals Construction of new solitary wave solutions of generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified form of Camassa-Holm equations

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 896-909 ◽  
Author(s):  
Dianchen Lu ◽  
Aly R. Seadawy ◽  
Mujahid Iqbal
Keyword(s):  
Solitary Wave ◽  
Nonlinear Partial Differential Equations ◽  
Research Work ◽  
Traveling Wave Solutions ◽  
Elliptic Functions ◽  
Mapping Method ◽  
New Method ◽  
Auxiliary Equation ◽  
Solitary Wave Solutions ◽  
Wave Solutions

AbstractIn this research work, for the first time we introduced and described the new method, which is modified extended auxiliary equation mapping method. We investigated the new exact traveling and families of solitary wave solutions of two well-known nonlinear evaluation equations, which are generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony and simplified modified forms of Camassa-Holm equations. We used a new technique and we successfully obtained the new families of solitary wave solutions. As a result, these new solutions are obtained in the form of elliptic functions, trigonometric functions, kink and antikink solitons, bright and dark solitons, periodic solitary wave and traveling wave solutions. These new solutions show the power and fruitfulness of this new method. We can solve other nonlinear partial differential equations with the use of this method.

Thermal investigations of microelectronic chip with non‐uniform power distribution: temperature prediction and thermal placement design optimization

2004 ◽  
Vol 21 (3) ◽  
pp. 29-43 ◽  
Author(s):  
Teck Joo Goh ◽  
K.N. Seetharamu ◽  
G.A. Quadir ◽  
Z.A. Zainal ◽  
K. Jeevan Ganeshamoorthy
Keyword(s):  
Power Distribution ◽  
Heat Dissipation ◽  
Thermal Analyses ◽  
Convection Heat Transfer ◽  
Multiple Linear Regression Model ◽  
Least Square Method ◽  
Least Square ◽  
Junction Temperature ◽  
Thermal Investigations ◽  
Placement Distance

This paper presents the thermal analyses carried out to predict the temperature distribution of the silicon chip with non‐uniform power dissipation patterns and to determine the optimal locations of power generating sources in silicon chip design layout that leads to the desired junction temperature, Tj. Key thermal parameters investigated are the heat source placement distance, level of heat dissipation, and magnitude of convection heat transfer coefficient. Finite element method (FEM) is used to investigate the effect of the key parameters. From the FEM results, a multiple linear regression model employing the least‐square method is developed that relates all three parameters into a single correlation which would predict the maximum junction temperature, Tj,max.

scholarly journals Approximation of the Orientation Distribution of Grains in Polycrystalline Samples by Means of Gaussians

1992 ◽  
Vol 19 (1-2) ◽  
pp. 9-27 ◽  
Author(s):  
D. I. Nikolayev ◽  
T. I. Savyolova ◽  
K. Feldmann
Keyword(s):  
Rolling Texture ◽  
Expansion Method ◽  
Operating Mode ◽  
Orientation Distribution ◽  
New Method ◽  
Gaussian Distributions ◽  
Positivity Condition ◽  
The Central Limit Theorem ◽  
Pole Figures ◽  
Series Expansion Method

The orientation distribution function (ODF) obtained by classical spherical harmonics analysis may be falsified by ghost influences as well as series truncation effects. The ghosts are a consequence of the inversion symmetry of experimental pole figures which leads to the loss of information on the “odd” part of ODF.In the present paper a new method for ODF reproduction is proposed. It is based on the superposition of Gaussian distributions satisfying the central limit theorem in the SO(3)-space as well as the ODF positivity condition. The kind of ODF determination offered here is restricted to the fit of Gaussian parameters and weights with respect to the experimental pole figures. The operating mode of the new method is demonstrated for a rolling texture of copper. The results are compared with the corresponding ones obtained by the series expansion method.

Development and Application of Multi-Physics Safety Analysis Code for Advanced Liquid Metal Cooled Reactor

2018 ◽  
Author(s):  
Chi Wang ◽  
Xuebei Zhang ◽  
Jingchao Feng ◽  
Muhammad Shehzad Khan ◽  
Minyou Ye ◽  
...  
Keyword(s):  
Nuclear Reactor ◽  
Safety Analysis ◽  
Coolant Temperature ◽  
Medium Size ◽  
High Tech ◽  
Fuel Temperature ◽  
Flow Phenomena ◽  
Nuclear Reactor Safety ◽  
Cfd Method ◽  
Point Kinetics

The simulation of 3D thermal-hydraulic problem for the pool type fast reactors, is one of the necessary and great importance. Most system codes can’t be used to simulate multi-dimensional thermal-hydraulics problems, whereas, the CFD method is suitable to deal with these type of simulation challenges. Based on the CFD method, a neutronics and thermohydraulic coupling code FLUENT/PK for nuclear reactor safety analysis by coupling the commercial CFD code FLUENT with the point kinetics model (PKM) and the pin thermal model (PTM) is developed by University of Science and Technology of China (USTC). The coupled code is verified by comparing with a series of benchmarks on beam interruptions in a lead-bismuth-cooled and MOX-fuelled accelerator-driven system. The variations of transient power, fuel temperature and outlet coolant temperature all agree well with the benchmark results. The validation results show that the code can be used to simulate the transient accidents of critical and sub-critical lead/lead-bismuth cooled reactors. Then this coupling code is used to evaluate the safety performance of MYRRHA (Multi-purpose Hybrid Research Reactor for High-tech Applications) at unprotected beam over-power (UBOP) accident, and M2LFR-1000 (Medium-size Modular Lead-cooled Fast Reactor) at the unprotected transient over-power (UTOP) and unprotected loss of flow (ULOF) accident. The transient power, the temperature of coolant and fuel and multi-dimensional flow phenomena in upper plenum and lower plenum are presented and discussed in this paper.

scholarly journals High Precision Position Measurement Method for Laguerre-Gaussian Beams Using a Quadrant Detector

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 4007 ◽  
Author(s):  
Qian Li ◽  
Jiabin Wu ◽  
Yunshan Chen ◽  
Jingyuan Wang ◽  
Shijie Gao ◽  
...  
Keyword(s):  
Maximum Error ◽  
Least Square ◽  
New Method ◽  
Beam Radius ◽  
Engineering Practice ◽  
Gaussian Beams ◽  
Good Prospect ◽  
Position Measurement ◽  
Beam Position ◽  
Mean Square Errors

In this paper, we propose a new method to improve the position measurement accuracy for Laguerre-Gaussian beams on a quadrant detector (QD). First, the error effects of the detector diameter and the gap size are taken into account, and the position error compensation factor is introduced into the conventional formula. Then, in order to reduce the number of parameters, the concept of effective radius is proposed. Thus, a new analytical expression is obtained with a best fit using the least square method. It is verified by simulation that this approach can reduce the maximum error by 97.4% when the beam radius is 0.95 mm; meanwhile, the root mean square errors under different radii are all less than 0.004 mm. The results of simulation show that the new method could effectively improve the accuracy of the QD measurement for different radii. Therefore, the new method would have a good prospect in the engineering practice of beam position measurements.

scholarly journals Weighted Measurement Fusion Particle Filter for Nonlinear Systems with Correlated Noises

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3242 ◽  
Author(s):  
Ke Wei Zhang ◽  
Gang Hao ◽  
Shu Li Sun
Keyword(s):  
Nonlinear Systems ◽  
Particle Filter ◽  
Series Expansion ◽  
Taylor Series ◽  
Asymptotic Optimality ◽  
Taylor Series Expansion ◽  
Full Rank ◽  
Expansion Method ◽  
Least Square ◽  
Correlated Noises

The multi-sensor information fusion particle filter (PF) has been put forward for nonlinear systems with correlated noises. The proposed algorithm uses the Taylor series expansion method, which makes the nonlinear measurement functions have a linear relationship by the intermediary function. A weighted measurement fusion PF (WMF-PF) was put forward for systems with correlated noises by applying the full rank decomposition and the weighted least square theory. Compared with the augmented optimal centralized fusion particle filter (CF-PF), it could greatly reduce the amount of calculation. Moreover, it showed asymptotic optimality as the Taylor series expansion increased. The simulation examples illustrate the effectiveness and correctness of the proposed algorithm.

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