Numerical Simulation of Multi-Physics Processes in Nuclear System Based on Galerkin Finite Element Method

2020 ◽  
Author(s):  
Baoxin Yuan ◽  
Wankui Yang ◽  
Songbao Zhang ◽  
Bin Zhong ◽  
Junxia Wei ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Heat Source ◽  
Neutron Field ◽  
Practical Significance ◽  
Nuclear System ◽  
Governing Equations ◽  
Galerkin Finite Element ◽  
Calculation Results ◽  
Element Theory

Abstract It is of practical significance to analyze the multi-physics process of nuclear system, which includes neutronics, heat transfer and thermoelasticity. Fission reaction is the heat source in system, the heat source will affect the distribution of temperature field, which will lead to the change of strain. Strain in turn will affect the distribution of neutron field. Therefore, it is necessary to analyze the distribution of neutron flux, temperature and strain in system. Three aspects of work have been carried out: 1) Based on Galerkin finite element theory, the governing equations of neutronics, heat transfer and thermoelasticity are established; 2) The multi-physics analysis code is developed; 3) The calculation results are analyzed and discussed.

Computational Study of Streamfunction-Vorticity Formulation of Incompressible Flow and Heat Transfer Problems

2011 ◽  
Vol 52-54 ◽  
pp. 511-516 ◽  
Author(s):  
Arup Kumar Borah
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Boundary Conditions ◽  
Incompressible Flow ◽  
Computational Study ◽  
The Other ◽  
Governing Equations ◽  
Flow And Heat Transfer ◽  
Continuity Constraint ◽  
Transfer Problems

In this paper we have studied the streamfunction-vorticity formulation can be advantageously used to analyse steady as well as unsteady incompressible flow and heat transfer problems, since it allows the elimination of pressure from the governing equations and automatically satisfies the continuity constraint. On the other hand, the specification of boundary conditions for the streamfunction-vorticity is not easy and a poor evaluation of these conditions may lead to serious difficulties in obtaining a converged solution. The main issue addressed in this paper is the specification in the boundary conditions in the context of finite element of discretization, but approach utilized can be easily extended to finite volume computations.

Coupled Thermoelasticity Analysis of Annular Laminate Disk Using Laplace Transform and Galerkin Finite Element Method

2014 ◽  
Vol 656 ◽  
pp. 298-304 ◽  
Author(s):  
S.M. Nowruzpour Mehrian ◽  
Amin Nazari ◽  
Mohammad Hasan Naei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Thermal Shock ◽  
Outer Edge ◽  
Galerkin Finite Element Method ◽  
Governing Equations ◽  
Space Domain ◽  
Annular Disk ◽  
Galerkin Finite Element ◽  
Element Method

In this paper, a dynamic analysis of annular laminate disk under radial thermal shock is carried out by employing a Galerkin Finite Element (GFE) approach. The governing equations, including the equation of the motion and energy equation are obtained based on Lord-Shulman theory. These two equations are solved simultaneously to obtain the displacement components and temperature distributions. A simply support boundary condition through outer edge is assumed for the annular disk. The inner radius is subjected to thermal shock and free of any traction. The outer edge is keeping at a constant temperature. Using Laplace transfer technique to transfer the governing equations into the space domain, where the Galerkin Finite Element Method is employed to obtain the solution in space domain. The inverse of Laplace transfer is performed numerically to achieve the final solution in the real time domain. The results are validated with the known data reported in the literature.

A Least-Squares/Galerkin Finite Element Method for Incompressible Navier-Stokes Equations

2008 ◽  
Author(s):  
Rajeev Kumar ◽  
Brian H. Dennis
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Least Squares ◽  
Basis Functions ◽  
Galerkin Finite Element Method ◽  
Governing Equations ◽  
Galerkin Finite Element ◽  
First Order ◽  
Convection Dominated ◽  
Element Method

The least-squares finite element method (LSFEM), which is based on minimizing the l2-norm of the residual, has many attractive advantages over Galerkin finite element method (GFEM). It is now well established as a proper approach to deal with the convection dominated fluid dynamic equations. The least-squares finite element method has a number of attractive characteristics such as the lack of an inf-sup condition and the resulting symmetric positive system of algebraic equations unlike GFEM. However, the higher continuity requirements for second-order terms in the governing equations force the introduction of additional unknowns through the use of an equivalent first-order system of equations or the use of C1 continuous basis functions. These additional unknowns lead to increased memory and computing time requirements that have prevented the application of LSFEM to large-scale practical problems, such as three-dimensional compressible viscous flows. A simple finite element method is proposed that employs a least-squares method for first-order derivatives and a Galerkin method for second order derivatives, thereby avoiding the need for additional unknowns required by pure a LSFEM approach. When the unsteady form of the governing equations is used, a streamline upwinding term is introduced naturally by the leastsquares method. Resulting system matrix is always symmetric and positive definite and can be solved by iterative solvers like pre-conditioned conjugate gradient method. The method is stable for convection-dominated flows and allows for equalorder basis functions for both pressure and velocity. The stability and accuracy of the method are demonstrated with preliminary results of several benchmark problems solved using low-order C0 continuous elements.

scholarly journals Convection Heat Transfer of MgO-Ag /Water Magneto-Hybrid Nanoliquid Flow into a Special Porous Enclosure

2020 ◽  
Vol 2 (2) ◽  
pp. 84-95
Author(s):  
Fateh Mebarek Oudina ◽  
◽  
Fares Redouane ◽  
Choudhari Rajashekhar ◽  
◽  
...  
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Computational Study ◽  
Convection Heat Transfer ◽  
Darcy Number ◽  
Governing Equations ◽  
Galerkin Finite Element ◽  
Element Technique ◽  
The Magnetic Field ◽  
Porous Enclosure

This work explores numerically a computational study of free convection in a grooved porous enclosure filled with water-based hybrid-nanoliquid in the presence of an external magnetic field. To solve the governing equations of the problem, the Galerkin finite element technique is utilized. For a several governing parameters such as Rayleigh number (102≤Ra ≤106), magnetic field parameter (0≤Ha≤100), Darcy number (10-2≤ Da ≤10-4) the results are obtained and discussed via streamlines, isotherms and average Nusselt number. The magnetic field has a good regulating effect for the fluid flow and the heat transfer in porous media

Analysis to Coupled Electromagnetic-Thermal Field of Brushless Doubly Fed Machine

2012 ◽  
Vol 433-440 ◽  
pp. 7312-7317
Author(s):  
Sheng Zhu Xia ◽  
Xian Ming Deng ◽  
Zhi Ye Wang ◽  
Meng Liu
Keyword(s):  
Finite Element ◽  
Electromagnetic Field ◽  
Heat Source ◽  
Thermal Field ◽  
Initial Conditions ◽  
Element Model ◽  
Electromagnetic Environment ◽  
Calculation Results ◽  
Doubly Fed ◽  
Doubly Fed Machine

this paper build up the brushless doubly fed machine (BDFM) finite element model of the coupled electromagnetic-thermal field, the electromagnetic joule heat calculated in electromagnetic environment will be loaded as the heat source to calculate in thermal field, the calculated results in thermal field will be the initial conditions to calculate the electromagnetic field, get the thermal field distribution when the motor is stable through cycle calculation at last. Calculation results show the effectiveness of this method.

Effect of a Shield on Mixed Convection in a Rectangular Enclosure with Moving Cold Sidewalls and a Heat Source on the Bottom Wall

2010 ◽  
Vol 297-301 ◽  
pp. 584-589
Author(s):  
Ghanbar Ali Sheikhzadeh ◽  
S.H. Musavi ◽  
N. Sadoughi
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Heat Source ◽  
Transfer Coefficient ◽  
Heat Dissipation ◽  
Bottom Wall ◽  
Governing Equations ◽  
Thermal Shield ◽  
The Heat Transfer Coefficient ◽  
Specific Distance

In this work, the mixed convention of air inside a rectangular cavity with moving cold sidewalls is studied numerically. A constant flux heat source is attached to the bottom wall of the cavity. A thin thermal shield is located at a specific distance above the heat source. The governing equations are solved using appropriate numerical methods. A parametric study has been conducted and the effects of heat source length, its location and the shield distance from the source on the heat transfer have been investigated. The results show that the heat dissipation increases as the heat source and the shield are moved up to a certain distance towards either sidewall. However, moving them beyond this limiting distance results in the reduction of heat dissipation. It is shown that the presence of shield results in the reduction of the heat transfer coefficient. However, for the normalized distance of the shield from the heat source greater than , the shield’s effect on the reduction of the heat transfer coefficient is less than.

scholarly journals Development of Finite Element Solver for Welding Analysis

2018 ◽  
Vol 2 (2) ◽  
Author(s):  
Abid Ali Khan ◽  
Farzeen Shahid ◽  
Ihtzaz Qamar
Keyword(s):  
Finite Element ◽  
Temperature Field ◽  
Heat Conduction ◽  
Heat Source ◽  
Welding Process ◽  
Transient Heat Conduction ◽  
Moving Heat Source ◽  
Structural Members ◽  
Final Solution ◽  
Governing Equations

Welding is a process of joining the similar or different metals. Improper welding process leads to inaccuracies and misalignments of structural members, causing high cost and delays in work. Therefore, it is essential to predict the temperature field during welding process. Different techniques can be used to predict the temperature field, which may lead to structure distortion. The present study aims to develop a finite element solver for transient heat conduction analysis. The final solution is calculated from the assumed solution and compared with the numerical computations. The solver is then modified for use of moving heat source. The modification comprise, change in governing equations with the inclusion of phase change. The moving heat source continuously increases the temperature during motion. When the heat source completes a pass, model is allowed to cool down in order to study the temperature distribution during cooling.

scholarly journals Finite Element Analysis of Mixed Convection in a Rectangular Cavity with a Heat-Conducting Horizontal Circular Cylinder

2009 ◽  
Vol 14 (2) ◽  
pp. 217-247 ◽  
Author(s):  
Md. M. Rahman ◽  
M. A. Alim ◽  
M. A. H. Mamun
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Heat Source ◽  
Mixed Convection ◽  
Rectangular Cavity ◽  
Heated Wall ◽  
Physical Parameters ◽  
Element Formulation ◽  
Heat Conducting ◽  
Coupled Equations

. Combined free and forced convection in a two dimensional rectangular cavity with a uniform heat source applied on the right vertical wall is studied numerically. A circular heat conducting horizontal cylinder is placed somewhere within the cavity. The present study simulates a practical system, such as a conductive material in an inert atmosphere inside a furnace with a constant flow of gas from outside. Importance is placed on the influences of the configurations and physical properties of the cavity. The development mathematical model is governed by the coupled equations of continuity, momentum and energy and is solved by employing Galerkin weighted residual finite element method. In this paper, a finite element formulation for steadystate incompressible conjugate mixed convection and conduction flow is developed. The computations are carried out for wide ranges of the governing parameters, Reynolds number (Re), Richardson number (Ri), Prandtl number (Pr) and some physical parameters. The results indicate that both the heat transfer rate from the heated wall and the dimensionless temperature in the cavity strongly depend on the governing parameters and configurations of the system studied, such as size, location, thermal conductivity of the cylinder and the location of the inflow and outflow opening. Detailed results of the interaction between forced airstreams and the buoyancy-driven flow by the heat source are demonstrated by the distributions of streamlines, isotherms and heat transfer coefficient.

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