FEMLAB class shl by 7UDEc2g

VIEWS: 6 PAGES: 38

									    The use and application
          of FEMLAB




               S.H.Lee and J.K.Lee

       Plasma Application Modeling Lab.
Department of Electronic and Electrical Engineering
   Pohang University of Science and Technology

                    24. Apr. 2006
What is FEMLAB?


   FEMLAB : a powerful interactive environment for modeling and
 solving various kinds of scientific and engineering problems based
 on partial differential equations (PDEs).

   Overview
    • Finite element method
    • GUI based on Java
    • Unique environments for modeling
      (CAD, Physics, Mesh, Solver, Postprocessing)
    • Modeling based on equations (broad application)
       Predefined equations and User-defined equations
    • No limitation in Multiphysics
    • MATLAB interface (Simulink)

   Mathematical application modes and types of analysis

    • Mathematical application modes
      1. Coefficient form : suitable for linear or nearly linear models.
      2. General form : suitable for nonlinear models
      3. Weak form : suitable for models with PDEs on boundaries, edges,
         and points, or for models using terms with mixed space and time
         derivatives.
    • Various types of analysis
      1. Eigenfrequency and modal analysis
      2. Stationary and time-dependent analysis
      3. Linear and nonlinear analysis


*Reference: Manual of FEMLAB Software                    Plasma Application
                                                         Modeling, POSTECH
Useful Modules in FEMLAB

  Application areas
    • Acoustics                                • Microwave engineering
    • Bioscience                               • Optics
    • Chemical reactions                       • Photonics
    • Diffusion                                • Porous media flow
    • Electromagnetics                         • Quantum mechanics
    • Fluid dynamics                           • Radio-frequency components
    • Fuel cells and electrochemistry          • Semiconductor devices
    • Geophysics                               • Structural mechanics
    • Heat transfer                            • Transport phenomena
    • MEMS                                     • Wave propagation

  Additional Modules
  1. Application of Chemical engineering Module
    • Momentum balances                   • Mass balances
      - Incompressible Navier-Stokes eqs. - Diffusion
      - Dary’s law                          - Convection and Conduction
      - Brinkman eqs.                       - Electrokinetic flow
      - Non-Newtonian flow                  - Maxwell-stefan diffusion and convection
    • Energy balances
      - Heat equation
      - Heat convection and conduction
  2. Application of Electromagnetics Module
    - Electrostatics
    - Conductive media DC
    - Magnetostatic
    - Low-frequency electromagnetics
    - In-plane wave propagation
    - Axisymmetric wave propagation
    - Full 3D vector wave propagation
    - Full vector mode analysis in 2D and 3D
  3. Application of the Structural Mechanics Module
    - Plane stress
    - Plane strain
    - 2D, 3D beams, Euler theory
    - Shells
FEMLAB Environment
                 Model Navigator




              Pre-defined Equations




                                      Plasma Application
                                      Modeling, POSTECH
User-defined Equations
                    Classical PDE modes




            PDE modes ( General, Coefficient, Weak)




                                                Plasma Application
                                                Modeling, POSTECH
Multiphysics Equations


     • Different built-in physics models are combined in the
       multi-physics mode.

              1. Select eqs.         2. Add used eqs. by using ‘add’ button.




                                       3. Multi-eqs. are displayed here.




                                                     Plasma Application
                                                     Modeling, POSTECH
FEMLAB Modeling Flow




 In FEMLAB, use solid modeling or boundary modeling to create objects
 in 1D, 2D, and 3D.
                            Draw menu




                                                     Plasma Application
                                                     Modeling, POSTECH
Physics and Mesh Menus




                         Plasma Application
                         Modeling, POSTECH
Solve and Postprocessing Menus




                                 Plasma Application
                                 Modeling, POSTECH
Magnetic Field of a Helmholtz Coil

   Introduction of Helmholtz coil
    • A Helmholtz coil is a parallel pair of identical circular coils spaced
      one radius apart and wound so that the current flows through both
      coils in the same direction.
    • This winding results in a very unifrom magnetic field between the
      coils.
    • Helmholtz field generation can be static, time-varying, DC or AC,
      depending on applications.

   Domain equations and boundary conditions




                                                           Plasma Application
                                                           Modeling, POSTECH
Procedure of Simulation (1)

  Procedure of simulation
 1. Choose 3D, Electromagnetic Module, Quasi-statics mode in
    Model Navigator.




  2. After Application Mode Properties in Model Navigator is clicked,
    the potential and Default element type are set to magnetic and
    vector, respectively. Gauge fixing is off.
  3. In the Options and setting menu, select the constant dialog box.
     Define constant value (J0=1) in the constant dialog box.
Procedure of Simulation (2)

  4. In the Geometry Modeling menu, open Work Plane Settings dialog
    box, and default work plane is selected in x-y plane.
  5. In the 2D plane, set axes and grid for drawing our simulation
    geometry easily as follows,




  6. Draw two rectangles by using Draw menu, then select these
     rectangles . Click Revolve menu to revolve them in 3D.
     In the 3D, add a sphere with radius of 1 and center of zero position.
     It determines a calculation area.




                                                          Plasma Application
                                                          Modeling, POSTECH
Geometry Modeling

          2D plotting                              3D plotting




                                Revolve
     Addition of a sphere with radius of 1 and center of zero position.




                                                       Plasma Application
                                                       Modeling, POSTECH
Procedure of Simulation (3)

 7. In the Physics Settings menu, select boundary conditions, and use
   default for boundary conditions.
   Select the Subdomain Settings, then fill in conductivity and external
  current density in the Subdomain Settings dialog box.
       Subdomain        1                       2,3

                       1                        1

            Je        000     -J0*z/sqrt(x^2+z^2) 0 J0*x/sqrt(x^2+z^2)
Procedure of Simulation (4)

 8. Element growth rate is set to 1.8 in Mesh Parameters dialog box
    in Mesh Generation menu, and initialize it.




                                                      Plasma Application
                                                      Modeling, POSTECH
Result of a Helmholtz Coil

 9. By using Postprocessing and Visualization menu, optimize your results.
   • by using the Suppress Boundaries dialog box in the Options menu,
     suppress sphere boundaries (1, 2, 3, 4, 21, 22, 31, 32).
   • select Slice, Boundary, Arrow in the Plot Parameter.
   • In the Slice tab, use magnetic flux density, norm for default slice data.
   • In the boundary tab, set boundary data to 1.
   • In the Arrow tab, select arrow data magnetic field.
   • for giving lighting effect, open Visualization/Selection Settings dialog
      box, and select Scenelight, and cancel 1 and 3.




                                                          Plasma Application
                                                          Modeling, POSTECH
Heated Rod in Cross Flow

  Introduction of Heated Rod in Cross Flow
  • Heat analysis of 2D cylindrical heated rod is supplied.
  • A rectangular region indicates the part of air flow.
  • A flow velocity is 0.5m/s in an inlet and pressure is 0 in an outlet.
  • The cross flow of rod is calculated by Incompressible Navier-Stokes
    application mode.
  • The velocity is calculated by Convection and Conduction application
    mode.




  Procedure of simulation
 1. Select 2D Fluid Dynamic, Incompressible Navier-Stokes, steady-state
    analysis in the Model Navigator.
 2. By using Draw menu, rectangle and half circle.
 3. In the Subdomain Settings of Physics settings, enter v(t0)=0.5 in init tab.



                                                         Plasma Application
                                                         Modeling, POSTECH
Subdomain Settings




 Subdomain settings (physics tab)        Subdomain settings (init tab)




  4. In the Boundary Settings dialog box, all boundaries are set to
    Slip/Symmetry. Boundaries of 7 and 8 are no-slip.



                                                         Plasma Application
                                                         Modeling, POSTECH
Boundary Settings and Mesh Generation

                              Inflow boundary




                              outflow boundary




  5. Generate Mesh, and click Solve button.




                                                 Plasma Application
                                                 Modeling, POSTECH
Result of Velocity Flow




  6. Add the Convection and Conduction mode in the Model Navigator.
  7. In the Subdomain Settings, enter T(t0)=23 in the init tab of subdomain
    of 1, 2.




                                                       Plasma Application
                                                       Modeling, POSTECH
Solving Convection and Conduction Eq.

 8. In the Boundary Settings dialog box, all boundary conditions are thermal
   insulation. 2 and 5 have the following boundary conditions.




 9. In the Solver Manager, click Solver for tab, and select convection and
   conduction. Click a Solve button.




                                                        Plasma Application
                                                        Modeling, POSTECH
Temperature Result of Heated Rod in Cross Flow




                                        Plasma Application
                                        Modeling, POSTECH
Steady-State 2D Axisymmetric Heat Transfer with Conduction


           #3               • Boundary conditions
#2
                            #1,2 : Thermal insulation


#6                  #4      #3,4,5 : Temperature



#1                          #6 : Heat flux

           #5
                                              k=52W/mK




                                             Plasma Application
                                             Modeling, POSTECH
Boundary condition variations - General Heat Transfer

• Boundary conditions variation
At #1,2 boundaries,
Thermal insulation  Temperature




• Boundary conditions variation
At #3 boundaries,
heat transfer coefficient is changed from 0 to 1e5.




                                                      Plasma Application
                                                      Modeling, POSTECH
Permanent Magnet

#1

                     • Relative permeability
                      At #1 subdomain : 1,
           #3
                #2      #2 subdomain :5000
           #4


                     • Magnetization
                     At #3 subdomain : 7.5e5 A/m,
                       #4 subdomain : -7.5e5 A/m




                                         Plasma Application
                                         Modeling, POSTECH
Electrostatic Potential Between Two Cylinder


  This 3D model computes the potential field in vacuum
  around two cylinders, one with a potential of +1 V and
  the other with a potential of -1 V.




                                                  Plasma Application
                                                  Modeling, POSTECH
  Porous Reactor with Injection Needle

                  Inlet species A




                                    Inlet species C

Inlet species B
                          A+BC




                                                      Plasma Application
                                                      Modeling, POSTECH
Thin Layer Diffusion

                       D: diffusion coefficient(5e-5)
                       R: reaction rate(0)
                       C: concentration(5)




                                         Plasma Application
                                         Modeling, POSTECH
Electromagnetic module(II) – Copper Plate

    Introduction of copper plate
• Imagine a copper plate measuring 1 x 1 m that also contains a small
hole and suppose that you subject the plate to electric potential
difference across two opposite sides.
•Conductive Media DC application mode.

The potential difference induces a current.

   Boundary conditions




     B.1                               B.4




                                                     Plasma Application
                                                     Modeling, POSTECH
Electromagnetic module – Copper Plate


   simulation Result




 The plot shows the electric potential in copper plate.
 The arrows show the current density.
 The hole in the middle of geometry affects the potential
 and the current leading to a higher current density above
 and below the hole.


                                                 Plasma Application
                                                 Modeling, POSTECH
2D Steady-State Heat Transfer with Convection


Introduction of 2D Steady-State Heat Transfer with Convection
• This example shows a 2D steady-state thermal analysis
including convection to a prescribed external (ambient) temperature.
• 2D in the Space dimension
  the Conduction node & Steady-state analysis


 Domain equations and boundary conditions
-Domain equation




 -Boundary condition




 material properties




                                                     Plasma Application
                                                     Modeling, POSTECH
Heat Transfer - 2D Steady-State Heat Transfer with Convection


   simulation Result( Temp. @Lower boundary : 100 ℃)




    556 elements is used as mesh.




                                              Plasma Application
                                              Modeling, POSTECH
2D symmetric Transient Heat Transfer

Introduction of 2D Transient Heat Transfer with Convection

 •This example shows an symmetric transient thermal analysis
 with a step change to 1000 ℃ at time 0.



 Domain equations and boundary conditions
-Domain equation




 -Boundary condition




 material properties




                                                Plasma Application
                                                Modeling, POSTECH
Heat Transfer - 2D symmetric Transient Heat Transfer


   simulation Result( T : 1000 ℃ @ time= 190s)




                                                 Plasma Application
                                                 Modeling, POSTECH
Semiconductor Diode Model

 Introduction of Semiconductor Diode Model
 •A semiconductor diode consists of two regions with different
 doping: a p-type region with a dominant concentration of holes,
 and an n-type region with a dominant concentration of electrons.
 • It is possible to derive a semiconductor model from Maxwell’s
 equations and Boltzmann transport theory by using
 simplifications such as the absence of magnetic fields and the
 constant density of states.
Domain equations and boundary conditions
                               -Domain equation




                               Where,

                                 RSRH:
                              -Boundary condition
                              : symmetric boundary conditions
                               neumann boundary conditions

                                                  Plasma Application
                                                  Modeling, POSTECH
Semiconductor Diode Model

Input parameter of Semiconductor Diode Model




 Simulation result ( Vapply : 0.5V)
                                      hole concentration




                                            Plasma Application
                                            Modeling, POSTECH
Momentum Transport

Introduction of Pressure Recovery in a Diverging Duct
 • When the diameter of a pipe suddenly increases, as shown
 in the figure below, the area available for flow increases.
 Fluid with relatively high velocity will decelerate into a
 relatively slow moving fluid.
 • Water is a Newtonian fluid and its density is constant at
 isothermal conditions.

Domain equations and boundary conditions
                                          -Domain equation
                  0.135m

                                          : Navier-Stokes equation
                                  0.01m
  0.005m                                   continuity equation




  -Boundary condition




                                                    Plasma Application
                                                    Modeling, POSTECH
Momentum Transport

Input parameter of Semiconductor Diode Model




Simulation result ( Vmax : 0.02 )     velocity distribution




It is clear and intuitive that the magnitude of the velocity vector
decreases as the cross-sectional area for the flow increases.


                                                     Plasma Application
                                                     Modeling, POSTECH

								
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