View
213
Download
0
Category
Tags:
Preview:
Citation preview
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?
Plasma ApplicationModeling, POSTECH
FEMLAB : a powerful interactive environment for modeling and solving various kinds of scientific and engineering problems based on partial differential equations (PDEs).
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
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)
*Reference: Manual of FEMLAB Software
Useful Modules in FEMLAB
Additional Modules1. Application of Chemical engineering Module
• Momentum balances - Incompressible Navier-Stokes eqs. - Dary’s law - Brinkman eqs. - Non-Newtonian flow
• Energy balances - Heat equation - Heat convection and conduction
• Mass balances - Diffusion - Convection and Conduction - Electrokinetic flow - Maxwell-stefan diffusion and convection
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
Application areas• Acoustics• Bioscience• Chemical reactions• Diffusion• Electromagnetics• Fluid dynamics• Fuel cells and electrochemistry• Geophysics• Heat transfer• MEMS
• Microwave engineering• Optics• Photonics• Porous media flow• Quantum mechanics• Radio-frequency components• Semiconductor devices• Structural mechanics• Transport phenomena• Wave propagation
FEMLAB Environment
Plasma ApplicationModeling, POSTECH
Pre-defined Equations
Model Navigator
User-defined Equations
Plasma ApplicationModeling, POSTECH
PDE modes ( General, Coefficient, Weak)
Classical PDE modes
Multiphysics Equations
Plasma ApplicationModeling, POSTECH
• 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.
FEMLAB Modeling Flow
Plasma ApplicationModeling, POSTECH
In FEMLAB, use solid modeling or boundary modeling to create objects in 1D, 2D, and 3D.
Draw menu
Physics and Mesh Menus
Plasma ApplicationModeling, POSTECH
Solve and Postprocessing Menus
Plasma ApplicationModeling, POSTECH
Magnetic Field of a Helmholtz Coil
Plasma ApplicationModeling, POSTECH
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
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)
Plasma ApplicationModeling, POSTECH
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.
Geometry Modeling
Plasma ApplicationModeling, POSTECH
2D plotting
Revolve
3D plotting
Addition of a sphere with radius of 1 and center of zero position.
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 0 0 0 -J0*z/sqrt(x^2+z^2) 0 J0*x/sqrt(x^2+z^2)
Procedure of Simulation (4)
Plasma ApplicationModeling, POSTECH
8. Element growth rate is set to 1.8 in Mesh Parameters dialog box in Mesh Generation menu, and initialize it.
Result of a Helmholtz Coil
Plasma ApplicationModeling, POSTECH
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.
Heated Rod in Cross Flow
Plasma ApplicationModeling, POSTECH
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.
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.
Procedure of simulation
Subdomain Settings
Plasma ApplicationModeling, POSTECH
4. In the Boundary Settings dialog box, all boundaries are set to Slip/Symmetry. Boundaries of 7 and 8 are no-slip.
Subdomain settings (physics tab) Subdomain settings (init tab)
Boundary Settings and Mesh Generation
Plasma ApplicationModeling, POSTECH
5. Generate Mesh, and click Solve button.
Inflow boundary
outflow boundary
Result of Velocity Flow
Plasma ApplicationModeling, POSTECH
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.
Solving Convection and Conduction Eq.
Plasma ApplicationModeling, POSTECH
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.
Temperature Result of Heated Rod in Cross Flow
Plasma ApplicationModeling, POSTECH
Plasma ApplicationModeling, POSTECH
Steady-State 2D Axisymmetric Heat Transfer with Conduction
k=52W/mK
#1
#2• Boundary conditions
#1,2 : Thermal insulation
#3,4,5 : Temperature
#6 : Heat flux
#6
#3
#4
#5
Plasma ApplicationModeling, 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 ApplicationModeling, POSTECH
Permanent Magnet
#1
#2#3
#4
• Relative permeability
At #1 subdomain : 1,
#2 subdomain :5000
• Magnetization
At #3 subdomain : 7.5e5 A/m,
#4 subdomain : -7.5e5 A/m
Plasma ApplicationModeling, POSTECH
Electrostatic Potential Between Two Cylinder
grounded
zero charge
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 ApplicationModeling, POSTECH
Porous Reactor with Injection Needle
Inlet species A
Inlet species B
Inlet species C
A + B C
Plasma ApplicationModeling, POSTECH
Thin Layer Diffusion
D: diffusion coefficient(5e-5)
R: reaction rate(0)
C: concentration(5)
Plasma ApplicationModeling, POSTECH
Electromagnetic module(II) – Copper Plate
Introduction of copper plate
Boundary conditions
• 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.
B.1 B.4
simulation Result
Plasma ApplicationModeling, POSTECH
Electromagnetic module – Copper Plate
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.
2D Steady-State Heat Transfer with Convection
Plasma ApplicationModeling, POSTECH
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
simulation Result( Temp. @Lower boundary : 100 ℃)
556 elements is used as mesh.
Plasma ApplicationModeling, POSTECH
Heat Transfer - 2D Steady-State Heat Transfer with Convection
Plasma ApplicationModeling, POSTECH
2D symmetric Transient Heat Transfer
Introduction of 2D Transient Heat Transfer with Convection
Domain equations and boundary conditions
•This example shows an symmetric transient thermal analysis with a step change to 1000 at time 0. ℃
-Domain equation
-Boundary condition
material properties
simulation Result( T : 1000 ℃ @ time= 190s)
Plasma ApplicationModeling, POSTECH
Heat Transfer - 2D symmetric Transient Heat Transfer
Plasma ApplicationModeling, POSTECH
Semiconductor Diode Model
Introduction of Semiconductor Diode Model
Domain equations and boundary conditions
•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 equation
Where,
RSRH:
-Boundary condition
: symmetric boundary conditions
neumann boundary conditions
Plasma ApplicationModeling, POSTECH
Input parameter of Semiconductor Diode Model
Simulation result ( Vapply : 0.5V) hole concentration
Semiconductor Diode Model
Plasma ApplicationModeling, POSTECH
Momentum Transport
Introduction of Pressure Recovery in a Diverging Duct
Domain equations and boundary conditions
• 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 equation
: Navier-Stokes equation
continuity equation 0.005m0.01m
0.135m
-Boundary condition
Plasma ApplicationModeling, POSTECH
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.
Momentum Transport
Recommended