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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

Modeling, POSTECH

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

- Application areas

- Microwave engineering
- Optics
- Photonics
- Porous media flow
- Quantum mechanics
- Radio-frequency components
- Semiconductor devices
- Structural mechanics
- Transport phenomena
- Wave propagation

- Acoustics
- Bioscience
- Chemical reactions
- Diffusion
- Electromagnetics
- Fluid dynamics
- Fuel cells and electrochemistry
- Geophysics
- Heat transfer
- MEMS

- Additional Modules

1. Application of Chemical engineering Module

- Momentum balances
- - Incompressible Navier-Stokes eqs.
- - Dary’s law
- - Brinkman eqs.
- - Non-Newtonian flow

- Mass balances
- - Diffusion
- - Convection and Conduction
- - Electrokinetic 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

Modeling, POSTECH

User-defined Equations

Classical PDE modes

PDE modes ( General, Coefficient, Weak)

Modeling, POSTECH

Multiphysics Equations

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

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

1. Select eqs.

3. Multi-eqs. are displayed here.

Modeling, POSTECH

FEMLAB Modeling Flow

In FEMLAB, use solid modeling or boundary modeling to create objects

in 1D, 2D, and 3D.

Draw menu

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

- 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.

Modeling, POSTECH

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.

Modeling, POSTECH

Geometry Modeling

2D plotting

3D plotting

Revolve

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

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.

Modeling, POSTECH

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.

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.

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.

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.

Modeling, POSTECH

Boundary Settings and Mesh Generation

Inflow boundary

outflow boundary

5. Generate Mesh, and click Solve button.

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.

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.

Modeling, POSTECH

Steady-State 2D Axisymmetric Heat Transfer with Conduction

- Boundary conditions
- #1,2 : Thermal insulation
- #3,4,5 : Temperature
- #6 : Heat flux

#3

#2

#4

#6

#1

#5

k=52W/mK

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.

Modeling, POSTECH

Permanent Magnet

#1

- Relative permeability
- At #1 subdomain : 1,
- #2 subdomain :5000

#3

#2

#4

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

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.

zero charge

grounded

Modeling, POSTECH

Porous Reactor with Injection Needle

Inlet species A

Inlet species C

Inlet species B

A + B C

Modeling, POSTECH

Thin Layer Diffusion

D: diffusion coefficient(5e-5)

R: reaction rate(0)

C: concentration(5)

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

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.

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

Modeling, POSTECH

Heat Transfer - 2D Steady-State Heat Transfer with Convection

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

556 elements is used as mesh.

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

Modeling, POSTECH

Heat Transfer - 2D symmetric Transient Heat Transfer

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

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

Modeling, POSTECH

Semiconductor Diode Model

- Input parameter of Semiconductor Diode Model

- Simulation result ( Vapply : 0.5V)

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

: Navier-Stokes equation

continuity equation

0.135m

0.01m

0.005m

-Boundary condition

Modeling, POSTECH

Momentum Transport

- Input parameter of Semiconductor Diode Model

- Simulation result ( Vmax : 0.02 )

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

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