the use and application of femlab

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


Pre-defined Equations

Model Navigator

User-defined Equations


PDE modes ( General, Coefficient, Weak)

Classical PDE modes

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.

FEMLAB Modeling Flow


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

Draw menu

Physics and Mesh Menus


Solve and Postprocessing Menus


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)

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.



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


2D plotting

Revolve

3D plotting

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.

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)



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


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


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


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


5. Generate Mesh, and click Solve button.

Inflow boundary

outflow boundary

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.

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.

Temperature Result of Heated Rod in Cross Flow



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


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.


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


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.


Porous Reactor with Injection Needle

Inlet species A

Inlet species B

Inlet species C

A + B C


Thin Layer Diffusion

D: diffusion coefficient(5e-5)

R: reaction rate(0)

C: concentration(5)


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


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


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 equation

-Boundary condition

material properties

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

556 elements is used as mesh.


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


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 equation

-Boundary condition

material properties

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


Heat Transfer - 2D symmetric Transient Heat Transfer


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 equation

Where,

RSRH:

-Boundary condition

: symmetric boundary conditions

neumann boundary conditions


Input parameter of Semiconductor Diode Model

Simulation result ( Vapply : 0.5V) hole concentration

Semiconductor Diode Model


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 equation

: Navier-Stokes equation

continuity equation 0.005m0.01m

0.135m

-Boundary condition


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

the use and application of femlab

Documents

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postprocessing modeling

boundary modeling

d vector wave propagation

modeling cad

solid modeling

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