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 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

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) 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

-J0*z/sqrt(x^2+z^2) 0 J0*x/sqrt(x^2+z^2) 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  Je 0 0 0 -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 #1,2 : Thermal insulation #3,4,5 : Temperature #6 : Heat flux #2 #4 #6 #1 #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 #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. zero charge grounded 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

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

Introduction of Pressure Recovery in a Diverging Duct 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 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