Multiphysics Modeling FEMLAB 2.3

Prague

Nov 7 , 2002

Kristin Bingen

• Presentation of our company, COMSOL• Introduction to FEMLAB

– Building the model• Application examples

– Chemical Engineering and transport phenomena– Electromagnetics– Structural Mechanics– Modeling with Partial Differential Equations (PDEs)

• Concluding remarks

Presentation overview

• Spin-off from The Royal Institute of Technology, KTH, Sweden, 1986

• Delivering modeling solutions for problems based on PDEs

• Develop FEMLAB®, based on MATLAB®

COMSOL

Modeling in FEMLAB

• Physics Mode:

– Built-in equations, called application modes

• PDEs:

– Define you own PDE or systems of PDEs

• Multiphysics:

– Combine different built-in physics models

– Combine your own equations and physics models

Introductory example

Philosophy and the Development of FEMLAB

• Usability to allow you to concentrate on the problem and not on the software.

• Flexibility to maximize the family of problems that you can formulate in FEMLAB.

• Openness to allow you, as an advance user, to implement your own code in FEMLAB and to change the built-in code .

FEMLAB

• Chemical Engineering– Fuel cells– Catalytic converters– Process industry reactors

• Fluid dynamics– Process industry– Automotive– Aeronautics– Petroleum

• Electromagnetics– Antenna design– Electric field simulations– Electronics and photonics

• Structural Mechanics– Stress and strain analysis– Mechanical design– Structural-multiphysics

interactions

FEMLAB application areas

FEMLAB is used within

Example: Introductory example

Purpose of the model

• Explain the modeling procedure using FEMLAB• Show the use of the predefined application modes• Introduce some very useful features for control of modeling

results

Introductory example

Modeling, Simulation and Analysis

• Draw your geometry in draw mode.• Specify how your process interacts with the

surroundings in boundary mode.• Specify physical properties or PDE coefficients in

your solution domain in subdomain mode.• Generate the mesh in mesh mode.• Solve the problem (solver parameters) in solve

mode.• Visualize the solution and intepret your results in

post mode.

Introductory example

Problem definition

• Heat equation• Linear stationary• Several subdomains

Introductory example

Problem definition

symmetry

Step 1

Step 2 0 T

1

1

212 10

1T

2T 0 nT

Introductory example - Definition

Example:Split waveguide

Problem definition

• A metal waveguide for microwaves has to be designed to split the incoming radiation in two branches, e.g. in order to feed a group antenna.

• A sudden change in cross-section gives rise to unwanted reflections.

• Inserting a dielectric cylinder of suitable permittivity in the branching region can reduce this effect.

• The design is explored using the TE-wave application mode in the Electromagnetics Module.

Waveguide geometry

Split waveguide - Problem definition

Standing wave gives low transmission

Split waveguide - Results

• A standing wave pattern arises due to improper choise of material, which gives reflections in the branching region.

Maximum transmission, parametric study

• The permittivity of a small cylindrical dielectricum is varied

• Maximum transmission for a permittivity, eps=3.6

eps = 3.6

Split waveguide - Results

Wave pattern

• The standing wave pattern has almost disappeared, which implies that we have a working design.

Split waveguide - Results

Example:Laminar Static Mixer

Tubular micro mixer

• Mixing is obtained without the need of moving parts.

• Several baffle sections can be added in sequence to assure that enough mixing is achieved.

Laminar static mixer - Model background

Results: Velocity

• The flow lines reveal the twisting path that the fluid undergoes through the mixer.

• The Reynolds number is around 60, which is well inside the laminar flow region. This implies that the pressure loss is very small in the mixer.

Laminar static mixer - Results

Results: Concentration

• The solute is uniformly distributed after the baffle sections.

• For increased mixing performance, additional baffle sections can be included in the mixer.

Laminar static mixer - Results

• The mixing quality is measured with the relative variance S.

• Kz is the plane intersecting the tube at distance z from the inlet.

Mixing quality

dKccs

ssS

zK

z

z

2

0

)(

S

z

Laminar static mixer – Results, Post Processing

Mixing performance, animation

Laminar Static Mixer - Results

Example:Shell elements, pressure

vessel

Vessel Dimensions

Internal pressure 0.8 MpaWall thickness 30 mm

4 m 1 m

2 m

0.5 m

1 m

0.25 m

0.2 m

Pressure Vessel - Geometry

Result

Pressure Vessel - Results

von Mises stress plot on deformed geometry

Resistive Heating –Multidimensional Multiphysics

Introduction • We will model the heating of a resistor in 3D

1.5 mm thick substrate

20 m copper conductor

An aspect ratio of 75 will create an extremelydense mesh

• 2D Geometry- Copper conductors

• 3D Geometry- Resistor and substrate

• APPLICATION MODES

- Conductive Media DC (2D and 3D)

- Heat Transfer (3D)

2

VQ

QTkt

TC

0 V

Extended Multiphysics

• MULTIDIMENSIONAL COUPLING- The voltage from the 2D conductors are coupled to the

corresponding ones in the 3D geometry- With a weak constraint the Dirichlet boundary condition

V2D = V3D is applied to the conductors

Extended Multiphysics

Coupling variable, V2D

VV2D2D = V = V3D3D

Boundary Conditions

V = 0 V

V = 5 V

Insulation, 0 Vn

Insulation,

0

0

Tk

V

n

n

Natural convection,

)TT(L

NuTk ref

n

)L,T,T(fGr

Pr),Gr(fNu

ref

Due to symmetry we can cut the geometry in half

And at the same time reduce the number of degrees of freedom (DOF)

Model Reduction

Material Parameters

Glass fiber substrate

Graphite resistor core

Steel connecting leg

Lead solder

Steel connecting leg

Lead solder

Copper connector

Copper connector

Stationary solution - Voltage distribution

2D Geometry 3D Geometry

Stationary solution - temperature field The highest temperature of

130 C occur at the mountings of the connecting legs

The solder also gets very hot and could possibly fail

Isosurface plot

Cross-Section surface plot of the symmetry plane

K

K

Time dependent solution - temperature field

• The resistor reaches its peak temperature in 18 ms while the substrate takes much longer to heat up

Piezo electric driver - fluid structure interaction

• The left rectangle, the membrane, is solid but susceptible to deformations• The right half circle consists of a compressible fluid (air)

• The compressible momentum equations are simplified to

Governing equation for the membrane• The Navier equation in a plane strain

formulation with viscous damping

Governing equation for the fluid

uXXX

ss GGt

2

2

,0

uuXX

bct

02

2

2

0

Material parameters for a steel membrane

Es = 210 GPa

s = 0.3

0,s = 7870 kg m-3

s = 7.3 kg m-1 s-1

G = Es*(2*(1+ s ))-1 = 80.77 GPa

= Es* s *((1-2*s)*(1+s))-1 = 121.15 GPa

Air at room temperature

c = 340 m s-1

0 = 1.13 kg m-3

= 1*10-4 kg m-1 s-1

b = 1*10-4 kg m-1 s-1

Material parameters

Initial velocity of the membrane

u(t=0) = 4*104*v0*y*(0.01-y)

                                        

                                                                                           

The wall induces compression and a traveling wave in the fluid, which is reflected back towards the moving wall

t = 0.5 s

t = 16.5 st = 14.5 st = 12.5 s

t = 10.5 st = 8.5 st = 6.5 s

t = 4.5 st = 2.5 s