![Page 1: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/1.jpg)
Multiphysics Modeling FEMLAB 2.3
Prague
Nov 7 , 2002
Kristin Bingen
![Page 2: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/2.jpg)
• 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
![Page 3: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/3.jpg)
• 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
![Page 4: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/4.jpg)
![Page 5: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/5.jpg)
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
![Page 6: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/6.jpg)
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
![Page 7: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/7.jpg)
• 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
![Page 8: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/8.jpg)
Example: Introductory example
![Page 9: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/9.jpg)
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
![Page 10: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/10.jpg)
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
![Page 11: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/11.jpg)
Problem definition
• Heat equation• Linear stationary• Several subdomains
Introductory example
![Page 12: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/12.jpg)
Problem definition
symmetry
Step 1
Step 2 0 T
1
1
212 10
1T
2T 0 nT
Introductory example - Definition
![Page 13: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/13.jpg)
Example:Split waveguide
![Page 14: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/14.jpg)
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
![Page 15: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/15.jpg)
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.
![Page 16: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/16.jpg)
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
![Page 17: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/17.jpg)
Wave pattern
• The standing wave pattern has almost disappeared, which implies that we have a working design.
Split waveguide - Results
![Page 18: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/18.jpg)
Example:Laminar Static Mixer
![Page 19: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/19.jpg)
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
![Page 20: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/20.jpg)
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
![Page 21: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/21.jpg)
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
![Page 22: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/22.jpg)
• 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
![Page 23: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/23.jpg)
Mixing performance, animation
Laminar Static Mixer - Results
![Page 24: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/24.jpg)
Example:Shell elements, pressure
vessel
![Page 25: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/25.jpg)
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
![Page 26: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/26.jpg)
Result
Pressure Vessel - Results
von Mises stress plot on deformed geometry
![Page 27: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/27.jpg)
Resistive Heating –Multidimensional Multiphysics
![Page 28: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/28.jpg)
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
![Page 29: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/29.jpg)
• 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
![Page 30: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/30.jpg)
• 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
![Page 31: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/31.jpg)
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
![Page 32: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/32.jpg)
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
![Page 33: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/33.jpg)
Material Parameters
Glass fiber substrate
Graphite resistor core
Steel connecting leg
Lead solder
Steel connecting leg
Lead solder
Copper connector
Copper connector
![Page 34: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/34.jpg)
Stationary solution - Voltage distribution
2D Geometry 3D Geometry
![Page 35: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/35.jpg)
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
![Page 36: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/36.jpg)
Time dependent solution - temperature field
• The resistor reaches its peak temperature in 18 ms while the substrate takes much longer to heat up
![Page 37: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/37.jpg)
Piezo electric driver - fluid structure interaction
![Page 38: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/38.jpg)
• The left rectangle, the membrane, is solid but susceptible to deformations• The right half circle consists of a compressible fluid (air)
![Page 39: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/39.jpg)
• 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
![Page 40: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/40.jpg)
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
![Page 41: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/41.jpg)
Initial velocity of the membrane
u(t=0) = 4*104*v0*y*(0.01-y)
![Page 42: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/42.jpg)
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
![Page 43: Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen](https://reader036.vdocuments.us/reader036/viewer/2022062518/56649e605503460f94b5b8cb/html5/thumbnails/43.jpg)