1. Multiphysics Modeling F EMLAB 2.3 Prague Nov 7, 2002 Kristin Bingen

2. 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

3. 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

5. 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

6. 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

7. 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

8. Example: Introductory example

9. 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

10. 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

11. Problem definition Heat equation Linear stationary Several subdomains Introductory example

12. Problem definition symmetry Step 1 Step 2 Introductory example - Definition

13. Example: Split waveguide

14. 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

15. 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.

16. 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

17. Wave pattern The standing wave pattern has almost disappeared, which implies that we have a working design. Split waveguide - Results

18. Modeling The plane strain approximation is used for the structural part of the model. An exact perpendicular hybrid-mode wave formulation is used for the optical mode analysis. Stress-optical effects

19. Example: Laminar Static Mixer

20. 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

21. 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

22. 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

23. The mixing quality is measured with the relative variance S. K z is the plane intersecting the tube at distance z from the inlet. Mixing quality Laminar static mixer – Results, Post Processing

24. Mixing performance, animation Laminar Static Mixer - Results

25. Example: Shell elements, pressure vessel

26. Vessel Dimensions Internal pressure 0.8 Mpa Wall thickness 30 mm 4 m1 m 2 m 0.5 m 1 m 0.25 m 0.2 m Pressure Vessel - Geometry

27. Result Pressure Vessel - Results von Mises stress plot on deformed geometry

28. Resistive Heating – Multidimensional Multiphysics

29. 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 extremely dense mesh

30. 2D Geometry -Copper conductors 3D Geometry -Resistor and substrate APPLICATION MODES -Conductive Media DC (2D and 3D) -Heat Transfer (3D) Extended Multiphysics

31. 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 V 2D = V 3D is applied to the conductors Extended Multiphysics Coupling variable, V 2D V 2D = V 3D

32. Boundary Conditions V = 0 V V = 5 V Insulation, Natural convection,

33. 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

34. Material Parameters Glass fiber substrate Graphite resistor core Steel connecting leg Lead solder Steel connecting leg Lead solder Copper connector

35. Stationary solution - Voltage distribution 2D Geometry 3D Geometry

36. 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

37. Time dependent solution - temperature field The resistor reaches its peak temperature in 18 ms while the substrate takes much longer to heat up

38. Piezo electric driver - fluid structure interaction

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

40. 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

41. Material parameters for a steel membrane E s = 210 GPa s = 0.3  0,s = 7870 kg m -3  s = 7.3 kg m -1 s -1 G = E s *(2*(1+ s )) -1 = 80.77 GPa = E s * 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

42. Initial velocity of the membrane u(t=0) = 4*10 4 *v 0 *y*(0.01-y)

43. 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  s t = 14.5  s t = 12.5  s t = 10.5  s t = 8.5  s t = 6.5  s t = 4.5  s t = 2.5  s