1. Scattering Control using COMSOL Multiphysics Modeling Billy D. Jones APL-UW 4 Feb 2016

2. Overview COMSOL intro: What can COMSOL do for you? Scattering intro: Brief, one slide & a picture Two scattering examples: – Acoustic scattering off a charged membrane in air controlled with an electric field – The best resonance of all: Acoustic scattering off an air bubble in the sea – Compare these examples: Show how membrane scattering can be as intense as bubble scattering (for certain frequencies) given a large enough electric field Future work: Multibubble acoustic scattering control from smart materials probed with electric & magnetic fields

3. Why Simulate? Understanding and Innovation: Most things are unknown SIMULATION ENABLES INNOVATION Design and Optimization – Simulation has the best Cost/Benefit return for most Analysis, but to be truly effective, in the end it must be matched with Observations. Testing and Verification – Virtual testing is much faster than testing physical prototypes Simulation of a swashplate mechanism used to control the orientation of helicopter rotor blades

4. Simulating with COMSOL Multiphysics® Simulations include Mechanical, Acoustic, Fluid, Electromagnetic, Thermal, and Chemical physics Multiphysics: Couples all domains together Single physics: One integrated development environment Enables cross-disciplinary product development

5. COMSOL Physics Interfaces HEAT TRANSFER with ADD-ON MODULE HEAT TRANSFER without ADD-ON MODULE

6. Two Main Ways to Couple Multiphysics Problems 1.Through Coefficients 2.Variable Itself 3.Volume Source 4.Through Flux (Boundaries & Convection) 5.Through Moving Mesh 6.Across Dimension and Scale Model illustrating the principles of a MEMS flow meter. Due to the fluid flow the obstacle in the channel is bending, which results in considerable change of the shape of the flow domain WAVE EQN DIFFUSION EQN SOURCES PHYSICS MODELING GEOMETRIC MODELING AREAVOL CONVECTION

7. Coupling through Moving Mesh Mesh movement tells flow structure moved GEOMETRIC MODELING

8. Coupling 1D Non-Isothermal Pipes with 3D Heat Cooled Injection Mold Polyurethane Wheel Steel Mold Mold water cooled GEOMETRIC MODELING: ACROSS DIMENSION & SCALE

9. Nonlinear Solvers COMSOL automatically detects nonlinearities and uses a nonlinear solver when needed Or by using the Full Coupled solver option you can take control over the nonlinear solver settings and select between different Newton methods or a Double Dogleg method (hybrid Steepest Descent/Newton method)

10. H L H L H Scattered Power Scattering Intro

11. Sound in the sea scattering off an air bubble INCIDENT PRESSURESCATTERED PRESSURE TOTAL PRESSURE

12. Xiao, Ping Sheng, et al., Appl. Phys. Lett. 106, 091904 (2015) spacing 0.5 mm diam: 30 mm, hard plastic DISK 400 mg rubber MEMBRANE diam: 54 mm Acoustic scattering off circular membrane with charged plastic disk IN AIR (everywhere)

13. Electric control of disk-membrane -Q Q d0d0 d w Electric Stress on Disk Anti-restoring force MEMBRANE TENSION MEMBRANE TENSION

14. Disk-membrane COMSOL details spacing 0.5 mm diam: 30 mm diam: 54 mm zoomed out Perfectly Matched Layer 1 meter diam: 54 mm Simulation details 200,000 vol cells (extra fine) eigenvalue runtime: 5.75 hr scatt strength runtime: 20.5 hr x86_64 Linux 12 core, 32 GB RAM incident sound disk-membrane in the middle

15. Disk-membrane vibrational modes 1st symmetric mode 164 Hz 2nd symmetric mode (nonlinear) 510 Hz 3rd symmetric mode 890 Hz 1st asymmetric mode 300 Hz

16. Anti-restoring force reduces resonance frequency Mode TypeApplied Voltage (Volts)Resonance Frequency (Hz) 1st symmetric mode0164 1st symmetric mode500160 1st symmetric mode1000147 2nd symmetric mode (nonlinear)0509 2nd symmetric mode (nonlinear)500508 2nd symmetric mode (nonlinear)1000505 3rd symmetric mode0889.9 3rd symmetric mode500889.6 3rd symmetric mode1000888.7 But the biggest effect of the Applied Voltage is on the Scattering Strength as shown next.

17. Disk-membrane acoustic resonance 164 asymmetric 300 absent 510 890

18. Disk-membrane scattering Scattered Pressure on resonance (890 Hz) Scattered Pressure off resonance (1000 Hz) 1 meter 0.04 Pa 1 meter 0.002 Pa incident sound

19. Disk-membrane scattering: 1st symmetric mode 164 Hz FARFIELD 10 meter COMSOL uses Helmholtz-Kirchhoff integral to integrate to the far field. 10 meter 0.0001 Pa SCATTERED PRESSURE incident sound

20. Air bubble scattering in the sea incident sound bubble in the middle disk-memb diam 54 mm bubble diam 39.5 mm scale comparison 1 meter The air bubble acoustic resonance was set up to resonate at the same frequency as the disk- membrane’s first mode at 164 Hz: f r r bub = 3.243 m/s AIR BUBBLE SURROUNDED BY SEA

21. Sound in the sea scattering off an air bubble INCIDENT PRESSURESCATTERED PRESSURE TOTAL PRESSURE

22. Air bubble in the sea acoustic resonance 164

23. Scattering Strength Comparison 164 510 890

24. Summary Introduced COMSOL (COMputer SOLution, 1986): a multiphysics finite element tool with a goal of handling all classical physics problems coupled together: – Mechanics (motion; matter: solid, liquid, gas, & plasma; acoustics & elasticity; turbulence & chaos) – Electrodynamics & Gravity – Thermodynamics & Statistical Mechanics Discussed two acoustic scattering examples – Scattering control of a charged membrane in air – Scattering resonance of an air bubble in the sea Future plan: Multibubble acoustic scattering control from smart materials probed with electric & magnetic fields

25. bjones@apl.uw.edu “If you need it, I can do it”

26. Disk-membrane scattering beampatterns Farfield scattered pressure (dB) z(vertical) x x y x y zoomed in Rfar = 5 m incident sound

27. Bubble scattering beampatterns x y z(vertical) x Farfield scattered pressure (dB) x y zoomed in Rfar = 1 m incident sound