Characterization of High Q Spherical Resonators

Characterization of High Q Spherical Resonators Kenneth Bader, Jason Raymond, Joel Mobley University of Mississippi Felipe Gaitan, Ross Tessien, Robert Hiller Impulse Devices, Inc. Grass Valley, CA Physics Colloquium 25 March, 2008

Outline Introduction/Motivation acoustic cavitation sonoluminescence Measurements in test resonator determination acoustic modes Comparison of theory and measurements shell vibration accommodation Measurements in High Q resonator

Introduction Cavitation is excitation of bubbles using acoustics pc pa Bubble's radial symmetry effective at concentrating energy pr Bubble action under acoustic source Sonoluminescence violent bubble collapse bubble wall supersonic gas temperature ~ 105 K energy concentration 12 orders magnitude picosecond flashes of light Single bubble sonoluminescence (30 khz, Water)

Motivation Project goal is maximize cavitation collapse how hot will the gas get? Methods for maximizing cavitation collapse liquids which promote violent collapse higher ambient pressure of system high Q resonators

High Q Resonator for Acoustic Cavitation Resonator Properties 10 OD stainless steel sphere excited with single acoustic horn fittings for high pressures Q > 10 000 Characterization of Resonator determine acoustic modes laser dopper vibrometry (LDV) surface piezoelectric transducer piezoelectric transducer in fluid (hydrophone)

Acoustic Modes Determine velocity potential from Helmholtz equation 2 k 2 =0 are spherical Bessel jn / j o P n j n k n,s r Y n, m un j 'n k n, s r Y n, m jn for n = 0-3 jo mode of interest Boundary condition at sphere p r =a edge ka i ur =a = r for infinitely rigid boundary ur =a = 0 k n, s =z n, s /a

Set-up for Cell Pressure Measurements Automated Positioning System Cell Hydrophone

Hydrophone Response in Cell Distance from SL Cell Center (mm) Normalized Pressure vs. Position, Frequency Frequency (khz)

Hydrophone Response in Cell Distance from SL Cell Center (mm) Normalized Pressure vs. Position, Frequency Frequency (khz) Distance from SL Cell Center (mm)

Hydrophone Response in Cell Distance from SL Cell Center (mm) Normalized Pressure vs. Position, Frequency Frequency (khz) Frequency (khz)

Comparison with Theory Motion of shell dictated by elasticity dynamics: ω 2 s=cl2 s c2t x xs s is shell displacement cl is longitudinal sound speed ct is transverse sound speed Shell motion modifies acoustic boundary condition as ur =a = j ' n ka = 0 Infinitively Rigid BC c2 j 'n ka = ka j n ka S n k l a s c 2l Elastic Shell BC Mehl, J. 1985, J. Acoust. Soc. Am. 78, 782.

Comparison with Theory Motion of shell dictated by elasticity dynamics: ω 2 s=cl2 s c2t x xs s is shell displacement cl is longitudinal sound speed ct is transverse sound speed Shell motion modifies acoustic boundary condition as c2 j 'n ka = ka j n ka S n k l a s c2l Sn k l a particle velocity pressure Solve for eigenfrequencies ka Mehl, J. 1985, J. Acoust. Soc. Am. 78, 782.

Calculated Acoustic Modes c2 j ' 0 ka, ka j 0 ka S 0 k l a vs. ka 2 s cl ' ka

Calculated Acoustic Modes c2 j ' 0 ka, ka j 0 ka S 0 k l a vs. ka 2 s cl ' Acoustic Mode 3 80.4 khz Acoustic Mode 1 30.4 khz Acoustic Mode 2 54.9 khz ka

Calculated Empty Shell Breathing Modes Divergence of So So Shell Mode 48.5 khz kla

Measured Amplitude of Acoustic, Shell Modes Pressure Profile at Cell Center vs. Frequency Hydrophone Response (mv) Shell Mode 49.0 khz Acoustic Mode 2 54.8 khz Acoustic Mode 1 30.4kHz Frequency (khz)

10 Resonator Measurements Experimental Setup Spectrum Analyzer IN Tracking Gen. OUT Hydrophone Automated Positioning System Power Amplifier Resonator Experimental arrangement used to measure acoustic pressure within the resonator

Resonance Frequencies - Q of Resonance 0 Resonance Half-width (Frequency) 17.8 khz (0,4) 38.0 Hz 24.2 khz (0,5) 8.3 Hz 31.0 khz (0,6) 4.9 Hz 37.9 khz (0,7) 1.8 Hz 10 Amplitude (db) Frequency Response Near Resonance (0,4) (0,5) (0,6) 20 Summary of Measured Resonance Frequencies 30 25 (0,7) Frequency (Hz) 25

Pressure vs. Radius Pressure Half-maximum (Distance) 17.8 khz (0,4) 38 mm 24.2 khz (0,5) 25 mm 31.0 khz (0,6) 18 mm 37.9 khz (0,7) 15 mm Intensity vs. Radius 1 Intensity vs. Radius 1 24.1 cm (0,4) (0,5) (0,6) (0,7) 10 cm Relative Intensity 0.5 Measured Theory Relative Intensity (0,4) 0 50 0 50 25 0 Distance (mm) 25 50 40 30 20 10 0 10 Distance (mm) 20 30 40 Relative amplitude of acoustic pressure for the radial acoustic (n=0) modes 50

Summary Maximizing cavitation collapse involves the use of high Q resonators Preliminary work requires developing techniques for characterizing high Q resonators Initial studies done in sonoluminescence cell zero order acoustic modes correlate well with Mehl theory empty shell breathing modes correlate well with Mehl theory 10 Resonator resonant frequencies, pressure profiles agree with theory Q range from ~ 400 to 20 000

Acknowledgements The authors would like to thank members of the Ultrasonics Group at NCPA for their help with this work. This work was supported by SMDC Contract NO. W9113M-07-C-0178

The End

Passive Cavitation Detector Response Cavitation Detector Response vs. Frequency 1.4 Cavitation detector response measured near resonance 1.2 Measurement based on highfrequency emissions from collapsing bubbles Passive acoustic sensor mounted near wall of resonator Response (Vpp) 1 Oscilloscope (0,4) 0.2 PZT-pin sensor Power Amplifier 0.6 0.4 H.P. Filter (400 khz) Function Generator 0.8 Resonator 0 24 24.05 24.1 24.15 Frequency (khz) 24.2 Amplitude of high-pass filtered signal from PZT-pin transducer mounted near wall of resonator

Radial Mode Resonance Frequencies Temperature Dependence Acoustic resonance frequencies measured at different temperatures agree well with those predicted by the theory 36 34 (0,5) 30 28 26 o (0,6) 25 C 10 (0,6) 32 Frequency Response Variation With Temperature 0 38 Frequency (khz) ~ 45 Hz/ C dependence (near room temperature) Amplitude (db) Resonance Frequency vs. Temperature 40 (0,6) 22 C o (0,4) 24 o (0,6) 20 C 22 0 5 10 15 20 25 30 Temperature (deg C) 35 40 Predicted (-) and measured (^) acoustic resonance frequencies vs. temperature 20 30.8 30.85 30.9 30.95 31 31.05 31.1 Frequency (khz) 31.15 31.2 31.25 31.3 45 50

Acoustic Resonances Rigid Approximation Radial Modes (n=0) 0.8 Acoustic Pressure (p/p0) Frequency Spectrum Rigid Approximation Radial Acoustic Modes 1 80 (0,2) 0.6 70 0.4 (0,3) 0.2 (0,4) 0 (0,5) 0.2 0.4 0 0.1 0.2 0.3 0.4 0.5 0.6 Radial distance (r/a) 0.7 0.8 0.9 Higher-order modes (n>0) of an ideal sphere have a (2n+1)-fold degeneracy Real cavities will be asymmetrical, therefore the originally degenerate modes will exhibit somewhat different resonance frequencies 1 (0,5) (0,4) (0,3) (0,2) Frequency (khz) 60 50 40 30 20 10 0 0 5 10 Mode Number, n Radial Acoustic Modes (n=0) 15

Acoustic Resonances Fluid-filled Shell Frequency Spectrum Solve for acoustic eigenvalues with shell motion completely accounted for using frequency dependant BC 80 70 Frequency (khz) 60 50 40 In detailed studies of gas-filled resonators, 30 Moldover et. al. found that: 20 Effect of radiation from shell to 10 surrounding fluid negligible (except near breathing resonance of shell) 0 0 5 10 Coupling of shell to mechanical supports Mode Number, n minimal provided acoustic frequencies are high Acoustic resonance frequencies affected by Moldover, Mehl & Greenspan, JASA 79(2), resonances (extensional modes) of the shell 15

Characterization of High Q Spherical Resonator Kenneth Bader SESAPS Nov. 2007

Measured Shell Surface Vibrations Amplitude (dbm) 49.3 khz 55 khz 30.3 khz frequency (khz)

Set-up for LDV Measurements Spectrum Analyzer Power Amp SL Resonator LDV

LDV Preliminary Results

Set-up for Hydrophone Measurements Hydrophone Function Generator Automated Positioning System Amplifier Resonator

Combined Pill, Hydrophone, and LDV Measurements

Scope Hydrophone Pill Automated Positioning System Function Generator LDV Power Amp