Characterization of High Q Spherical Resonators
Transcript of Characterization of High Q Spherical Resonators
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Characterization of High Q Spherical Resonators
Kenneth Bader, Jason Raymond, Joel MobleyNational Center for Physical Acoustics
University of Mississippi
Felipe Gaitan, Ross Tessien, Robert HillerImpulse Devices, Inc.
Grass Valley, CA
Physics Colloquium25 March, 2008
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
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
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
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
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
• Cavitation is excitation of bubbles using acoustics
• Bubble's radial symmetry effective at concentrating energy
• Sonoluminescence– violent bubble collapse– bubble wall supersonic– gas temperature ~ 105 K– energy concentration 12
orders magnitude– picosecond flashes of light
Bubble action under acoustic source
Single bubble sonoluminescence(30 kHz, Water)
Introduction
pa
pr
pc
National Center for Physical Acoustics1986
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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
National Center for Physical Acoustics1986
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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)
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Acoustic Modes• Determine velocity potential
from Helmholtz equation
• are spherical Bessel
– jo mode of interest
• Boundary condition at sphere edge
– for infinitely rigid boundary
∇2k 2 =0
i ur=a=−∂pr=a
∂ r
kaj n /
j o
jn for n = 0-3
ur=a= 0kn, s=zn,s /a
Pn∝ jnkn ,s r Y n,m
un∝ j 'n kn, s r Yn ,m
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
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
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Cell Hydrophone
Automated Positioning System
Set-up for Cell Pressure Measurements
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Normalized Pressure vs. Position, Frequency
Frequency (kHz)
Dis
tan
ce f
rom
SL
Cel
l Cen
ter
(mm
)
Hydrophone Response in Cell
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Normalized Pressure vs. Position, Frequency
Frequency (kHz)
Dis
tan
ce f
rom
SL
Cel
l Cen
ter
(mm
)
Distance from SL Cell Center (mm)
Hydrophone Response in Cell
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Hydrophone Response in CellNormalized Pressure vs. Position, Frequency
Frequency (kHz)
Dis
tan
ce f
rom
SL
Cel
l Cen
ter
(mm
)
Frequency (kHz)
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
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
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
• Motion of shell dictated by elasticity dynamics:
– s is shell displacement
– cl is longitudinal sound speed
– ct is transverse sound speed
• Shell motion modifies acoustic boundary condition as
−ω2s=cl2∇∇⋅s−ct
2∇ x∇ xs
j 'n ka =−c2
sc l2 ka jn ka Sn k la
Mehl, J. 1985, J. Acoust. Soc. Am. 78, 782.
ur=a= j 'n ka = 0
Comparison with Theory
Infinitively Rigid BC
Elastic Shell BC
National Center for Physical Acoustics1986
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Comparison with Theory • Motion of shell dictated by elasticity dynamics:
– s is shell displacement
– cl is longitudinal sound speed
– ct is transverse sound speed
• Shell motion modifies acoustic boundary condition as
• Solve for eigenfrequencies ka
−ω2s=cl2∇∇⋅s−ct
2∇ x∇ xs
j 'nka =−c2
sc l2 ka jn ka Snk la
Mehl, J. 1985, J. Acoust. Soc. Am. 78, 782.
Sn kla ∝particlevelocity
pressure
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
'
Calculated Acoustic Modesj ' 0 ka , −
c2
s c l2 ka j 0 ka S0 k l a vs. ka
ka
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Calculated Acoustic Modes
Acoustic Mode 130.4 kHz
j ' 0 ka , −c2
s c l2 ka j 0 ka S0 k l a vs. ka
Acoustic Mode 254.9 kHz
ka
'
Acoustic Mode 380.4 kHz
National Center for Physical Acoustics1986
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Calculated Empty Shell Breathing Modes
kla
So
Shell Mode48.5 kHz
Divergence of So
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Measured Amplitude of Acoustic, Shell Modes
Acoustic Mode 130.4kHz
Acoustic Mode 254.8 kHz
Shell Mode49.0 kHz
Frequency (kHz)
Pressure Profile at Cell Center vs. FrequencyH
ydro
ph
one
Res
pons
e (m
V)
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
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
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
10” Resonator Measurements Experimental Setup
Experimental arrangement used to measure acoustic pressure within the resonator
SpectrumAnalyzer
PowerAmplifier
Resonator
HydrophoneAutomatedPositioningSystem
Tracking Gen.OUT
IN
SpectrumAnalyzer
PowerAmplifier
Resonator
HydrophoneAutomatedPositioningSystem
Tracking Gen.OUT
IN
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Resonance Frequencies - Q of Resonance
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
Summary of Measured Resonance Frequencies 25 2530
20
10
0
Frequency (Hz)
Ampl
itude
(dB)
Frequency Response Near Resonance
(0,4)
(0,5)
(0,6)
(0,7)
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
50 40 30 20 10 0 10 20 30 40 500
0.5
1
Distance (mm)
Rela
tive
Inte
nsity
Intensity vs. Radius
(0,4)(0,5)(0,6)(0,7)
Pressure vs. Radius
Relative amplitude of acoustic pressure for the radial acoustic (n=0) modes
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
24.1 cm
10 cm
24.1 cm
10 cm
50 25 0 25 500
1
Distance (mm)
Rela
tive
Inte
nsity
Intensity vs. Radius
(0,4)
MeasuredTheory
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
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
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
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
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
The End
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Passive Cavitation Detector Response
24 24.05 24.1 24.15 24.20
0.2
0.4
0.6
0.8
1
1.2
1.4
Frequency (kHz)Re
spon
se (V
pp)
Cavitation Detector Response vs. Frequency
↑ (0,4)
Cavitation detector response measured near resonance Measurement based on high-
frequency emissions from collapsing bubbles
Passive acoustic sensor mounted near wall of resonator
Amplitude of high-pass filtered signal from PZT-pin transducer mounted near wall of resonator
FunctionGenerator
PZT-pin sensor
Oscilloscope
H.P. Filter(400 kHz)
PowerAmplifier
Resonator
FunctionGenerator
PZT-pin sensor
Oscilloscope
H.P. Filter(400 kHz)
PowerAmplifier
Resonator
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Radial Mode Resonance Frequencies -Temperature Dependence
Acoustic resonance frequencies measured at different temperatures agree well with those predicted by the theory
~ 45 Hz/°C dependence (near room temperature)
0 5 10 15 20 25 30 35 40 45 5022
24
26
28
30
32
34
36
38
40
Temperature (deg C)
Freq
uenc
y (k
Hz)
Resonance Frequency vs. Temperature
(0,4)
(0,5)
(0,6)
Predicted (-) and measured (^) acoustic resonance frequencies vs. temperature
30.8 30.85 30.9 30.95 31 31.05 31.1 31.15 31.2 31.25 31.320
10
0
(0,6) 20oC(0,6) 22oC
(0,6) 25oC
Frequency (kHz)
Ampl
itude
(dB)
Frequency Response Variation With Temperature
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Acoustic Resonances – Rigid Approximation
Radial Modes
(n=0)
0 5 10 150
10
20
30
40
50
60
70
80
Mode Number, n
Freq
uenc
y (k
Hz)
Frequency Spectrum Rigid Approximation
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.4
0.2
0
0.2
0.4
0.6
0.8
1
Radial distance (r/a)
Acou
stic
Pre
ssur
e (p
/p0)
Radial Acoustic Modes
(0,2)
(0,3)
(0,4)
(0,5)
Radial Acoustic Modes(n=0)
(0,2)(0,3)(0,4)(0,5)
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
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Acoustic Resonances – Fluid-filled Shell
Solve for acoustic eigenvalues with shell motion completely accounted for using frequency dependant BC
0 5 10 150
10
20
30
40
50
60
70
80
Mode Number, n
Freq
uenc
y (k
Hz)
Frequency Spectrum
Acoustic resonance frequencies affected by resonances (extensional modes) of the shell
In detailed studies of gas-filled resonators, Moldover et. al. found that: Effect of radiation from shell to
surrounding fluid negligible (except near breathing resonance of shell)
Coupling of shell to mechanical supports minimal provided acoustic frequencies are high
Moldover, Mehl & Greenspan, JASA 79(2), 1986
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Characterization of High Q Spherical Resonator
Kenneth BaderSESAPS Nov. 2007
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Measured Shell Surface Vibrations
frequency (kHz)
Am
plitu
de (
dBm
)
30.3 kHz
49.3 kHz55 kHz
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Set-up for LDV Measurements
Spectrum Analyzer
Power Amp SL Resonator LDV
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LDV Preliminary Results LDV Preliminary Results
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Set-up for Hydrophone MeasurementsSet-up for Hydrophone Measurements
Function Function GeneratorGenerator AmplifierAmplifier
ResonatorResonator
HydrophoneHydrophone
Automated Automated Positioning Positioning SystemSystem
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Combined Pill, Hydrophone, and LDV Measurements
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Combined Pill, Hydrophone, and LDV Measurements
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Combined Pill, Hydrophone, and LDV Measurements
National Center for Physical Acoustics1986
The University of Mississippi 1 8 4 8
Power AmpLDV
Automated Automated Positioning Positioning SystemSystem
Pill
Function Generator
ScopeHydrophone