impact data analysis and sensor modification for pressure data of granular gases in reduced gravity...
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Impact Data Analysis and Sensor Modification for Pressure Data of
Granular Gases in Reduced Gravity
Aaron Coyner, Justin Mitchell, and Matthew Olson
University of Tulsa
April 9, 2003
Granular Gases Excited granular media can
simulate molecules similar to those in ideal gases
Excitation results in kinetic motion
• Velocities have distribution of amplitudes
• Random directions
Modified gas laws can be applied
• Granular Temperature
• Theory shows v2
proportionality*
• Granular Pressure• One experiment shows
v3/2 proportionality** Theory predicts ordering
(inelastic collapse)
** É. Falcon et al. , Phys. Rev. Lett. 80. 440 (1999).
* A. Puglisi, A. Baldassarri, and V. Loreto, Phys. Rev E 66 061305.
Importance of Impact Data
Impact data can aid in development of speed distributions.• Can apply results to large systems of particles without
individual tracking
Each experiment set should have a distinct set of collision frequencies• Frequency response should depend on number of particles
and driving parameters.
Data should also reflect the predicted collapse if it occurs
Relevance to Reduced Gravity
Inelastic Collapse of granular systems in reduced gravity could explain:• Asteroid Formation
• Planetary Rings
• Other celestial systems that could not for by gravitation alone.
Ways to Achieve Reduced Gravity
Sounding Rocket• Falcon et al. (1999)
Nasa’s KC-135 “Weightless Wonder”
Space Shuttle Flight• Get Away Special
KC-135
The Gr.A.I.N.S. Experiment
Box set of 8 sample cells
• Each cell ~1 in3
• Each cell contain varied number of brass ball
• Sapphire walls
• Each cell has an impact sensor
• Impact data stored in external data drive
Mechanical Shaker System
• Varies amplitude and frequency
Cameras and Mirrors
• Cameras record video of 3 faces of the cube.
Impact Sensors (Initial Run)
0.75” diameter APC 850 ceramic
piezoelectric material• lead zirconate titanate
formulation 2 MHz Bandwidth Wired into Camera Audio
Channels
• Subminiature coax used
Piezoelectric Disk
Steps in Data Analysis
Determine camera effects• Amplification of signal
• Signal coupling (unexpected)
• 300 mV signal on right channel appears on left channel with equal amplitude at > 600 Hz
Initial run of time series and power spectra• FFT analysis
• Low frequency and high frequency responses
Audio parsing to obtain low frequency peaks evident in time series
Camera Effects Camera Amplification
• Test signal 300 mV sine wave
• Frequency 10-1050 Hz
Plot Amplification (Vcam/Vin) vs frequency
Frequency Dead Spots at 150 Hz multiples
Amplification vs.Frequency
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
-150 50 250 450 650 850 1050
Hz
Vca
m/V
app
Mag
Time Series Analysis Low Frequency
~68 ms ~15 Hz
Time Series Excerpt from Reduced Gravity Parabola. Driving Frequency approximately 13 Hz. The variation in frequency involves higher harmonics
Time Series (high frequency)
~2ms
High frequency analysis of time series shows systematic peaks every 2ms.FFT should have peak ~500 Hz.
Initial FFT Analysis
474.7 Hz
952 Hz
Series of harmonic peaks in high frequency (474.7 Hz fundamental)Insufficient resolution (~1.5 Hz) to distinguish low frequency response
Audio Parsing Data Files split into 8 files
each containing every 8th point
Sample rate decreases to 6 kHz (resolution improved to ~0.25 Hz)
Parabola 19 driving frequency 17.5 Hz from motor data
Peaks in FFT show harmonics of 20 Hz
A few questions remain about the effectiveness/ problems of parsing.
Parabola 19 Box B Parsing 8
0
0.05
0.1
0.15
0.2
0.25
0.3
-10 10 30 50 70 90 110 130 150
frequency
Per
cen
t F
ull
Sca
le (
V)
Series1
Modifications/Improvements for 2003 Flight
Sensors reconstructed and more solidly bonded to central plate of box set.
Sensor voltage amplified using standard inverting op-amp (impacts easier to detect)
Data collection controlled by a microcontroller and stored on a hard drive. (Sampling rate reduced to 2kHz)
Reliance on camera function for impact information avoided.
Coupling of signal eliminated
Impact Data SampleCH.0 Day 2 Parabola 4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0 800 1600 2400 3200 4000
Sample
Vo
ltag
e
Ch.0
Acknowledgements
Dr. Michael Wilson -- National Academy of Sciences
Mr. Shawn Jackson -- University of Tulsa
Rebecca Ragar, Jeffrey Wagner, Justin Eskridge, Adrienne McVey, Erin Lewallen, and Ian Zedalis.
Dr. Roger Blais -- University of Tulsa