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

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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)

A. Puglisi, A. Baldassarri, and V. Loreto,
Phys. Rev E 66 061305.
É. Falcon et al. , Phys. Rev. Lett. 80. 440
(1999).
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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

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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.

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Ways to Achieve Reduced Gravity

• Sounding Rocket
• Falcon et al. (1999)
• Nasas KC-135 Weightless Wonder
• Space Shuttle Flight
• Get Away Special

KC-135
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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.

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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
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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 gt 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

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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

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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
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Time Series (high frequency)
2ms
High frequency analysis of time series shows
systematic peaks every 2ms. FFT should have peak
500 Hz.
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Initial FFT Analysis
952 Hz
474.7 Hz
Series of harmonic peaks in high frequency (474.7
Hz fundamental) Insufficient resolution (1.5 Hz)
to distinguish low frequency response
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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.

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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

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Impact Data Sample
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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