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Impact Data Analysis for Pressure Data of Granular Gases in Reduced Gravity

This study explores the impact data of granular gases in reduced gravity and its application in understanding inelastic collapse and its relevance to celestial systems. The data analysis includes camera effects, signal amplification, frequency response, and audio parsing.

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Impact Data Analysis for Pressure Data of Granular Gases in Reduced Gravity

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  1. 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

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

  3. 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

  4. 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.

  5. 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

  6. 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. The Gr.A.I.N.S. Experiment

  7. 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

  8. 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

  9. 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

  10. 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

  11. Time Series (high frequency) ~2ms High frequency analysis of time series shows systematic peaks every 2ms. FFT should have peak ~500 Hz.

  12. 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

  13. 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.

  14. 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

  15. Impact Data Sample

  16. 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

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