Impact Data Analysis and Sensor Modification for Pressure Data of Granular Gases in Reduced Gravity Aaron Coyner, Justin Mitchell, and Matthew Olson University.

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