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Granular Fluidization in Reduced Gravity

University of TulsaSupported by Research Corp.

Justin Mitchell, Aaron Coyner, Rebecca Ragar, Matt Olson, Ian Zedalis, Adrienne McVey, Whitney Marshall

Michael Wilson*, Shawn Jackson

*Currently at National Research Council

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Project Description Goals

Look for definitive inelastic collapse of a 3-d granular system in zero gravity.

Determine parameters necessary for a granular gas, the precursor to collapse.

Methods Preliminary

testing on NASA KC-135A low gravity aircraft

Future flight on Space Shuttle

Testing on sounding rocket*

* É. Falcon et al. , Phys. Rev. Lett. 80. 440 (1999).

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Why Investigate Granular Gases?

Large granular systems, such as planets, are not well understood.

Asteroids, planetary rings, etc. are not fully explained by gravity because sizes are too small for gravity to act alone.

Inelastic collapse models provide plausible method for formation of these smaller objects.

Small scale granular gas studies allow for lab testing of the models on reasonable time scales.

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Experimental Description Box set: 8 sapphire

walled cubes, 1 in3 each.

Box set mechanically shaken sinusoidally along body diagonal.

Each cube has one free wall attached to a piezoelectric sensor.

Video cameras view 3 orthogonal box set faces.

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Box Set as Flown on KC-135A

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System Acceleration

Shaking direction is perpendicular to mean effective gravity.

In “microgravity” the residual acceleration is ~0.03 gearth *.

Residual acceleration is usually pointed up.

shaking

gearth

Residual acceleration

* From Charles Thomas, Boston University

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Granular Phases

SolidGrains pack in one corner

FluidGrains slosh around box walls

Gas~uniform distribution of kinetic grains

gresidual

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Phase Diagram

=A2/gresidual

is the ratio of wall acceleration to gresidual

diverges as gresidual goes to zero.

o Wall acceleration, density and gresidual define the phase.

0 10 20 30 40 50

gas

fluid

solid

c

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Experiment Geometries

• Shaking parallel to g

c2.0 *• A2 = 19.6 m/s2

g

shaking

gresidual

shaking

Normal Geometry Our Geometry

• Shaking normal to gresidual

c17

• A2 = 5.00 m/s2

*Y. Lan, A. D. Rosato, Phys. Fluids 7, 1818 (1995).

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Conclusions

There is a c that defines the phase transition to a

granular gas.

Geometry and density affect the value of c.

=A2/gresidual is a convenient way to compare

shaken granular experiments.

o Our geometry requires a higher wall accelerations

(in proportion to gresidual) to show a phase

transition.

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Future Work Ball tracking to give speed distribution.

Analyze impact data to obtain pressure information for gas phases.

First flight was preparation for later experiments.

Second KC-135A flight

Make free floating

Space Shuttle

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Ball diameter 0.50 mm Ball diameter 1.0 mmCell # #balls mfp (mm) L/mfp %Oc.Vl. Cell # #balls mfp (mm) L/mfp %Oc.Vl.

1 1000 17.1 1.4 0.5 4 250 17.1 1.4 1.02 3100 5.5 4.3 1.5 5 775 5.5 4.3 3.03 10000 1.7 13.9 4.9 6 2500 1.7 13.9 9.87 3100 0.50 mm balls

775 1.00 mm balls 4.5 Cell volume 13400 mm3Mean edge length 23.7 mm

Experiment Parameters

0.50 mm and/or 1.00 mm grade 200 brass

Mean free path (mfp) ~Vol./(Nd2)

%Oc.Vl. = % of volume occupied by balls

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0 0.1 0.2 0.3 0.4 0.5

time (sec)

Hei

gh

t (m

m)

Residual Acceleration Balls above dense clusters follow parabolic

path. gResidual 0.023 gEarth

Within 25% of BU Data