Direct Measurement of Particle Behavior in the Particle-Lagrangian Reference

Frame of a Turbulent Flow

James A. BickfordM.S.M.E. Defense

10 August 1999

Advisor : Chris Rogers (Tufts University)

Committee Members : Vincent Manno (Tufts University)

Martin Maxey (Brown University)

Outline

• Overview and Applications• Quasi-numerical Simulation

– QNS Method– Velocity autocorrelations, spectra– Integral scales– u’– Anomalous drift

• Digital Particle Image Velocimetry– DPIV Method– Kolmogorov estimates– Effects of preferential concentration

Particles and Turbulence

• Turbulent Fluid Fluctuations– Occur on a range of length and

time scales

– Suspended particles respond to these scales

f

pSt

18

2pd

p

d

plf

dg

u

vS

'pd gv

Applications

• Engine combustion, radiation and pollution control, volcanic erruptions

• Aeolian Martian processes

• Formation of planetary bodies and large scale structure of the universe

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Three-tiered research approach

• Tactical approach uses separate but complimentary methods– Microgravity flight experiments

– Direct numerical simulations

– Quasi-numerical simulations

Quasi-Numerical Overview

• Technique– Hybrid numerical-experimental– Two-axis traverse emulates a virtual particle in a water flow– Measures turbulence statistics in the particle’s reference frame

• Variable Parameters– Particle time constant

• (size)

– Drift velocity • (gravity)

– Reynolds number • (turbulence intensity)

• Data Acquisition Methods– Laser Doppler Velocimetry– Digital Particle Image Velocimetry

QNS Methodology

gVUdt

dvpf

p

p 1Read Fluid Velocity

Update Traverse Velocity

gVUdt

vdpf

p

p ˆˆˆ1ˆ

Repeat >> Tk

Particle Response to Turbulence1 7 .5

-2 5 .0

-2 2 .5

-2 0 .0

-1 7 .5

-1 5 .0

-1 2 .5

-1 0 .0

-7 .5

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2 .5

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7 .5

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4 5 0 0 .00 .0 5 0 0 .0 1 0 0 0 .0 1 5 0 0 .0 2 0 0 0 .0 2 5 0 0 .0 3 0 0 0 .0 3 5 0 0 .0 4 0 0 0 .0

F lu id V e lo c ity (mm/ s )

P a rtic le V e lo c ity (mm/ s )

3 0 .0

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5 5 0 0 .00 .0 5 0 0 .0 1 0 0 0 .0 1 5 0 0 .0 2 0 0 0 .0 2 5 0 0 .0 3 0 0 0 .0 3 5 0 0 .0 4 0 0 0 .0 4 5 0 0 .0 5 0 0 0 .0

F lu id V e lo c ity (mm/ s )

P a rtic le V e lo c ity (mm/ s )

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F lu id V e lo c ity (mm/ s )

P a rtic le V e lo c ity (mm/ s )

f

pSt

18

2pd

p

d

TimeTime

Vel

ocit

yV

eloc

ity

Vel

ocit

y

Particle Velocity

Fluid Velocity (along particle path)

Movie - “QNS in action”

Effect of Gravity on Velocity Autocorrelations

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4 0 0 0 .00 .0 5 0 0 .0 1 0 0 0 .0 1 5 0 0 .0 2 0 0 0 .0 2 5 0 0 .0 3 0 0 0 .0 3 5 0 0 .0

Sg = 0

Sg = 0.6

Sg = 1.3

Sg = 2.0

Sg = 2.6

Streamnormal Fluid Velocity Autocorrelation (Tp = 250 ms)

Gravity• Decreases Correlation times

•“crossing trajectories” effect

• Increases relative particle energy at higher frequencies•Little effect on fluid spectra

Time

Rii /

u’2

Effect of Particle Inertia on Velocity Autocorrelations

Particle Inertia• Increases particle correlation times• Almost no effect on fluid correlations or spectra•Decreases relative energy at higher frequencies

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4 0 0 0 .00 .0 5 0 0 .0 1 0 0 0 .0 1 5 0 0 .0 2 0 0 0 .0 2 5 0 0 .0 3 0 0 0 .0 3 5 0 0 .0

St = 2.6

St = 4.4

St = 6.1

St = 8.8

St = 12.3

St = 17.5

Streamnormal Fluid Velocity Autocorrelation (Sg = 0)

Time

Rii /

u’2

Effect of Gravity on Integral Scales

1.500

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1.000

1.100

1.200

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1.400

3.00.0 0.5 1.0 1.5 2.0 2.5

Best Fit

St = 2.6

St = 4.4

St = 6.1

St = 8.8

St = 17.5

Sg

Gravity• Fluid Scales Decrease

• Streamwise• Streamnormal (more)

• Particle Scales•Possible decrease (tiny)

• p-L fluid scales • ME = pL @ Sg = 1

T2p-

L /

T2m

e

Effect of Particle Inertia on Integral Scales

T1p-

L /

T1m

e

Stme

2.400

0.800

1.000

1.200

1.400

1.600

1.800

2.000

2.200

2.00.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Best Fit

Drift = 0%

Drift = 2.5%

Drift = 5%

Drift = 7.5%

Drift = 10%

Inertia•General increase in fluid and particle integral scales•Possible local peaks

• Tf ~ 1 (particle)• Tf ~ 0.7 (fluid)•SW more prominent

Anomalous Drift Velocities

0.007

-0.002

-0.001

0.000

0.001

0.002

0.003

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0.006

2.00.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Best Fit

Drift = 0%

Drift = 2.5%

Drift = 5%

Drift = 7.5%

Drift = 10%

(Mea

sure

d D

rift

- I

mpo

sed

Dri

ft)

/ U

Stme

U’ Dependence on Gravity and Particle Inertia

U’ ipl

/ U

’ ime

Streamwise Streamnormal1.0

0.6

0.7

0.8

0.9

2.00.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Drift = 0%

Drift = 2.5%

Drift = 5%

Drift = 7.5%

Drift = 10%

1.0

0.6

0.7

0.8

0.9

4.00.5 1.0 1.5 2.0 2.5 3.0 3.5

Stme Stme

Mechanisms Dictating Particle Behavior

Looking beyond single point statistics• Vorticity as a governing force for particle motion

•Preferential concentration

Digital Particle Image Velocimetry

• Four computers used during simultaneous QNS– Master control

– Traverse control (DSP)

– Frame grabber

– Laser and camera pulse control

• 750 mW pulsed diode laser illuminates a 2-D plane of the flow

• Dichroic filter allows camera and LDV regions to coincide

• Kodak ES-1 camera grabs 1008x1018 pixel images at 30 Hz

Image Correlations

• Images broken into sections (interrogation windows)

• Sub-images cross-correlated to produce vector field

Bad Vector Identification

• Bad correlations (lighting, dirt, 3-D effects)

• Bad vectors are identified by comparing the velocity of a given vector to its surrounding neighbors.

22iii dvdu

γ = 2 (good)

γ = 2 (good)γ = 8 (bad) γ = 6 (bad)

Tagged Vector Replacement

• Average with surrounding vectors

– iterate to fix coincident vectors– inaccurate velocities– reduced resolution

• Replace with higher order interpolated value

– more accurate interpolation– same reduced resolution

• Use secondary correlation peaks– no loss of resolution or

accuracy

Estimation of the Kolmogorov Fluid Time Scale

• Kolmogorov Fluid Time Scale

21115 xu

21

• Results

Re Tk (ms) Std (ms) V ectors

3300 201 11 336350

6600 57 6 168175

Effect of Preferential Concentration on Particle Path

Conclusion

• Gravity and Inertia– Affect particle trajectory

which in turns affects• Integral scales

• Measured u’

• Measured vorticity

• Observed Anomalies– Drift– Integral scale

dependence

Acknowledgements

• Committee Members– Chris Rogers *

– Vincent Manno

– Martin Maxey

• Staff– Jim Hoffmann, Vinny Maraglia

– Audrey-Beth Stein, Joan Kern

• TUFTL– Becca Macmaster, AJ

Bettencourt

– Dave McAndrew, Dan Groszmann, Scott Coppen, Jon Coppeta, Merre Portsmore

Ainley & Bickford Rii Comparisons

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Ainley Data, Ainley Code

Ainley Data, Groszmann Code

Bickford Data, Groszmann Code

U Fluid Velocity Autocorrelations1 .1

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Ainley Data, Ainley Code

Ainley Data, Groszmann Code

Bickford Data, Groszmann Code

U Particle Velocity Autocorrelations• Fluid Velocity Autocorrelation • Particle Velocity Autocorrelation