Direct Measurement of Particle

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22 Φεβ 2014 (πριν από 3 χρόνια και 4 μήνες)

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Direct Measurement of Particle
Behavior in the Particle
-
Lagrangian
Reference Frame of a Turbulent Flow

James A. Bickford

M.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
p
St






18
2
p
d
p
d

pl
f
d
g
u
v
S
'

p
d
g
v


Applications



Engine combustion,
radiation and pollution
control, volcanic
erruptions


Aeolian Martian
processes


Formation of planetary
bodies and large scale
structure of the universe



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



g
V
U
dt
dv
p
f
p
p




1
Read Fluid Velocity

Update Traverse Velocity



g
V
U
dt
v
d
p
f
p
p
ˆ
ˆ
ˆ
1
ˆ




Repeat >> T
k

Particle Response to Turbulence

f
p
St






18
2
p
d
p
d

Time

Time

Velocity

Velocity

Velocity

Particle Velocity

Fluid Velocity (along particle path)

Movie
-

“QNS in action”

Effect of Gravity on

Velocity Autocorrelations

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


R
ii

/ 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


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


R
ii

/ u’
2

Effect of Gravity on

Integral Scales

1.500
0.500
0.600
0.700
0.800
0.900
1.000
1.100
1.200
1.300
1.400
3.0
0.0
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



T
2
p
-
L

/ T
2
me

Effect of Particle Inertia on
Integral Scales


T
1
p
-
L

/ T
1
me

St
me

2.400
0.800
1.000
1.200
1.400
1.600
1.800
2.000
2.200
2.0
0.2
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
0.004
0.005
0.006
2.0
0.2
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%
(Measured Drift
-

Imposed Drift) / U

St
me

U’ Dependence on Gravity

and Particle Inertia

U’
i
pl

/ U’
i
me

Streamwise

Streamnormal

1.0
0.6
0.7
0.8
0.9
2.0
0.2
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
4.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
St
me

St
me

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.




2
2
i
i
i
dv
du



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






2
1
1
15
x
u







2
1






Results



Re
Tk (ms)
Std (ms)
Vectors
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

Ainley Data, Ainley Code
Ainley Data, Groszmann Code
Bickford Data, Groszmann Code
U Fluid Velocity Autocorrelations
Ainley Data, Ainley Code
Ainley Data, Groszmann Code
Bickford Data, Groszmann Code
U Particle Velocity Autocorrelations

Fluid Velocity Autocorrelation





Particle Velocity Autocorrelation