Experimental and numerical investigations of particle clustering in isotropic turbulence

Workshop on Stirring and Mixing: The Lagrangian ApproachLorentz Center

Leiden, The NetherlandsAugust 21-30, 2006

International Collaboration for Turbulence Research (ICTR)

Cornell University SUNY Buffalo Max Planck Institute

Dr. Lance R. Collins Dr. Hui Meng Dr. Eberhard Bodenschatz

Juan Salazar Scott Woodward

Dr. Zellman Warhaft Lujie Cao

S. Ayyalasomayajula Jeremy de Jong

Particle Clustering in Turbulence

Vortices

Strain Region Maxey (1987); Squires & Eaton (1991); Wang & Maxey (1993) Shaw, Reade, Verlinde & Collins (1997) Falkovich, Fouxon & Stepanov (2002); Zaichik & Alipchenkov (2003); Chun, Koch, Rani, Ahluwalia & Collins (2005)

QuickTime™ and aCompact Video decompressorare needed to see this picture.

Turbulence in Clouds

BuoyancyCloud CondensationNuclei (CCN)

€

103 m

€

10−3 m

d2 Lawmass

energy

ddt

d(t) =′ K

d(t)

d2(t)∝ td(t)

Current microphysical models predicto too slow “condensational” growtho too narrow cloud droplet distributions

Shaw (2003)

Beard & Ochs (1993)

“… At this rate, we are quite a way off from being able topredict, on firm micro-physical grounds, whether it willrain.” 0.1 m

1 m

10 m

Clouds in Climate Models

Visible Wavelengths Infra Red

High, cold clouds

Low, warm clouds

Distribution of cloud cover profoundly influences global energy balance

Raymond Shaw

Collision Kernel

Particle clustering impacts the RDF

€

Nijc = π dij

2 ni n j gij (dij ) (− wij ) Pij (wij | dij ) dwij− ∞

0

∫

€

dij = (di + d j ) / 2

gij (r) = radial distribution function (RDF)

wij = relative velocity

P(wij | r) = PDF of relative velocity

Sundaram & Collins (1997); Wang, Wexler & Zhou (1998)€

St =1

18

ρ p

ρ

⎛

⎝ ⎜

⎞

⎠ ⎟dη

⎛

⎝ ⎜

⎞

⎠ ⎟2

Monodisperse clustering: drift

€

A ≡St τ η

2

3S2 − R2

[ ]p

€

qrd = − A

rτ η

g(r)

Chun, Koch, Sarma, Ahluwalia & Collins, JFM 2005

€

η

€

r

€

St <<1

Monodisperse clustering: diffusion

Chun, Koch, Sarma, Ahluwalia & Collins, JFM 2005

€

qrD ≡ − B

r2

τ η

∂g∂r

€

BL = 0.153

BNL = 0.093

Monodisperse clustering: RDF

St = 0.7

€

g(r) =ηr

⎡ ⎣ ⎢

⎤ ⎦ ⎥

A B

0.25

0.20

0.15

0.10

0.05

0.00

A / B

0.200.150.100.050.00

St

Theory 1 Theory 2 DNS Stochastic 1 Stochastic 2

Chun, Koch, Sarma, Ahluwalia & Collins, JFM 2005

Bidisperse clustering

Chun, Koch, Sarma, Ahluwalia & Collins, JFM 2005

€

α€

β€

qrd = − A

rτ η

g(r)

€

A ≡Stβ τ η

2

3S2 − R2

[ ]p

€

η

Bidisperse clustering

Chun, Koch, Sarma, Ahluwalia & Collins, JFM 2005

€

qrD ≡ − B

r2

τ η

∂g∂r

€

BL = 0.153

BNL = 0.093

€

qra = − D

∂g∂r

€

D = ΔSt( )2 a0 Rλ( )

η 2

τ η2 τ a

Bidisperse clustering: stationary

Chun, Koch, Sarma, Ahluwalia & Collins, JFM 2005

€

g(r) =η 2

r2 + rc2

⎡

⎣ ⎢

⎤

⎦ ⎥

A 2 B

1

2

3

4

5

6

7

8

910

g(r)

0.0012 3 4 5 6 7

0.012 3 4 5 6 7

0.12 3 4 5 6 7

1

r / η

(0.2, 0.2) (0.2, 0.19) (0.2, 0.175)

RDF Measurements

Experiments and Simulations

Direct Numerical Simulations

Turbulence Chamber

38 cm

Fans

Optical Access

Isotropic Turbulence Chamber

Flow Characterization

€

Rλ

€

Urms

€

Vrms

€

ε

€

L

€

η

€

91

€

117

€

130

€

140

€

161

€

173

€

0.286

€

0.447

€

0.564

€

0.651

€

0.777

€

0.906

€

0.283

€

0.451

€

0.577

€

0.651

€

0.790

€

0.942

€

0.817

€

3.16

€

6.63

€

9.72

€

15.9

€

25.5

€

1.26 ×10−2

€

1.31×10−2

€

1.28×10−2

€

1.30 ×10−2

€

1.43×10−2

€

1.39 ×10−2

€

2.54 ×10−4

€

1.81×10−4

€

1.50 ×10−4

€

1.37 ×10−4

€

1.21×10−4

€

1.07 ×10−4

Conditions at 6 Fan Speeds (MKS)

€

ε =1r

DLL

C2

⎛

⎝ ⎜

⎞

⎠ ⎟

3/2

Metal-Coated Hollow Glass Spheres

Mean = 6 micronsSTD = 3.8 microns1-10 particles/cm3

V = 10-7

Measurements of RDF

Wood, Hwang & Eaton (2005)Saw, Shaw, Ayyalasomayajula, ChuangGylfason, Warhaft (2006)

Turbulence Box Wind Tunnel

Why 3D?

2D Sampling 1D Sampling

1

2

3

456

10

2

3

456

100

2

3

4

g(r)

0.01 0.1 1 10r / η

g3D( )r g2D( )r g1D( )r

€

g2D

rδ

⎛ ⎝ ⎜

⎞ ⎠ ⎟= 2 g3D

rδ

⎛ ⎝ ⎜

⎞ ⎠ ⎟2

+ v2 ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟dv

0

1

∫

€

g1D

rδ

⎛ ⎝ ⎜

⎞ ⎠ ⎟= 4 g3D

rδ

⎛ ⎝ ⎜

⎞ ⎠ ⎟2

+ v2 + w2 ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟dv dw

0

1

∫0

1

∫

Relations

Holtzer & Collins (2002)

€

g3D ri( ) ≡Npi

NpVi V

3D Particle Position Measurement Techniques

1. Particle Tracking Velocimetry (PTV)• Advantages – Lagrangian particle information• Disadvantages – Limited particle number density.

2. Holographic Particle Image Velocimetry (HPIV)• Advantages – Better particle number density than PTV, larger 3D volume

than Stereo PIV• Disadvantages – Cannot resolve time evolution of particles.

40 c

m

1k x 1k CCD

Z

Fan

F

an

F

an

Optical Window

(4 cm)3 Volume

V2

V1V3

X

Y

Z

Numerical ReconstructionIntensity-Based Particle Extraction

Hybrid Digital HPIVNd:YagLaser 532 nm

ReferenceBeam

Beam Expander

Variable BeamAttenuator

Particle Concentration and Phase Averaging

Size Distribution Evolution

0.0

0.1

0.2

0.3

0.4

0.5

0.6

1 2 3 4 5 6 7 8 9

Particle size group

Probability

Phase 01Phase 02Phase 03Phase 04Phase 05

Time Dependence of RDF

€

η=150 μm

€

η=120 μm

Direct Numerical Simulations

1283 Grid Points R = 80 1.2 Million Particles (one way coupling) Experimental Particle Size Distribution

Keswani & Collins (2004)

Filtering by camera

Mean = 6 micronsSTD = 3.8 microns

Metal-coated hollow glass spheres

Filtering by camera

Mean = 6 micronsSTD = 3.8 microns

Metal-coated hollow glass spheres

Comparison at R = 130

1

2x100

3

4

g(r)

1086420r / η

St > 0 St > 0.05 St > 0.1 St > 0.15 St > 0.2 St > 0.25 St > 0.3 St > 0.35 St > 0.4 Exp dαtα

Comparison at R = 161

1

2

3

4

5

g(r)

1086420r / η

St > 0 St > 0.05 St > 0.1 St > 0.15 St > 0.2 St > 0.25 St > 0.3 St > 0.35 St > 0.4 Exp dαtα

Summary Clustering results from a competition between inward

drift and outward diffusion Radial Distribution Function (RDF) is the measure for

collision kernel Analysis of RDF involves Lagrangian statistics along

inertial particle trajectories RDF mainly found in direct numerical simulation 3D measurements of RDF using holographic imaging

Reasonable agreement between experiments and DNS Challenges for the measurement

Characterizing flow (dissipation rate, ε) Particle size distribution (will separate particles) Increasing resolution of experiment (smaller separations)

International Collaboration for Turbulence Research (ICTR)