Experimental and numerical investigations of particle clustering in isotropic turbulence
description
Transcript of Experimental and numerical investigations of particle clustering in isotropic turbulence
![Page 1: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/1.jpg)
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
![Page 2: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/2.jpg)
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.
![Page 3: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/3.jpg)
Turbulence in Clouds
BuoyancyCloud CondensationNuclei (CCN)
€
103 m
€
10−3 m
![Page 4: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/4.jpg)
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)
![Page 5: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/5.jpg)
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
![Page 6: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/6.jpg)
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
![Page 7: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/7.jpg)
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
![Page 8: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/8.jpg)
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
![Page 9: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/9.jpg)
Monodisperse clustering: diffusion
Chun, Koch, Sarma, Ahluwalia & Collins, JFM 2005
€
qrD ≡ − B
r2
τ η
∂g∂r
€
BL = 0.153
BNL = 0.093
![Page 10: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/10.jpg)
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
![Page 11: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/11.jpg)
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
![Page 12: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/12.jpg)
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
![Page 13: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/13.jpg)
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)
![Page 14: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/14.jpg)
RDF Measurements
Experiments and Simulations
Direct Numerical Simulations
![Page 15: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/15.jpg)
Turbulence Chamber
38 cm
Fans
Optical Access
Isotropic Turbulence Chamber
![Page 16: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/16.jpg)
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
![Page 17: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/17.jpg)
Metal-Coated Hollow Glass Spheres
Mean = 6 micronsSTD = 3.8 microns1-10 particles/cm3
V = 10-7
![Page 18: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/18.jpg)
Measurements of RDF
Wood, Hwang & Eaton (2005)Saw, Shaw, Ayyalasomayajula, ChuangGylfason, Warhaft (2006)
Turbulence Box Wind Tunnel
![Page 19: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/19.jpg)
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
![Page 20: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/20.jpg)
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.
![Page 21: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/21.jpg)
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
![Page 22: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/22.jpg)
Particle Concentration and Phase Averaging
![Page 23: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/23.jpg)
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
![Page 24: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/24.jpg)
Time Dependence of RDF
€
η=150 μm
€
η=120 μm
![Page 25: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/25.jpg)
Direct Numerical Simulations
1283 Grid Points R = 80 1.2 Million Particles (one way coupling) Experimental Particle Size Distribution
Keswani & Collins (2004)
![Page 26: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/26.jpg)
Filtering by camera
Mean = 6 micronsSTD = 3.8 microns
Metal-coated hollow glass spheres
![Page 27: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/27.jpg)
Filtering by camera
Mean = 6 micronsSTD = 3.8 microns
Metal-coated hollow glass spheres
![Page 28: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/28.jpg)
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
![Page 29: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/29.jpg)
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
![Page 30: Experimental and numerical investigations of particle clustering in isotropic turbulence](https://reader036.fdocuments.in/reader036/viewer/2022070413/56814d0b550346895dba4452/html5/thumbnails/30.jpg)
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)