Using DNS to Understand Aerosol Dynamics

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1 APS Division of Fluid Dynamics Meeting East Rutherford, NJ November 23-25, 2003 Using DNS to Understand Aerosol Dynamics Lance R. Collins Sibley School of Mechanical & Aerospace Engineering Cornell University

2 Direct Numerical Simulations of Microstructures Aerosols! Dispersion! Turbulence modulation! Coagulation Droplets*! Breakup! Coalescence * M. Loewenberg J. Blawzdziewicz V. Cristini Polymer Molecules! Orientation! Stretch! Drag Reduction * J. G. Brasseur

3 Outline " Background on aerosols " Direct numerical simulations (DNS) " Numerical Results " Theory " Experiments " Summary

4 Examples Cloud Condensation Nuclei (CCN) DuPont TiO 2 Process Ti Cl 4 Region II Buoyancy Air, T = 2000 K Region I Region III R. Shaw, ARFM 2003 Ti Cl 4

5 Turbulent clustering Aerosol particles in a turbulent flow field cluster outside of vortices due to a centrifugal effect, sometimes referred to as preferential concentration. Maxey (1987) Squires & Eaton (1991) Wang & Maxey (1993) Vortices Strain Region

6 Snapshot of particle clustering in DNS Snapshot from a DNS (St=1 and R λ = 54). The green tubes are vortex tubes where fluid circulates rapidly and the white shows where the particle concentration is greater than 10 times the mean. How does this affect coalescence rates? How does this affect coalescence rates?

7 Direct numerical simulation dilute loading of spheres u = 0 u t + u u + p ρ = ν 2 u + F

8 Particle update dx p (i) dt = v p (i) η d η << 1 dv p (i) dt [ = u(x (i) (i) p,t) v p ] (i) + F (ij) τ p Stokes drag (i) 1 ρ p τ p = d 18 ρ η 2 j i collisions (neighborhood search)

9 Particle-particle interactions Elastic Rebound: Coalescence: Interpenetration:

10 Parameters Flow: U turbulence intensity ε dissipation rate ν kinematic viscosity Particles: d ρ p n diameter density loading R λ 15 U 2 νε St = τ p d η Φ τ η Stokes number size parameter volumetric loading

11 Parameter Ranges System R λ St d/η Φ Clouds <10 6 DNS * <10 5 Exp't > <10 5 We are not able to simulate atmospheric Reynolds numbers It s therefore critical that we understand the importance of this parameter (from experiments, theory, etc.) * High end DNS is , corresponding to R λ ~ 1000 Gotoh & Fukayama (2001)

12 Limiting theories for collision Saffman and Turner (1956) Zero Stokes number: N c = 1 2 n2 d 3 8π ε 15 ν 1/2 Abrahamson (1975) Infinite Stokes number: N c = 1 2 n2 d 2 16π v 2 p 3 1/2 Brunk, Koch & Lion (1998) Wang, Wexler and Zhou (1998) n v p 2 number density particle kinetic energy Reade & Collins (1998)

13 Collision vs Stokes number Sundaram & Collins (1997)

14 Evolution of size distribution St 1 = 0.2 d 1 = d 1 = d 1 = Number Number d 1 = St = Inf St = Size 30 St 1 = 0.2 St 1 = 0.3 St 1 = 0.5 St 1 = Number St = Inf St = St 1 = 0.7 Size d 1 = d 1 = d 1 = Reade & Collins JFM (2000) 10 0 St = Inf St = Size

15 General collision formula N c = π d ij 2 ni n j g ij (d ij ) 0 ( w) P ij (w d ij ) dw d ij = (d i + d j )/2 g ij (r) = radial distribution function (RDF) w = relative velocity P(w r) = PDF of relative velocity RDF corrects for preferential concentration (dominant effect at low Stokes numbers) Sundaram & Collins (1997) Wang, Wexler and Zhou (1998)

$volume fraction! Stokes number! size parameter!$

16 RDF g(r) # pairs expected # pairs Parametric Dependence! volume fraction! Stokes number! size parameter! Reynolds number

17 Stokes number dependence Re = 82.5 Re = 69.7 Re = 54.5 Re = RDF St 3 4

18 Bi-disperse St dependence Suppression of off-diagonal collisions broadens the distribution

19 Size parameter RDF ghost d/η = d/η = d/η = r / η

20 RDF - 1 RDF Re λ = 65 Re λ = 81 Re λ = 107 Re λ = 152 St = (r/η) Re λ = 65 Re λ = 81 Re λ = 107 Re λ = 152 Reynolds Number Dependence St = (r/η) RDF - 1 RDF Re λ = 65 Re λ = 81 Re λ = 107 Re λ = 152 St = (r/η) Re λ = 65 Re λ = 81 Re λ = 107 Re λ = 152 St = (r/η)

21 Physics of clustering r(t) Maxey (1987) Rotation Frame moving with a test particle Strain

22 Recent Theoretical Developments! Wang, Wexler & Zhou (2000) relative velocity clustering effect! Falkovich, Fouxon and Stepanov (2002) clustering effect in clouds! Zaichik & Alipchenkov (2003) relative velocity clustering! Chun, Koch, Ahluwalia & Collins (2003) clustering (St << 1) g r = c 0 η c 0 c 1 η r ( R λ, St, Φ) ( R λ, St, Φ) RDF c Re λ = 65 Re λ = 81 Re λ = 107 Re λ = (r/η)

23 Chun et al. (2003) St<<1 ( ) g t = 1 r 2 Arg r 2 r + 1 r 2 r r2 Br 2 g r A = St ( S 2 3 τ ) p R2 nonlocal diffusion p η S 2 St p = σ 2 ε ε T 2 εε ρ εςσ ε σ ς ε 2 Steady State g(r) = c 0 η r c 1 c 1 = A / B = 6.6 St 2 c 1 = 3.6 St ( S 2 ) p R2 p T ες, St R 2 St p DNS = ρ εςσ ε σ ς T ε 2 ςε σ 2 ς ε 2 Stoch Theory T ςς

24 Chun et al. (2003) Bidisperse! Fluid accelerations give rise to relative diffusion η 2 g AB (r) = c 0 r r c r c = B' St A St B η c 1 /2

25 Reynolds Number Dependence c 1 = 3.6 St ( S 2 ) p R2 p inc R λ 0.4 S 2 and R inc R λ St

Experimental 3D Particle Imaging Professor Hui Meng Why 3D? RDF 100 10 4 3 2 6 5 4 3 2 g 3D (r) g 2D (r), δ / η = 0.

26 Experimental 3D Particle Imaging Professor Hui Meng Why 3D? RDF g 3D (r) g 2D (r), δ / η = 0.64 g 2D (r), δ / η = 1.28 g 2D (r), δ / η = r / η! Cover a Broader Range of R λ! Validate DNS and Theory Holtzer & Collins (2002)

Preliminary Results 10 9 8 7 DNS HPIV 1 HPIV 2 6 5 RDF 4

27 Preliminary Results DNS HPIV 1 HPIV RDF r / η

Particle Tracking Eberhard Bodenschatz and Zellman Warhaft Wind Tunnel (active grid) QuickTime and a YUV420 codec decompressor are needed to see this picture.

28 Particle Tracking Eberhard Bodenschatz and Zellman Warhaft Wind Tunnel (active grid) QuickTime and a YUV420 codec decompressor are needed to see this picture.! Track droplets Multiple (4) cameras High speed (above 50,000 fps) Integral time and length scales! Measure accelerations Compare with DNS Test theoretical predictions Droplets microns

29 Summary " Particle clustering in turbulent flows " Increases collision frequency 1-2 orders of magnitude " Strongly favors like collisions; broadens particle size distribution " Theoretical predictions for RDF " Stokes number dependence " Size parameter " Reynolds number dependence remains in dispute (key for cloud physics) " Experiments " Validate DNS and theory " Increase the range of Reynolds numbers " Enabling Technologies " 3D imaging essential " Holographic imaging (RDF at an instant) " High-Speed Stereoscopic Tracking (Lagrangian statistics) DNS has continuously guided theoretical and experimental work DNS has continuously guided theoretical and experimental work

W. Reade (Kimberly Clark)! A. Keswani (Goldman Sachs)! A. Ahluwalia (Epic Sys.)! S. Rani Undergraduate Students!

30 Acknowledgments Colleagues! Prof. Hui Meng (SUNY-Buffalo)! Prof. Don Koch (Cornell)! Prof. E. Bodenschatz! Prof. Z. Warhaft! Prof. R. Shaw (Mich. Tech)! Prof. M. Loewenberg (Yale) Grad Students and Postdoc! S. Sundaram (CFD Research)! W. Reade (Kimberly Clark)! A. Keswani (Goldman Sachs)! A. Ahluwalia (Epic Sys.)! S. Rani Undergraduate Students! Carolyn Nestleroth! Melissa Feeney! Anthony Fick NAG CTS PHY

31 Future Work " High-resolution DNS (JC.001) " Effect of shear flow " Hydrodynamic interactions " Extend theory to coalescing system " Experimental measurements " HPIV at an instant " Lagrangian statistics RDF ghost particles finite particle DNS - 5% DNS - 25% r / η

Effects of Forcing Scheme on the Flow and the Relative Motion of Inertial Particles in DNS of Isotropic Turbulence

Effects of Forcing Scheme on the Flow and the Relative Motion of Inertial Particles in DNS of Isotropic Turbulence Rohit Dhariwal PI: Sarma L. Rani Department of Mechanical and Aerospace Engineering The