Experimental and numerical investigations of particle clustering in isotropic turbulence Workshop on Stirring and Mixing: The Lagrangian Approach Lorentz Center Leiden, The Netherlands August 21-30, 2006 International Collaboration for Turbulence Research (ICTR) Cornell UniversitySUNY BuffaloMax Planck Institute Dr. Lance R. CollinsDr. Hui MengDr. Eberhard Bodenschatz Juan SalazarScott Woodward Dr. Zellman WarhaftLujie Cao S. AyyalasomayajulaJeremy 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)

Turbulence in Clouds Buoyancy Cloud Condensation Nuclei (CCN)

d 2 Law mass energy Current microphysical models predict o too slow “condensational” growth o too narrow cloud droplet distributions Shaw (2003)

Beard & Ochs (1993) “… At this rate, we are quite a way off from being able to predict, on firm micro-physical grounds, whether it will rain.” 0.1  m 1  m 10  m

Clouds in Climate Models Visible WavelengthsInfra 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 Sundaram & Collins (1997); Wang, Wexler & Zhou (1998)

Monodisperse clustering: drift Chun, Koch, Sarma, Ahluwalia & Collins, JFM 2005

Monodisperse clustering: diffusion Chun, Koch, Sarma, Ahluwalia & Collins, JFM 2005

Monodisperse clustering: RDF St = 0.7 Chun, Koch, Sarma, Ahluwalia & Collins, JFM 2005

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

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

Bidisperse clustering: stationary Chun, Koch, Sarma, Ahluwalia & Collins, JFM 2005

RDF Measurements Experiments and Simulations Direct Numerical Simulations

Turbulence Chamber

Flow Characterization Conditions at 6 Fan Speeds (MKS)

Metal-Coated Hollow Glass Spheres Mean = 6 microns STD = 3.8 microns 1-10 particles/cm 3  V = 10 -7

Measurements of RDF Wood, Hwang & Eaton (2005) Saw, Shaw, Ayyalasomayajula, Chuang Gylfason, Warhaft (2006) Turbulence Box Wind Tunnel

Why 3D? 2D Sampling1D Sampling Relations Holtzer & Collins (2002)

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 cm 1k x 1k CCD ZZ FF aa nn FF aa nn FF aa nn  Optical Window (4 cm) 3 Volume Numerical Reconstruction Intensity-Based Particle Extraction Hybrid Digital HPIV Nd:Yag Laser 532 nm Reference Beam Expander Variable Beam Attenuator

Particle Concentration and Phase Averaging

Size Distribution Evolution

Time Dependence of RDF

Direct Numerical Simulations  Grid Points  R = 80  1.2 Million Particles (one way coupling)  Experimental Particle Size Distribution Keswani & Collins (2004)

Filtering by camera Mean = 6 microns STD = 3.8 microns Metal-coated hollow glass spheres

Filtering by camera Mean = 6 microns STD = 3.8 microns Metal-coated hollow glass spheres

Comparison at R = 130

Comparison at R = 161

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,  ) Particle size distribution (will separate particles) Increasing resolution of experiment (smaller separations) International Collaboration for Turbulence Research (ICTR)