**Acknowledgments**I would like to thank all the people who have provided me help and support during the completion of this thesis.

First, to my advisor, Dr. Hui Meng and Mr. Scott Woodward, who have provided me with academic guidance and financial support to throughout this thesis. Thanks to Dr. Xiaoqin Jiang for working together with me both in the lab and acedemically during his visiting scholar tenure here at UB.

Furthermore, I wish to thank Dr. Jeremy de Jong, Dr. Lujie Cao and Dr. Gang Pan for their ground work developing the hybrid digital holographic particle field measurement system, and the particle image velocimetry calibration work; Dr. lance Collins and Juan Salazar at Cornell University for the DNS results and valuable discussions; My committee members Dr. David Forliti and Dr. Mattew J. Ringuette for reviewing my thesis.

Special thanks to my family, for their endless encouragement and love.

## Nomenclature

**Abbreviations**3D three-dimensional

CCD charge coupled device

DD data-data particle pairs

DNS direct numerical simulations

DR data-random particle pairs

FFT fast Fourier transform

LDA laser Doppler anemometry

NI National Instruments

PDF probability density function

PIV particle image velocimetry

PSD particle size distribution

PTV particle tracking velocimetry

RDF radial distribution function

RAM random access memory

RR random-random particle pairs

SNR signal-to-noise ratio

VI virtual instrument

**Mathematical symbols***A *constant, from the scaling argument method

A first frame of double-pulsed holographic imaging

*B *spatial spectral-filtering function

B second frame of double-pulsed holographic imaging

*I *pixel intensity

*I*_{0} reconstructed wave signal intensity

*I*_{H}* *hologram intensity

*K*_{z} Fourier transform of the diffraction kernel

*k*_{z} *L *depth of sample volume

*L*_{e} large eddy length scale

*N *number of points for the Fourier transform of the velocity vector field

*N*_{A}* *number of particles extracted from A hologram

*N*_{B}* *number of particles extracted from B hologram

*N*_{c} collision frequency

*N*_{i} number of particle pairs in i

^{th} shell

*N*_{p} total number of particles in a field

*N*_{r}* *total number of random particles in a field

*N*_{x}* *number of PIV vectors in the x direction

*N*_{y}* *number of PIV vectors in the y direction

**O **amplitude of object wave (spherical wave)

*P*(

*w*_{r}|

*r*) probability density function of

*w*_{r} conditioned on the particle pair separation distance

*P*_{XY}(

*r*) probability density function for pairs particle pair separations in the Monte Carlo RDF method

**R **amplitude of reference wave (plane wave)

*Re*_{} Taylor microscale Reynolds number

*St *Stokes number

*T*_{e} large eddy time scale

*V* volume of the particle field

*dt *time separation between laser pulses

*g*(

*r*) radial distribution function

**h**_{z}* *Fresnel diffraction kernel

*j * *k *wave frequency

*k*_{e}* *turbulent kinetic energy

two-particle separation vector

*t*_{} Kolmogorov time scale

**U**_{z}* *reconstructed wave front

PIV velocity vector

root mean square of the velocity fluctuations

*u*_{}* *Kolmogorov velocity scale

individual particle velocity vector

two-particle relative velocity vector

*w*_{r} radial component of the relative velocity between two particles

PIV vector location

*x*_{p}* *position of a particle in the x direction

*y*_{p}* *position of a particle in the y direction

*z *distance from the hologram to the reconstructed plane

*z*_{o}* *normal distance of the particle to the hologram

*z*_{p}* *position of a particle in the z direction

* *"window" size over which velocity field is spatial averaged

_{x} PIV vector spacing in x direction

_{y} PIV vector spacing in y direction

_{CCD} CCD camera pixel size

_{RDF} bins width used in calculating the RDF

* *hologram angular aperture

* *proportionality constant for the Lin spectrum

* *particle image depth-of-focus

turbulent kinetic energy dissipation rate

* *phase-lag of spherical wave front

Kolmogorov length scale

* *wavelength of laser light

kinematic viscosity

* *scattering angle between the incident laser light and the hologram recording plane

_{f}* *fluid density

_{p}* *particle density

particle diameter

_{p}_{ }particle response time

**Abstract** Quantification of the inertial particle clustering and the dispersion and collision processes is of fundamental importance to the validation of our theoretical understanding of the dynamics of inertial particles in both natural and industrial turbulent flows. The particle collision kernel contains two important parameters, the radial distribution function (RDF) and the mean inward radial relative velocity (Sundaram and Collins 1997). The sensitivity of these parameters on the particle inertia or Stokes number and the turbulence characteristic namely the Reynolds number based on the Taylor microscale, R

_{} is key to advancing our understanding of the phenomena. Due to the complicated physics of the particle collision process it is typically studied using direct numerical simulation (DNS). There is a pressing need to experimentally validate the DNS results as well as to extend the data to Reynolds number beyond what is currently possible. Using the hybrid digital holographic system as a tool the particle inertial effect on both RDF and two particle radial relative velocity PDF was studied in a stationary, homogenous and isotropic turbulent box experimentally and compared with DNS. The optical set was modified to improve the quality of the holograms and then optimized to minimize the error in the depth position accuracy use mono dispersed particles scattered on the glass plate. By analyzing the angular aperture theoretically and experimentally it was determined to be limited by the long focal length microscopic lens system.

Three inertial particles were employed to obtain 3 different Stokes numbers. The PDF and RDF were quantified using two different particle matching and two calculation methods to compare their performance. Finally the Stokes number effects on the two particle radial relative velocity PDF and RDF were compared with DNS results under similar flow and particle Stokes number conditions.